A Beginner's Adventures in Genetic Genealogy (a work in progress)

by Paddy Waldron

Last updated: 29 May 2024.

Introduction

The purposes of this web page are two-fold:

1. to encourage my relatives and the population at large to submit DNA samples to online genetic genealogy databases in order to improve everybody's chances - the chances of all genealogists and particularly of adoptees and foundlings - of finding cousins in those databases and proving their relationships to those cousins; and
2. to explain for my own benefit, and for that of anyone else who is interested, the basic statistical and scientific principles behind the relatively new and rapidly evolving science of DNA matching.

Why submit your DNA?

It was only after a lot of thought over a number of years that I submitted a sample of my own DNA to FamilyTreeDNA (FTDNA) on 20 October 2013, receiving the results on 15 November 2013.

At the time, FamilyTreeDNA was really the only practical and affordable option for those residing outside the United States of America, where the first three big DNA companies were based. The alternatives at the time were AncestryDNA and 23andMe.

The basic selfish reasons that motivate most people to submit DNA samples to a genetic genealogy database are to confirm their own genealogical relationships and to find their own long lost cousins.

However, you should consider submitting your DNA not just for your own benefit, but for the benefit of others, including those only distantly related to you. You can rest assured that your own descendants will be literally eternally grateful to you for doing so. It is much cheaper and easier to do it now than for your survivors to do it when you are dead. Even if submitting your DNA doesn't help you directly, you might have the missing jigsaw pieces that will solve someone else's mystery.  Genetic genealogy databases are of particular value to those who don't know much about their biological ancestry due to adoption, abandonment, infidelity, sperm or egg donation and similar causes.

The value of an online genetic genealogy database to those searching for relatives depends fundamentally on the number of people in the database. The first to join do need to make a leap of faith and exercise patience until the database reaches critical mass. When you do join, there are huge positive externalities for those already in the database and also for those who join subsequently. If your close relatives are not in the database, then you cannot be matched with them. If your close relatives are already in the database, then by joining you are presenting them with a valuable and much appreciated gift.

The first three major genetic genealogy companies were all based in the USA and some either do not welcome DNA samples from outside the USA or have a pricing policy designed to rip off those resident outside the USA. For those whose roots are in the USA, the databases were already approaching critical mass by 2014. Critical mass for those in countries like Ireland, where I live, was much further off when I submitted my sample. Someone has to get the ball rolling, so why not you? If members of your extended family (like all families in Ireland) emigrated to the USA, then you already have a good chance of finding their descendants. And you may even find cousins among the early participants from other jurisdictions. Or you may just help distant relatives without a well documented family tree to focus their searches in the correct direction, whether that is on your own branch of the family or on another branch of the family.

On the other hand, if there is a family secret that you, or others in your family, would like to remain a secret, then genetic genealogy may not be for you. Conversely, if you feel that now is the time to bring the family secret into the open and obtain closure for all involved, then genetic genealogy is definitely the way to go.

Genetic genealogy can also reveal family secrets that nobody ever suspected, for example an inadvertent baby swap at Fordham Hospital in The Bronx in 1913 which went unnoticed for over a century.

In fact, a disproportionate number of those resorting to DNA to trace their family history are adoptees, or parents or descendants of adoptees, or even foundlings with no paper trail at all on their biological family. I will do my best to assist and advise any such people among my own DNA matches, insofar as this is possible without putting unwanted pressure on those on the other side of the family secret who may want to keep it a secret. Doing my best includes encouraging all my relatives to submit DNA samples to one of the DNA companies so that I will be able to tell those with matching DNA and no paper trail as precisely as possible on which side of my ancestry they are likely to be related to me.

I also have my own, possibly selfish, reasons for wanting my own relatives to join a genetic genealogy database. Having submitted my own DNA, I now want to compare my results with those of:

• known relatives whose precise genealogical relationship to me is proven;
• probable relatives whom I know personally and with whom I suspect that I have a genealogical relationship, still unproven; and
• possible relatives whom I do not know personally but whose DNA results suggest that there is a significant probability, small or large, that we have a genealogical relationship, close or distant, but also unproven.

If you are reading this, then there is a fair chance that you are already in one of these categories, so please read on! Even if you have no reason to suspect that you are closely related to me, I hope that what follows will help your understanding of what you can learn from your own DNA results.

If you belong to one of the first two categories and you have already submitted a sample of your DNA to one of the DNA companies, then please get in touch so that we can compare results. If you belong to the third category, then we will be automatically put in touch through either the databases maintained by the DNA companies or a third party database like GEDmatch.com (to which you should copy your results right now, if you have not already done so). However, if you have not published the information that you already have on the relevant website, or explained in your profile why you have not done this, then I will assume that you are not sufficiently interested in your ancestry to want to correspond further with me.

To be a successful genealogist, you must record what you know of your relatives in a good software package, offline (preferably) or online (if you have very fast broadband and more faith than I do in cloud computing, and trust your online service provider and your cloud data not to evaporate, as my Vodafone e-mail, mundia.com messages, etc., have done). I use Ancestral Quest. All good genealogy software packages will export selected information, typically just names, dates and places for your direct ancestors, to a GEDCOM file (a standardised format for exchange of genealogical data) which can be uploaded to the relevant DNA website. When a FamilyTreeDNA customer uploads a GEDCOM file, the list of ancestral surnames on the FamilyTreeDNA profile is automatically populated, but the names of your most distant known patrilineal and matrilineal ancestors must be entered separately. You must also link the DNA sample to the correct individual in the family tree. I have a seen a few cases of DNA data purporting to be from an individual who has been dead for hundreds of years, something that is not yet commercially available. If the family genealogist persuades you to provide a DNA sample, he or she should be able in return to provide a GEDCOM file to go with it, although it may initially cover only your shared ancestors. I have written much more about this here.

At GEDmatch.com, multiple DNA samples can be linked to a single e-mail address and a single GEDCOM file.

I recognise that there are conflicting opinions on how much detail adoptees should include on their FamilyTreeDNA profiles; the onus is on those who choose to leave their profiles blank to initiate contact with all their possible relatives. My general guidance for those aiming to reunite families separated by adoption, whether using DNA or more conventional methods, is not to rush in without the advice of an experienced genetic genealogist and/or an experienced social worker, as there will only be one chance to make the critical first contact a success.

If you are one of my known or probable relatives and you have not yet submitted a DNA sample to one of the DNA companies, then please consider doing so.

As of 7 June 2018, the two best initial options are:

1. For USD69 [Father's Day sale price] plus taxes plus shipping plus a possible surcharge for ordering from outside the U.S. or having a non-U.S. address plus recurring annual membership fees, use AncestryDNA.com; or
2. For a one off payment of USD79 [regular price] or USD59 [Father's Day sale price] plus shipping, use Family Finder which can be ordered from https://www.familytreedna.com/family-finder-compare.aspx#/shoppingCart?pid=215 

FamilyTreeDNA is clearly less expensive, particularly for those outside the USA and for those not already paying annual membership fees to ancestry.com. FamilyTreeDNA also has the advantage of geographic and surname projects and Y-DNA and mitochondrial DNA products.  However, AncestryDNA has a much bigger customer base (over 5 million as of August 2017, about five times the size of FTDNA, but representing only 30 countries as of October 2016) and will probably find you more relatives.  The choice is yours.  If you choose AncestryDNA, you can still join the FamilyTreeDNA database via the free autosomal transfer. However, you will need to send a second sample direct to FamilyTreeDNA for Y-DNA or mitochondrial DNA analysis.

There are a growing number of DNA comparison websites and those interested in finding long-lost relatives should be in all of them. While helping an adoptee who is married to a Murphy, I coined what I have called Murphy's Law of Genetic Genealogy:

If there are N DNA comparison websites and your DNA is in N-1 of them, then your most important match will be in the Nth.

In the words of another widely used metaphor, there are many online gene pools out there and there are many people who are in only one or two of them; for maximum effect, you must fish in all of these pools.

I strongly urge all those who have sent DNA samples to AncestryDNA and those who sent DNA samples to 23andMe between November 2010 and August 2017 to transfer their autosomal DNA data to FamilyTreeDNA.com if they do not already have a Family Finder presence.  You may find new long lost relatives who have sent their DNA to FamilyTreeDNA but have not yet transferred their data to GEDmatch.com. This free service was announced on 16 February 2017.

If you have used FamilyTreeDNA for Y-DNA or mitochondrial DNA but used one of the other companies for autosomal DNA, then this advice also applies to you.

Before May 2016 (see here), AncestryDNA and FamilyTreeDNA used the same set of autosomal SNPs, so importing AncestryDNA data to the FamilyTreeDNA database and running comparisons was straightforward. After AncestryDNA changed to a different and smaller set of autosomal SNPs, it took nine months to develop a new matching algorithm.

Whichever DNA company you use, you can copy your results file to www.gedmatch.com for free to compare with people who have used the other lab (or 23andMe.com, which is a poor third from a genealogical perspective).

End-of-year sales have become an annual tradition in the world of genetic genealogy. For the end-of-2013 sale, a USD100 restaurant.com gift card and Family Finder Testing together cost only USD99, so those living in the USA who like eating out could actually profit by USD1 by submitting DNA samples! While this particular offer is unlikely to be repeated, keep an eye out for other special offers. Prices are also traditionally cut around DNA Day (25 April), Mother's Day in the United States (the second Sunday of May) and Father's Day in the United States (the third Sunday of June).

The more remote our known connection, the more interesting I think the results will be.

On my paternal side, I am naturally interested in exploring the various origins of the Waldron surname in Ireland. If you are a male Waldron with Irish roots, I particularly urge you to please consider purchasing a kit! In this case, I initially recommend not Family Finder Testing but the Y-DNA37, Y-DNA67, Y-DNA111 or Big Y-700 products, whichever suits your budget. I would love to see some other Irish Waldron ancestors listed in the Paternal Ancestor Name column on The WALDRON Surname DNA Project - Y-DNA Colorized Chart (where I am kit number 310654). If you are a male Waldron and are already a FamilyTreeDNA customer, please click the Join Request link on this page to join the project. My genealogical research has been stuck for many decades at my GGgrandfather Thomas Waldron (c1825/6 Roscommon-1902 Limerick). I would love to find a Waldron Y-DNA match to give me some idea where I should be looking in order to go back another generation. Likewise, I would love to find more Irish Waldron Y-DNA non-matches in order to rule out some of the wild goose chases on which I have gone over the years.

Also on my paternal side, I am particularly interested in exploring my relationship to a number of reputed fifth cousins, whom I know about from notes in my County Clare grandmother's diaries and in her letters about meetings with various sets of her third cousins. In particular, these include the Nolans of Kilkee, the Houlihans of Killard, the Burkes of Cloonnagarnaun and their apparent descendants the O'Maras and O'Connells of Moveen. While the family friendship with all of these families remains strong down to the present day, nobody remembers any longer who our common ancestors were, and furthermore the genealogical records which might unlock these secrets have not survived. There are also the Clancys of Cranny who remained the closest of friends with the Clancys of Killard (one of whom was my greatgrandmother) long after the details of their relationship were forgotten. If you belong to one of these families, I particularly urge you to please consider purchasing a kit and ordering Family Finder Testing! I also encourage all Clancys to order Y-DNA analysis. If you have any ancestors from any part of County Clare, then as soon as you get a password for your FTDNA kit, I recommend that you visit the Clare Roots project Activity Feed and hit the JOIN button at the top right. (Disclaimer: I am Administrator of this project. Project administrators can see your DNA results when you join their projects and can help you to interpret them.)

Finally on my paternal side, DNA helped to confirm the relationship between the Blackalls and Clancys of Killard in County Clare.

Similarly, on my maternal side, I am particularly interested in exploring whether my grandparents (both Durkans by birth) or my grandfather's parents (also both Durkans by birth) might have been related other than by marriage. Both couples lived in the townland of Cuilmore (the one in the civil parish of Kilconduff in County Mayo). I would also like to explore how my mother was related to her "Aunt Ellie" McDonagh, who clearly wasn't a genealogical aunt, but did have a Durkan grandmother. Aunt Ellie was from the townland of Cuillalea in County Mayo, from an area apparently known locally as Cartoonbawn or Cortoonbawn or Cortoon Bawn or Ballincurry or Ballinacurry, or however you would like to spell it yourself. If you are connected to the Durkans or to the McDonaghs, please consider purchasing a kit and ordering Family Finder Testing! [Sending my DNA to AncestryDNA in 2015 threw up a critical clue in the "Aunt Ellie" mystery.] I am not yet aware of a County Mayo project at FTDNA, but would love to see one started.

If you descend from any of these families and have already submitted a DNA sample, then please copy your raw data to GEDmatch.com and let me know your GEDmatch kit number; mine is VA864386C1. I am aware of at least one Nolan descendant and of several Houlihan descendants who have submitted DNA samples but have not yet sent me a GEDmatch kit number.

On all sides, for reasons which will become clear as you read on, I would like to have the DNA of at least eight third cousins available for comparison, at least one of them descended from each pair of my greatgreatgrandparents.

I have prepared this web page in an effort to help my known and probable and possible relatives, and anyone else who is interested, to understand the rapidly evolving, but often poorly explained and poorly understood, discipline of genetic genealogy. It may even be of help to the service providers struggling to help their customers to make their way more easily up the steep learning curve that I have experienced in my own adventures in genetic genealogy. I certainly hope that it will help customers and FamilyTreeDNA itself respectively to get more out of the FamilyTreeDNA.com website and to fix some of its shortcomings.

If you fall into one of the categories of my known, probable or possible relatives and would like to consult my password-protected online family tree, please read on or scroll down to the end of this web page for details of how to obtain a password.

Some people are reluctant to submit DNA samples to commercial organisations and/or to submit the resulting raw data to third party DNA-comparison websites and/or to publish kit numbers which would allow strangers to do one-to-one DNA comparisons, often for reasons that they cannot articulate. For example, one person considered it a bad idea to publish GEDmatch kit numbers in a closed facebook.com group with only 2,824 members, monitored by a handful of administrators of great integrity.  Any information posted in such a group is far less public than information that is posted at GEDmatch.com itself, where the audience is orders of magnitude larger and registration is automated and not monitored.  All GEDmatch.com users have already happily handed over their actual DNA to a commercial organisation and handed over all the raw data extracted from it by the commercial organisation to GEDmatch, so there is no reason to think that merely giving the kit number in a closed facebook group is a bad idea.  Of course, DNA may reveal unknown or unsuspected relationships, but GEDmatch.com users must have been aware of that before sending off their samples, and we cannot change history.  Those whose genetic ancestry has been concealed from them have a right, and usually a great desire, to know it.

The genetic locations examined for genealogical purposes are generally not the same as the genetic locations that have been examined for evidence of possibly elevated risk of certain diseases. It is widely believed that some individuals have "good genes" and are likely to live longer, and other individuals have "bad genes" and are likely to suffer more ill health. The margins of error associated with health predictions derived from DNA are just as hard to find, and probably just as large, as the margins of error associated with the estimated ethnicity percentages derived from DNA and peddled by many DNA companies.

Revealing to insurers and financiers that one has good genes is likely to make one's health care less expensive and one's pensions more expensive, and conversely revealing that one has bad genes is likely to make one's pensions less expensive and one's health care more expensive. If an insurance company got its hands on one's raw data (which it certainly wont do merely by knowing the GEDmatch.com kit number), it might wish to reduce premiums for illness and death insurance, as I call them, and increase premiums for pensions, or vice versa. (The marketing people call these products health and life insurance, but somehow still market fire and theft insurance!)  In many jurisdictions (certainly in the U.S.), law prohibits insurance companies from charging higher premiums to those whose bad genes put them at higher-than-average risk of certain diseases.  This is referred to as "non-discrimination", although the law actually discriminates against those whose good genes put them at lower-than-average risk of the same diseases, by forcing them to pay the same as if they were at average risk.

Others worry that DNA samples sent to genetic genealogy companies may be used, with or without search warrants, to identify them or their close or distant relatives as suspects for criminal offences. Those of us who are not criminals need not worry about our DNA being used to convict us of crime. Those who don't trust the courts and juries to see reasonable doubts in DNA evidence probably don't trust courts and juries to process other types of evidence fairly either. The DNA locations used to uniquely identify criminal suspects beyond reasonable doubt are the fastest-mutating locations, large numbers of which are unlikely to be the same for any two individuals bar identical twins. The DNA locations used to identify closely related individuals are slower-mutating locations, which are very likely to be the same for those who are closely related.

This long introduction may have raised lots of questions in the minds of readers. Please read on for the answers to those questions.

Statistical and Scientific Principles

Table of contents

• Chapter 1: Thoughts and questions on DNA, sampling, testing and marketing
• Chapter 2: Interpreting autosomal DNA results (including Example I and Example II)
• Chapter 3: Example III - Paddy and Terry
• Chapter 4: Example IV - Paddy and Anthea
• Chapter 5: Interpreting Y-DNA results
• Chapter 6: Interpreting X-DNA results
• Chapter 7: Interpreting mtDNA results
• Chapter 8: Aggregating autosomal DNA matches from different websites
• Chapter 9: Integrating genetic and traditional genealogy to find and confirm new relatives

[The text of these chapters still needs to be embellished with many more illustrations, which I might have to borrow from someone like Maurice Gleeson!]

Other internal links:

• Why submit your DNA?
• Best options
• Waldrons
• Durkans
• Types of DNA and their inheritance paths
• Tips for computer programmers
• Mutation
• Units of measurement for segments of DNA
• Converting between units of measurement
• Comparative length of autosomes in SNPs and cMs
• Comparing two people's DNA in practice
• Half-identical by chance regions
• Dispelling myths
• The IBD v. IBS debate: where to draw the line?
• Ethnicity
• Jargon busting
• The FamilyTreeDNA.com website
• FTDNA Relationship estimates
• Phasing and Triangulation
• The GEDmatch.com website
• Getting your data from FTDNA to GEDmatch
• Getting your data from AncestryDNA to GEDmatch
• Getting your GEDCOM file to GEDmatch and linking DNA kits to individuals in the GEDCOM
• My GEDmatch.com kit number
• AncestryDNA custom groups
• Using the AncestryDNA search button
• The DNAGedcom.com website
• Who might match you?
• False positives and false negatives
• Setting thresholds and designing matching algorithms
• How can I find people who match two kits on a segment where those two match each other?
• Probability that relatives share a half-identical region
• Triangulation groups
• Pile-up regions and pile-up groups
• E-mail addresses
• Etiquette
• Linked Relationships (and associated tricks)
• In Common With (ICW) matches
• Ancestral surname lists
• My autosomal results, or lack thereof
• AncestryDNA
• McDonaghs
• Sharing AncestryDNA match lists
• Transitive relations
• FTDNA's chromosome browser
• Don Worth's Autosomal DNA Segment Analyzer
• Homozygosity and heterozygosity
• FTDNA's strange restrictions on one-to-one comparisons
• Lengths of half-identical regions
• Establishing parentage
• How long is "long" and how close is "close"?
• Anne and Terence: why siblings have different sets of matches
• Ordering Y-DNA analysis
• Surname/DNA switches
• Estimating the age of SNPs
• Notifications
• Waldron Y-DNA
• Genetic Distance
• Grouping Project Members
• New branches of the haplotree
• What to do when your Big Y-700 results appear
• X-DNA Inheritance paths
• An X-DNA example
• The bisection strategy
• While waiting ...

Chapter 1:

Thoughts and questions on DNA, sampling, testing and marketing

Background

Having been increasingly addicted to genealogy from the age of 12 or earlier and having a degree in mathematical sciences with a particular interest in probability and statistics, it was inevitable that I would develop an interest in DNA and in genetic genealogy.

I attended various one-off lectures on these subjects over a number of years, and read lots of explanations, often ending up more confused rather than less confused after an effort to improve my understanding. I have still not found the inspirational book or inspirational teacher that suddenly fits everything into place within the context of my prior knowledge, such as happened with probability and statistics when I took Adrian Raftery's course (251) as a third year undergraduate at Trinity College Dublin back in 1983/4. (In the genetic genealogy field, my brief exposure to lectures by Maurice Gleeson and Dan Bradley has, however, helped a lot.)

The more I have read, the more sceptical I have become about the lack of scientific and statistical rigour in genetic genealogy and about some of the inferences apparently drawn from DNA evidence, to the extent that I considered entitling this web page "A Sceptic's Adventures in Genetic Genealogy". Then I discovered that there is an ongoing debate about whether the second letter of sceptic should be a C or a K and whether the spelling difference reflects a slight nuance in the meaning of the word rather than merely the side of the Atlantic Ocean on which I grew up! When I was publicly accused of being a DNA "Luddite", I thought I should perhaps put that word in the title, or perhaps just admit to being "confused", but I eventually settled for the more neutral "beginner".

My scepticism made me reluctant to submit my DNA for analysis, and I continue to exercise caution rather than jump to unwarranted conclusions on the basis of sloppy statistical analysis, sloppy science and sloppy explanations, all of which I still believe are typical of the DNA industry.

On the third day of the joint Back To Our Past (BTOP) and Genetic Genealogy Ireland 2013 shows at the Royal Dublin Society (20 Oct 2013), Kathy Borges of the International Society of Genetic Genealogists (ISOGG) eventually did persuade me to purchase Y-DNA and autosomal DNA products from Family Tree DNA. Notification arrived by e-mail that my autosomal DNA results were available online on 16 Nov 2013 and that my Y-DNA results were available online on 21 Nov 2013.

I should probably try to weave my initial thoughts and the answers that I have found to my questions into the ISOGG Wiki, but for now I still have more questions than answers and it is much quicker and easier to post them all together here on this single web page on my own personal web site documenting my own adventures as a sceptic in genetic genealogy.

Perhaps I should go and study the subject formally somewhere like The Mathematical Genetics Group at the University of Oxford.

I hope that this chapter will help to dispel some myths, in particular about the need for a little jargon, and that the next chapter will get me some feedback about interpreting my own autosomal DNA results, or lack thereof. To begin with, however, some definitions will help to add some rigour.

Definitions

Basics

My good friend Kevin O'Brien summarised the difficulties of DNA research succinctly in one sentence:

If you are reading this page, you hopefully have some basic understanding of DNA and of genetic genealogy. For those who don't, I had better begin by outlining some basic definitions.

DNA (short for deoxyribonucleic acid) is material contained within human cells (and the cells of any living organism) and inherited by children from their parents. Genetic genealogy is the use of variations in DNA between individuals in order to assist genealogical research. For the purposes of genetic genealogy, DNA is represented by long strings of the letters A, C, G and T, for example ACCTGAGTCAGTAC. As far as genetic genealogy is concerned, the precise details of the chemical structures which these four letters represent are unimportant. (If you must know, they are initials representing the four bases adenine (A), cytosine (C), guanine (G) and thymine (T).)

As an occasional computer programmer, I like to describe something like ACCTGAGTCAGTAC as a string of letters and something like GTCAGT as a substring of ACCTGAGTCAGTAC. The words sequence and subsequence may be used by others as synonyms of string and substring.

A person's genome is the very long string containing his or her complete complement of DNA. For the purposes of genetic genealogy, various shorter strings from within the genome will be of greater relevance. These shorter strings include, for example, chromosomes, segments and short tandem repeats (STRs).

The human genome is made up, inter alia, of 46 chromosomes.

The FTDNA glossary (faq id: 684) defines a DNA segment as "any continuous run or length of DNA" "described by the place where it starts and the place where it stops". In other words, a DNA segment runs from one location (or locus) on the genome to another location. For example, the segment on chromosome 1 starting at location 117,139,047 and ending at location 145,233,773 is represented by a long string of 28,094,727 letters (including both endpoints).

For simplicity, I will refer to the value observed at each location (A, C, G or T) as a letter; others may use various equivalent technical terms such as allele, nucleotide or base instead of 'letter'.

The FTDNA glossary does not define the word block, but FTDNA appears to use this word frequently on its website merely as a synonym of segment.

A short tandem repeat (STR) is a string of letters consisting of the same short substring repeated several times, for example CCTGCCTGCCTGCCTGCCTGCCTGCCTG is CCTG repeated seven times.

A gene is any short segment associated with some physical characteristic, but is generally too short to be of any great use or significance in genetic genealogy.

Every random variable has an expected value or expectation which is the average value that it takes in a large number of repeated experiments. For example, if an unbiased coin is tossed 100 times, the expected value of the proportion of heads is 50%. Similarly, if a person has many grandchildren, then the expected value of the proportion of the grandparent's autosomal DNA inherited by each grandchild is 25%. Just as one coin toss does not result in exactly half a head, one grandchild will not inherit exactly 25% from every grandparent, but may inherit slightly more from two and correspondingly less from the other two.

Types of DNA and their inheritance paths

There are four main types of DNA, which each have very different inheritance paths, and which I will discuss in four separate chapters later:

Y-DNA

A human being's 46 chromosomes include two sex chromosomes. Males have one Y chromosome containing Y-DNA and one X chromosome containing X-DNA. Females have two X chromosomes, but do not have a Y chromosome. Y-DNA is inherited patrilineally by sons from their fathers, their fathers' fathers, and so on, "back to Adam". (Most geneticists are not creationists, but the concept of "Adam" is still useful and used. However, there is a subtle difference. The "biblical Adam" was the first and only male in the world at the time of creation. The "genetic Adam", the most recent common patrilineal ancestor of all men alive today, was merely the only male in the world in his day whose male line descendants have not yet died out. There were almost certainly many other males alive at the same time as genetic Adam who have no male line descendants alive today. Just think through the men in your grandparents' or greatgrandparents' generation to get a feel for how precarious the survival of the male line is through even a handful of generations. Or think of the surnames of your distant ancestors which no longer survive as surnames of your living cousins.)
Some people are actually confused by the simple concept that Y-DNA follows the male line, and even by the simpler concept that in most cultures the surname follows the same male line. If you belong to (or join) the relevant facebook groups, you can read about examples of this confusion in discussions in the County Clare Ireland Genealogy group, the County Roscommon, Ireland Genealogy group and The Waldron Clan Association group. Another interesting discussion concerns whether those confused by poor explanations about the inheritance path of Y-DNA are more likely to be those who don't themselves have a Y chromosome!

X-DNA

Every male inherits his single X chromosome from his mother. Every female inherits two X chromosomes, one each from her father and from her mother. The X chromsome inherited from the mother is usually further broken down, because it is one of the chromosomes subject to the random process of recombination, into smaller segments represented by shorter strings of A, C, G and T. In this context, recombination is the process by which the X chromosome inherited from the mother crosses over randomly along its length from being a copy of that inherited by the mother from the maternal grandfather to being a copy of that inherited by the mother from the maternal grandmother or vice versa. Thus, the segments in the X chromosomes which everyone inherits from his or her mother are expected to come equally from both maternal grandparents. The recombination process is sometimes described as being analogous to shuffling two packs of playing cards and splitting the combined pack into two equal halves. Going back another generation, the segments in the X chromosome which every woman inherits in its entirety from her father are expected to have originally come equally from two greatgrandparents, her father's maternal grandparents. While the average or expected breakdown between the relevant paternal and maternal sources is 50:50, we will see later than the observed breakdown can be anywhere between 0:100 and 100:0.

Autosomal DNA

Autosomal DNA (or atDNA for short) is inherited by everyone in the other 22 pairs of chromosomes which are not sex chromosomes. These autosomal chromosomes are often referred to for short as autosomes and are numbered from 1 (the longest) to 22 (the shortest). One chromosome in each pair comes from the father and the other from the mother. Just like the maternal X chromosome, all 44 of these chromosomes are subject to recombination, which means that the segments in each of the 22 paternal chromosomes are expected to come equally from both paternal grandparents, and those in each of the 22 maternal chromosomes likewise are expected to come equally from both maternal grandparents.

Because of recombination, segments come ultimately from all ancestors in recent generations, but those large enough to be of genealogical value can be traced back to a vanishingly small proportion of the exponentially increasing number of ancestors in earlier generations.

"Genealogical value" is not something that can be precisely defined, but it will be argued below that autosomal DNA contains a few hundred segments of genealogical value per individual.

mtDNA

The nucleus of every human cell contains 23 pairs of chromosomes, comprising 22 pairs of autosomal chromosomes and one pair of sex chromosomes. Outside the nucleus, every human cell also contains mitochondrial DNA (or mtDNA for short). Similarly to the patrilineal inheritance of Y-DNA from male to male along the direct male line, mtDNA is inherited matrilineally, but by both sons and daughters along the direct female line, from their mothers, their mothers' mothers, and so on, "back to Eve". Although it is also passed from female to male, the males do not transmit it further.

While autosomal DNA comes equally from both parents, this is not true of DNA as a whole. Not only does mtDNA come from the mother only, but we will also see below that the Y chromosome is much shorter than the X chromosome. Thus everyone inherits slightly more DNA from the mother than from the father, and this is particularly true for men.

The first exposure to DNA analysis for some readers may have been the two-part Blood Of The Irish television documentary first broadcast in 2008. The second part can be viewed on YouTube. The genetic narrative jumps back and forth, without any explanation, between Y-DNA and mtDNA. The climax of the programme was the revelation that three children from a sample of unspecified size from Carron and Kilnaboy in County Clare had similar mitochondrial DNA to ancient remains found in a nearby cave, estimated to be 3,500 years old.

The objective of the programme may have been to investigate whether the direct male line and direct female line ancestors thousands of years ago of those living in Ireland today were men and women who also lived in Ireland thousands of years ago. However, much of the programme appeared to assume that this desired conclusion had already been proven, and to extrapolate from the direct male line and.direct female line ancestors to the billions of other ancestors living at the same time.

There have been great scientific, technological and commercial advances in the world of DNA analysis since 2008, but, even by the standards of its time, this programme left much to be desired.

Tips for computer programmers

If you are not a computer programmer or software developer, then you may want to skip ahead to the next section on mutation.

Traditional genealogy applications will produce pedigree charts and descendancy charts for any individual in a GEDCOM file showing respectively all the ancestors from whom the root individual may have inherited autosomal DNA and all the descendants to whom the root individual may have passed on autosomal DNA (and their spouses). These charts were probably not designed with autosomal DNA in mind. It is just coincidence that one can potentially inherit autosomal DNA from all of one's ancestors, and that one can potentially pass on autosomal DNA to all of one's descendants.

I am still looking for a genealogy application which will produce similar pedigree charts and descendancy charts showing the inheritance paths of the other three types of DNA. For example, an X pedigree chart should show just the ancestors from whom the root individual could have inherited segments of X-DNA and an X descendancy chart should show just the individuals to whom the root individual might have passed on segments of X-DNA.

Blank X descendancy charts are widely available, but software to fill them in for specific individuals is hard to find.

It is surprising that even GEDmatch.com has not as of September 2014 implemented X pedigree charts.

Back in 1991, I wrote a program myself to produce descendancy charts showing only descendants inheriting the Y chromosome from the root individual, but it assumed the underlying database was in the original PAF format and contained less than 32K individuals, so is hardly worth resurrecting now (as PAF has been discontinued and had switched to a new format before its discontinuation, and as my own database is now several times that maximum size limit and as it has become almost impossible to find a PASCAL compiler for a modern computer).

My hope is that these charts can be most easily added to TNG which I use for my own genealogy website. I have started a discussion of this topic in the TNG forums.

Programmers working on genealogy software may be interested in the minor modifications to existing code required to provide these options. A new variable with four possible values (Y, X, autosomal [the current default] and mt) is required. Four cases must be dealt with depending on the value of this new variable. The default autosomal case remains unchanged, certainly if there is already a choice as to whether spouses of descendants (who clearly do not inherit the root individual's autosomal DNA) are included or omitted. The other three cases are dealt with as follows:

Y inheritance path

For the pedigree chart, just follow the direct male line in a single column format.

For the descendancy chart, insert something along these lines:

IF descendant is female THEN
	proceed to next descendant
ELSE {descendant is male}
	output descendant
	stack descendant's children for later processing
	proceed to next descendant
 

X inheritance path

For the pedigree chart, insert something along these lines:

IF ancestor is female THEN
	stack ancestor's father and mother for later processing
	output ancestor
	proceed to next ancestor
ELSE {ancestor is male}
	stack ancestor's mother for later processing
	output ancestor
	proceed to next ancestor

For the descendancy chart, insert something along these lines:

IF descendant is female THEN
	output descendant
	stack descendant's children for later processing
	proceed to next descendant
ELSE {descendant is male}
	output descendant
	stack descendant's daughters for later processing
	proceed to next descendant

"Cascading" X-descendants charts would also be a nice feature, i.e. going back generation by generation, a descendants chart for each X-ancestor, showing those of his or her X-descendants not yet shown on a previous X-descendants chart. The full set of these cascading X-descendants charts would show all the cousins with whom one could theoretically share X-DNA.

It has been suggested that Charting Companion "can automatically color all your X-chromosome ancestors in your Ancestor charts & Fan charts" although I can find no mention of this on the product's own website.
Blaine Bettinger has written an article on Unlocking the Genealogical Secrets of the X Chromosome in which he includes nice colour-coded blank fan-style pedigree charts showing the ancestors from whom men and women can potentially inherit X-DNA.

mt inheritance path

For the pedigree chart, just follow the direct female line in a single column format.

For the descendancy chart, insert something along these lines:

IF descendant is male THEN
	output descendant
	proceed to next descendant
ELSE {descendant is female}
	output descendant
	stack descendant's children for later processing
	proceed to next descendant
 

Ann Turner did this for the MS-DOS version of Personal Ancestral File (PAF) away back in 1994.

Mutation

The letters observed at each location on a child's genome are typically inherited unchanged (other than by recombination) from one or other parent.

A son inherits his Y chromosome and one set of 22 autosomes virtually unchanged from his father and inherits his X chromosome, his mitochondrial DNA and another set of 22 autosomes virtually unchanged from his mother.

Similarly, a daughter inherits one X chromosome and one set of 22 autosomes virtually unchanged from her father and inherits her mitochondrial DNA, another X chromosome and another set of 22 autosomes virtually unchanged from her mother.

However, isolated mutations, essentially just transcription errors, can occur.

Mutation rates vary greatly along the human genome.

At most locations on the genome, the mutation rate is effectively zero and the same letter is observed for all humans.

Some locations have a slightly greater mutation rate, in the range of one mutation in the entire history of mankind. Such locations on the Y-chromosome and in mitochondrial DNA are very useful for slotting individuals into the appropriate locations on the relevant evolutionary tree or phylogenetic tree. While a great deal of effort has gone into identifying such locations, they are not useful for practical genealogical purposes, as two individuals with the same letters at a set of such locations may still not have any common ancestor within thousands of years. By 2015, hopes were high that some surname-specific Y-DNA mutations might soon be identified.

If locations have a higher mutation rate, perhaps as high as 1-in-20 or even 1-in-10 reproductions, then comparing the letters observed at a set of such locations can have great genealogical value. Two individuals with the same observations at a set of such fast-mutating locations are very likely to have a relatively recent common ancestor or common ancestral couple.

Estimation of the time to most recent common ancestral couple depends crucially on both the number of locations compared and on the estimated mutation rates for each of those locations, based on research involving many parent/child observations.

Units of measurement for segments of DNA

There are two different basic units in which the length of a segment of DNA is frequently measured, and a third unit used only for the types of DNA which are subject to recombination, namely autosomal DNA and X-DNA:

base pair (bp)

Each chromosome comprises two complementary strands of DNA, known as the forward strand and the reverse strand, and entwined in the shape of a double helix, which looks like a twisting or rotating ladder. If the letters in one of the complementary strands are known, then those in the other can be deduced, since A can pair only with T and C can pair only with G. A base pair, sometimes called a Watson-Crick base pair, comprises a letter from the forward strand and the corresponding letter from the reverse strand. So the value of a base pair can be one of AT, TA, CG or GC. Similarly, for example, the substring TTAACGGGGCCCTTTAAATTTAAACCCGGGTTT in one strand must pair with the substring AATTGCCCCGGGAAATTTAAATTTGGGCCCAAA in the other strand. For the purposes of genetic genealogy, once the string of letters representing the forward strand is known, the information in the reverse strand is redundant. Nevertheless, the phrase base pair is used as the fundamental unit in which the length of a DNA segment is measured.

Don't be confused by the fact that autosomal chromosomes come in pairs (the paternal chromosome and the maternal chromosome) and that each of these chromosomes in turn contains two strands of DNA (the forward strand and the reverse strand). Thus, one person's autosomal DNA comprises 22 pairs of chromosomes, 44 chromosomes or 88 strands of DNA. When comparing two people's autosomal DNA, one is looking at 44 pairs of chromosomes, 88 chromsomes or 176 strands of DNA.

One thousand base pairs is a kilobase (kb) and one million base pairs is a megabase (Mb).

(The length in base pairs of the genome is referred to as the physical map length.)

single-nucleotide polymorphism (SNP)

As already observed, the vast majority of the base pairs in the genome of most humans are identical.

A single-nucleotide polymorphism, abbreviated SNP and pronounced snip, is a single location in the genome where, due to mutations, there is a relatively high degree of variation between different people.

The word polymorphism comes from two ancient Greek roots, "poly-" meaning "many" and "morph" meaning "shape" (mathematicians reading this will be familiar with the notion of isomorphism). Each of these roots can be somewhat misleading.

In the context of a SNP, "many" misleadingly suggests "four", but typically means "two", as only two of the four possible letters are typically observed at any particular SNP. These typical SNPs are said to be biallelic. Those rare SNPs where three different letters have been found are said to be triallelic. The word polyallelic is used to describe SNPs where three or four different letters have been found. See Hodgkinson and Eyre-Walker (2010). Polyallelic SNPs would be of enormous value in genetic genealogy, but are rarely mentioned, other than to acknowledge their existence. Why not?

Furthermore, since the 1990s, the verb "morph" has appeared in the English language with a meaning more akin to "change shape". In this new sense of "morph", "polymorphic" misleadingly suggests "fast-mutating". In fact, many SNPs are slow-mutating rather than fast-mutating locations. As already noted, SNPs where mutations are observed once in the history of mankind are just as useful for their own purposes as SNPs with greater mutation rates.

Like both the propensity for recombination and the propensity for mutation at individual SNPs, the density of SNPs which have been identified varies markedly along the genome. Thus, when looking at DNA which is subject to recombination (X-DNA and autosomal DNA), the number of consecutive SNPs at which two individuals match is of greater genealogical significance than the total number of consecutive base pairs at which they match.

The number of SNPs identified in a given segment can also vary between companies, researchers or technologies. Specific SNPs have been chosen for the Illumina chips as they are ancestry-informative as distinct from medically informative.

The SNPs which the DNA companies examine are not necessarily all the SNPs. In other words, the locations not examined are not necessarily locations at which all humans are identical. Thus, it is possible that two people match at a long sequence of consecutive observed SNPs, but that there are unobserved SNPs between the observed SNPs at which the two people do not match. Dave Nicolson has written a paper about this.

centiMorgan (cM)

Unlike the other two units of measurement, the centiMorgan is applicable only to the types of DNA which are subject to recombination, namely autosomal DNA and X-DNA. It can not be used to measure Y-DNA or mtDNA.

The propensity for recombination varies along each chromosome. One can plot the estimated expected cumulative number of crossovers or recombination events encountered so far against the location (measured in base pairs) along each chromosome. The expected number of crossovers encountered between two locations can be read from the graph. The distance in centiMorgans between the two locations is just this expected number divided by 100. (The full unit, the Morgan, is no longer used.)

As one recombination is expected every 100 centiMorgans, it follows (because of a mathematical result known as Jensen's Inequality) that the expected length of the typical segment of DNA inherited by a child from a parent on a very long chromosome would be just over 100 cM. Similarly, the expected length of the typical segment inherited by a grandchild from a grandparent (with two opportunities for recombination) would be of the order of 50cM; for a greatgrandchild from a greatgrandparent, of the order of 25cM, and so on. The next segment in each case will be inherited from a different ancestor.

As chromosomes are no longer than a couple of hundred centiMorgans, segments are broken up by the end of a chromosome almost as often as by a recombination event, so in practice average segment lengths are shorter than suggested by the above rule of thumb.

If we assume that crossovers are statistically independent, then it follows that recombination follows what statisticians call a Poisson process. The number of crossovers in one generation in a segment of DNA x centiMorgans long has a Poisson probability distribution with parameter x/100. The number of crossovers in n generations in a segment of DNA x centiMorgans long has a Poisson probability distribution with parameter n*x/100.

For example, the probability of no crossover in 299.6cM is 5%. This result is worth remembering, as it can be used in many ways. If you share a segment of, say, 30.98 cM with another randomly selected person, then you can deduce that there is only a 5% probability that this segment has gone through ten or more reproductions without recombination (since 299.6/30.98 is just under 10). Equivalently, there is a 95% probability that you are a fourth cousin or closer of the other person.

Similarly, the probability of no crossover in 69.3cM is 50%.

The abbreviation cM (with a capital M) is used to distinguish the centiMorgan from the centimetre (abbreviated cm with a small m).

The number of base pairs to which a centiMorgan corresponds varies widely across the genome because different regions of a chromosome have different propensities towards crossover. These expectations and propensities presumably come from experimental data and change as more data is collected, so that the definition of centiMorgan may also vary over time and between DNA companies using different experimental data. The number of base pairs per centiMorgan varies both from chromosome to chromosome and within chromosomes. As can be calculated from the table below, a centiMorgan in one part of chromosome 3 can be under 800,000 base pairs, but a centiMorgan in one part of chromosome 11 can be over 6,000,000 base pairs.

CHROMOSOME	START LOCATION	END LOCATION	LENGTH	CENTIMORGANS
1	44805958	47175419	2369461	1.08
2	106254302	116973471	10719169	8.09
2	157113214	159347591	2234377	2.44
3	11537627	12600665	1063038	1.41
4	165504024	167423895	1919871	2.29
6	29267608	31571470	2303862	1.53
11	46718718	56273717	9554999	1.54
11	103382220	105990699	2608479	2.38
17	36593956	38838321	2244365	1.92

As can be seen from the above table, from the FTDNA website, when no unit of measurement is specified, length is apparently assumed to mean length in base pairs.
FamilyTreeDNA and GEDmatch use different centiMorgan scales.  Here's an extreme example from chromosome 9:
FTDNA: 9    81,628,878    90,218,677    18.04    2,500
GEDmatch: 9    81,369,061    90,503,719    13.2    2,433
In base  pairs, the GEDmatch length is far longer than the FTDNA length; but in centiMorgans, the GEDmatch length is far shorter than the FTDNA length.

(The length in centiMorgans of the genome is referred to as the genetic map length.)

If a segment of X-DNA or autosomal DNA has lots of SNPs, then two people's DNA is unlikely to be identical purely by chance on that segment.

Conversely, if a segment is small in terms of centiMorgans, then it wont have seen many recombinations over the generations, and may have been inherited unchanged from a very distant ancestor, particularly in the case of X-DNA which is not subject to recombination when passed from father to daughter.

Thus, to be sure that a segment is inherited from a recent common ancestor, one would like to see that it is long on both the centiMorgan and SNP scales.

Converting between units of measurement

There must be plots somewhere showing the monotonic relationship between the length along each chromosome measured in base pairs, the length along the chromosome measured in centiMorgans and the length along the chromosome measured in SNPs, but I have not yet come across them.

Genealogists are probably used to variables which can be measured in either of two units of measurement which are linearly related to each other. For example, those with nineteenth century rural Irish ancestors will have converted the areas of their ancestors' landholdings from the Irish acres generally used in the Tithe Applotment Books to the statute acres used in Griffith's Valuation using the fixed conversion ratio 121 Irish acres=196 statute acres. A graph of areas in Irish acres versus areas in statute acres will look like a straight line.

For the three units of measurement in which DNA is measured, there are no such fixed conversion ratios, as the relationships between the units of measurement are non-linear. The local conversion ratios between base pairs, centiMorgans and SNPs vary considerably along the genome. Graphs of the relationship between base pairs and centiMorgans or between base pairs and SNPs or between centiMorgans and SNPs will slope upwards, but otherwise will not look anything like a straight line.

In the absence of such representative graphs, the best that I can show here is a table based on the local conversion ratios in a (non-random) sample of 4,339 regions (those where I am half-identical with one or more of my 381 FTDNA-overall-matches as of 10 Jan 2014; by construction, this is an unrepresentative sample). These may be biased estimates of the average conversion ratios throughout the genome.

Each of the measurement units defined above can also be converted into percentages of the total length of the genome, which are a much simpler way of viewing the results for autosomal DNA and X-DNA, which both come in segments from multiple ancestors.

The use of percentages assumes that a precise value of the total (the denominator in the percentage calculation) is known.

The total length of the human genome in base pairs is typically imprecisely specified as "over 3 billion DNA base pairs" (see table in Wikipedia). This total length, however, includes only one copy of each of the 22 autosomal chromosomes. The genome actually contains around 6 billion base pairs, as it contains two copies of each autosomal chromosome. James Michael Connor (Medical Genetics for the MRCOG and Beyond, RCOG, 2005, page 3) confirms, for example, that there are "280Mb in each copy of chromosome 1", so that the base pairs figures in the Wikipedia table clearly represent the numbers of base pairs in one copy of each autosomal chromosome. Gianpiero Cavalleri confirms that, roughly speaking, "Each of us inherits 6 billion letters of DNA, 3 billion from our mother and 3 billion from our father."

Since it is common to speak about the length of DNA, the width of the human genome can correspondingly be viewed as two base pairs for the autosomal chromosomes and for a woman's X chromosomes; elsewhere it can be viewed as one base pair wide. The following table summarises the details:

Note that the X chromosome contains almost three times as many base pairs as the Y chromosome, so the total number of base pairs in the female human genome is greater than the total number of base pairs in the male human genome.

Despite this confusion about the total length of the genome, the base pair remains the most precise and unambiguous of the three units of measurement; however, it is also the least appropriate as a measure of the genealogical relevance of a shared segment of DNA.

The total number of cM is also imprecisely specified, apparently varying slightly from one DNA website to another. Figures for the length in cM of the autosomal chromosomes only and figures for the length in cM of the autosomal chromosomes and the X chromosome combined may be seen and should not be confused. Furthermore, the definition of the centiMorgan is based on empirical observation of recombination frequencies, and thus can vary based on the particular experimental data on which it is based.

The total number of SNPs used by a particular DNA company is at least directly observable in the raw data downloadable from the company. For example, my raw autosomal DNA data from FamilyTreeDNA.com includes precisely 696,752 SNPs, with one letter from my paternal chromosome and one letter from my maternal chromosome observed at each SNP. My raw X-DNA data includes one letter from each of precisely 17,797 SNPs. If I were female, then I would have another letter from my second X chromosome at each of these 17,797 SNPs. As with centiMorgans, the definition of SNPs is based on empirical observation of variation, and thus can also vary based on the particular experimental data on which it is based and on the DNA company collecting the data. A location where no variation is observed in a small sample may exhibit variation in a larger sample and be reclassified as a SNP. DNA observation is also subject to measurement error, so there will be occasional SNPs which result in no calls so that there can be slight variation in the number of SNPs observed between different individuals even with the same DNA company.

For all these reasons, it is critically important to avoid ambiguity by giving precise details of how the centiMorgan or the SNP has been defined, including specifying the full length of the genome and its components according to the relevant definition.

One way of getting a feel for the length of your autosomes in SNPs and cMs is to do a one-to-one comparison of your own kit with your own kit at GEDmatch.com. This table shows my details:

The End Location column may understate the chromosome lengths in bps, as it probably refers to the location of the last SNP on the chromosome, and there may several thousand more bps beyond that last SNP.

Note that the variation in the overall ratios between the different units of measurement from one chromosome to another is small compared to the variation between smaller segments illustrated in an earlier table and that the various ratios are very different from those in the earlier unrepresentative sample.

While the length in centiMorgans of each chromosome appears to be the same from one FTDNA customer to another, the number of SNPs observed on every chromosome varies from customer to customer and the end locations can also vary in some cases.

Note that for each of the chromosomes, the probability of recombination is greater than 50%, ranging from 50.4% for Chromosome 21 to 94.0% for Chromosome 1. Conversely, the probability of inheriting an entire chromosome intact from one grandparent ranges from 6.0% for Chromosome 1 to 49.6% for Chromosome 21.

Although in theory the chromosomes are numbered in order of decreasing length, this is not the case in the table, where Chromosome 22 is longer on all three scales than Chromosome 21.

Observing DNA

It is neither practical nor essential nor affordable to observe all 6,072,624,261 base pairs in the female human genome, as the vast majority of these have the same value for all women, and similarly for men.

Instead we just observe the locations which are known to vary from one person to another.

In the case of autosomal DNA, FTDNA makes observations at 696,752 paternal SNPs and at the corresponding 696,752 maternal SNPs.

For each of the 696,752 locations, two letters are observed, say A and G, but it is not possible to tell whether the A comes from the paternal copy of the relevant chromosome and the G from the maternal copy, or vice versa.

Presumably if we moved along the genome observing every letter along the way we could keep track of which were the paternal letters and which were the maternal letters; instead, we pop in just once every 4000 or so base pairs, at which stage we can no longer look back and see which is the paternal chromosome and which the maternal chromosome.

In other words, instead of observing 696,752 ordered pairs of letters (of which there are 16 possible values, namely any one of ACGT with any one of ACGT: AA, AC, AG, AT, CA, CC, CG, CT, GA, GC, GG, GT, TA, TC, TG and TT), since the parental source of the letters can not be observed, we observe 696,752 unordered pairs (of which there are ten possible values: AA, CC, GG, TT, AC, AG, AT, CG, CT and GT).

In other words, observed autosomal DNA is represented not by two (unobservable) ordered strings of letters, but by one array of unordered pairs of letters.

The observed unordered data is said to be unphased; the unobservered ordered data which we would like to have is said to be phased. There are various limited techniques available for phasing the unordered data. A certain amount of simple phasing of a child's data is possible if samples are available from both of the child's parents. Ancestry.com uses more sophisticated phasing algorithms, particularly in the new matching process which it introduced in November 2014.

I took an interest in equine pedigrees from a very young age, even before I began to be interested in human pedigrees. I have long taken an interest in the activities of Equinome, a University College Dublin campus company which claims to have identified a SNP called the speed gene which predicts a racehorse's distance perference. It was only when I realised that the unordered pairs observed at the location of Equinome's speed gene can be C:C, C:T and T:T that I realised the vast difference between the two possible A-with-T and C-with-G base pairs in a single chromosome and the ten possible unordered pairs observed in maternal and paternal chromosome pairs.

A region is a run of unordered pairs, starting at one specified locus on a specific chromosome and ending at another specified locus on the same chromosome. In theory, the region comprises one DNA segment on the paternal copy of the chromosome and another DNA segment on the maternal copy of the same chromosome. In practice, neither of these segments is independently observed.

Comparing W's DNA and Z's DNA in theory

Consider the comparison between person W's DNA and person Z's DNA in a particular region on a particular chromosome. (Since the mathematician's usual generic variables X and Y refer to chromosomes in genetics, I'll try to avoid confusion by using V, W and Z instead as variables to denote generic people.)

If we could observe W's paternal segment, W's maternal segment, Z's paternal segment and Z's maternal segment in this region, then we could tell whether or not one of W's segments was identical to one of Z's segments. If we found two matching segments, then we could state that these segments were identical by state (IBS) and that W and Z segment-match on this segment.

Provided that W's paternal segment is different from W's maternal segment and likewise Z's paternal segment is different from Z's maternal segment, then we can start to investigate whether these IBS segments are identical by descent (IBD).

If

1. there is a proven family tree connecting W to Z via a common ancestor;
2. we also have DNA samples from the relevant ancestors of W and Z back to their most recent common ancestor (MRCA) and from the spouses of those ancestors; and
3. the IBS segment matches only one spouse at each generation back to the MRCA,

then we have proven that the matching segments are IBD. The term IBD is often loosely used when this level of rigorous proof is lacking.

Even if no DNA samples are available for some of the people on the family tree, it may still be possible to prove that the matching segments are IBD.

More generally, the unavailablility of some DNA samples means that we can merely draw conclusions about the likelihood of a hypothesised relationship given the DNA or, equivalently, the probability of the observed DNA given the hypothesised relationship.

In general, the longer two IBS segments, the more likely they are to be IBD.

Comparing W's DNA and Z's DNA in practice

Since we do not independently observe W's paternal segment, W's maternal segment, Z's paternal segment and Z's maternal segment in the region of interest, we must base comparisons on the unordered pairs that we do observe.

Think of W as yourself and Z as another person who has been selected at random from a DNA database.

Let us first consider a particular location or SNP.

At this single location, W's unordered pair matches Z's unordered pair if it is possible that one of W's unobservable segments matches one of Z's unobservable segments. In other words, they match if at least one letter is common to both pairs.

Things could get confusing here, as we are comparing two people, each of whom has a pair of letters at every point on the chromosome. Remember that pair refers to the two letters, not to the two people.

For example, at a biallelic SNP, where either A or G can be observed on each chromosome, the unordered pairs which can be observed are AA, AG and GG.

• If W is AG, then W automatically matches Z, whether Z is AA, AG or GG.
• If W is AA, then W matches Z provided that Z is not GG.
• Conversely, if W is GG, then W matches Z provided that Z is not AA.

To avoid the confusion which would arise if the word 'match' was used in multiple different senses, we say that unordered pairs which match in this sense are half-identical pairs and if their pairs are half-identical, we say that W is half-identical to Z at this location.

A person whose paternal and maternal letters are the same at a particular location (AA, CC, GG or TT) is said to be homozygous (or homozygotic) at that location. A person whose paternal and maternal letters are different at a particular location (e.g. AC) is said to be heterozygous (or heterozygotic) at this location.

At locations which are biallelic (the vast majority), someone who is heterozygous will automatically be half-identical to everyone. Thus, observing a heterozygous pair provides no information whatsoever about the possibility that the two people are related.

All the relevant information comes from locations at which both W and Z are homozygous, and the few locations which are polyallelic.

If W and Z are homozygous at a particular location, but with different letters (e.g. W is AA and Z is GG), then they clearly did not inherit that location from a common ancestor.

However, if W and Z are homozygous at a particular location with the same latter (e.g. both W and Z are AA), then they may have inherited their autosomal DNA at that location from a common ancestor.

When investigating the possibility of a relationship, we can discard any biallelic SNPs at which either W or Z is heterozygous, since those SNPs provide no information about the likelihood of a relationship. We just need to compare the locations at which both W and Z are homozygous, i.e. their mutually homozygous locations.

The more consecutive mutually homozygous locations we find, the more likely it is that the relevant region includes a segment of DNA inherited from a common ancestor.

To explore the probabilities involved, let us suppose that the SNP we are considering is biallelic with the proportions p and 1-p of the population having each value, say A and C respectively, and correspondingly, assuming independence of paternal and maternal letters, the proportions p², 2p(1-p) and (1-p)² of the population having each unordered pair, say AA, AC and CC respectively.

If you are homozygous AA at that SNP, then the other person is half-identical to you unless he or she is CC, in other words half-identical with probability 1-(1-p)(1-p)=2p-p²=p(2-p).

Similarly, if you are homozygous CC, then the other person is half-identical to you with probability 1-p².

If you are heterozygous AC or CA, then the other person is half-identical to you with probability 1, since everyone is half-identical to you.

This table shows these probabilities for different values of p, shown in the first column.

The next three columns show the corresponding proportions of the population who are homozygous AA (p²), heterozygous (2p(1-p)) and homozygous CC ((1-p)²).

The second block of three columns shows the probability that a randomly chosen individual is half-identical to you conditional on your letters at the relevant location.

The last column shows the unconditional (ex ante) probability that a randomly chosen individual is half-identical to you at the relevant location.

Before you see your own results, the last column gives the relevant probability; once you know your own results, you can update the probability by looking at the fifth, sixth or seventh column, whichever is relevant.

The first point to note from this table is that for all biallelic SNPs, you can expect ex ante to be half-identical to at least 87.5% of the population. This proportion rises if you subsequently discover that you are heterozygous, or homozygous with a very common value (>64.6% probability) at the SNP; it falls if you discover that you are homozygous with a less common value (<64.6% probability).

At a polyalleic SNP, the probability that W and Z are half-identical is smaller. (We have already noted that such locations are very rare, if not non-existent.)

For example, suppose that the four letters A, C, G and T occur equally often in the population at the chosen polyallelic SNP. Under this simplifying assumption, for a quarter of the population the first pair will comprise two identical letters, AA, CC, GG or TT; the remaining three-quarters of the population will be heterozygous.

If W is homozygous, say AA, then 7 of the 16 possible values of Z's ordered pair will match W (AA, AC, AG, AT, CA, GA, TA).

If W is heterozygous, say AC, then 12 of the 16 possible values of Z's ordered pair will match W (all except GT, TG, GG and TT).

So the probability of finding a match in this sense for this example is 0.25*(7/16)+0.75*(12/16)=43/64=0.671875 or 67.1875%, much lower than for a biallelic SNP, whatever the distribution of the two letters in the popluation at the biallelic SNP.

In practice, we know that the distribution of letters at most SNPs is far from uniform: rather than A, C, G and T each occuring 25% of the time, at some SNPs A may occur 90% of the time, G 10% of the time and C and T never.

If we look at 10 consecutive biallelic SNPs, what is the probability that the two people are half-identical at all 10 locations?

If we assume that both letters are equally likely at each SNP, then the ex ante probability that W and Z are half-identical at 10 consecutive locations is 0.875 to the power of 10, which is around 26.3%. For 20 consecutive biallelic SNPs, the probability drops to roughly 6.9%. For 50 consecutive biallelic SNPs, it is of the order of 0.1%. For 100 consecutive SNPs, it is of the order of 10^-6 and it soon becomes vanishingly small.

If we assume, as in our other example, that the (unobservable) ordered pairs for the two people at each SNP are independently chosen randomly from a uniform distribution with four possible values, then the answer is 0.671875 to the power of 10, which is only around 1.9%, compared to around 67.2% for a single SNP. For 20 consecutive SNPs, the probability drops to roughly 0.04%. For 50 consecutive SNPs, it is of the order of 10^-9. For 100 consecutive SNPs, it is of the order of 10^-18 and it becomes vanishingly small more quickly than for biallelic SNPs.

As can be seen from the table above, these probabilities decline less quickly if one letter is more common than the other at each SNP.

Nevertheless, it holds as a general principle that the probability that two individuals are half-identical throughout a long region purely by chance becomes vanishingly small as the length in SNPs of the region increases.

Note, however, that the more SNPs in a region at which you are homozygous and the rarer the letters you have at those homozygous SNPs, the smaller all the probabilities are, and the less likely you are to be half-identical to another randomly chosen individual purely by chance on that region. These are the regions in which you should begin your search for relatives.

The likelihood that W and Z's DNA is half-identical purely by chance throughout a particular region decreases the more mutually homozygous SNPs they share in the region.

While the total number of SNPs in such regions is universally reported, I have yet to find any comparison tool which routinely reports the far more informative total number of mutually homozygous SNPs.

A region in which all the pairs are half-identical is known as a half-identical region. It would be more sensible to call it a half/half identical region, as it is a region in which half of one individual's DNA matches half of the other individual's DNA. The two individuals could be said to region-match in this region.

In practice, consecutive base pairs or consecutive SNPs are not independent, as was implicitly assumed in all of the above probability calculations, but are inherited in chunks from both parents. So we observe many more half-identical regions in practice than pure chance would suggest. The longest (in mutually homozygous SNPs) of these half-identical regions arise not by chance, but by inheritance.

There are several possible origins of a half-identical region when comparing W and Z:

The region may be half-identical by omission:

As already noted, there may be SNPs within the region which have not been observed and where W and Z are not half-identical at all.

The region may be half-identical by chance:

Neither of W's (unobservable) segments within the region matches either of Z's segments throughout the region. For example, there is one subregion where W's paternal segment matches Z's paternal segment but not Z's maternal segment, and another subregion where W's paternal segment matches Z's maternal segment but not Z's paternal segment. In other words, the half-identical region is made up of a sequence of short identical paternal segments and short identical maternal segments. I have written in much more detail about half-identical by chance regions here.

The region may be half-identical by state:

One of W's segments matches one of Z's segments throughout the region. This could be viewed as a full/full match. In other words, there are (at least) two identical by state segments. It could even be the case that W's paternal segment matches W's maternal segment, or that W and Z match each other on both the paternal and maternal sides.

The region may be half-identical by descent:

As with IBS segments, it may be possible to prove, or to infer with high probability, that half-identical by state regions are actually half-identical by descent.

In the course of investigation, it may be possible to deduce with high probability that there is a full/half match: that one of W's segments is half-identical to Z's DNA in a particular region. Typically, this deduction will be made when W and one or more of W's known relatives (who are not doubly related to W) all exhibit half/half matches with Z.

Once again, in general, the longer two half-identical by chance regions, the more likely they are to be half-identical by descent

Half-identical regions which are both more than 1 cM long and more than 500(?) SNPs long are described at familytreedna.com as shared segments.

Logically, if two people have identical segments (a full/full match), then they have a half-identical region.

The converse, that there are identical segments in a half-identical region (a half/half match), does not automatically follow.

It should be possible to do some probability calculations to estimate the probability that a half-identical region of a given length (in SNPs) contains an identical segment.

Ann Turner's "Identity Crisis" article in the Journal of Genetic Genealogy (Volume 7, Fall, 2011) looks at several cases where a half-identical region is made up of overlapping segments, but it considers only the possibility of two or at most three overlapping segments. She describes a region with several alternating identical paternal and maternal segments as "identical by state" or a "pseudo-segment"; a region including a long segment from one parent in the middle, with a short segment from the other parent at either or both ends as having "a fuzzy boundary"; and a region comprised of one paternal segment and one similarly sized maternal segment as a "compound segment".

A cautionary tale and data-mining

When a golfer, no matter how good, strikes a tee-shot, the probability of a hole-in-one is miniscule.

When a golfer plays a 72-hole tournament, the probability of a hole-in-one during the tournament is much larger.

In the course of a 72-hole tournament, the probability of a hole-in-one by one of a field of perhaps hundreds of players is much larger again than the probability that any individual named player scores a hole-in-one.

Some gamblers who understood this principle made a lot of money at the expense of bookmakers who did not.

Similar principles apply when comparing DNA.

When comparing the DNA of two individuals who have a priori evidence suggesting a relationship, the probability that a reasonably long half-identical region is half-identical by chance is miniscule.

When comparing the DNA of one individual with that of all the other individuals who have sent their DNA to a DNA company, the probability that one or more of the half-identical regions identified are half-identical by chance is much larger.

When comparing the DNA of one individual with that of all the other individuals in a meta-database like GEDmatch.com containing observations from many DNA companies, the probability that one or more of the half-identical regions identified are half-identical by chance is much larger again.

This can also be viewed as an example of data-mining - the principle that if you look hard enough for a pattern in a large database, you will eventually find one.

Statistical inference

The word test is used with many different meanings in many different fields. To a scientist or a medic, it may be a deterministic test with a definite positive or negative outcome. To a statistician, it is a hypothesis test which can accept or reject (but not prove or disprove) a hypothesis based on the observed outcome of one or more random experiments. The word is used loosely by genetic genealogists with other meanings, but I will try to stick to the rigorous statistical meaning. In particular, I prefer to refer to the companies involved in genetic genealogy simply as DNA companies rather than "DNA testing companies" or "DNA sequencing companies" as they are more often described. The term "DNA sampling company", which more accurately describes what the companies really do, is rarely used. It will become clear from what follows what the DNA companies do, what they don't do, what they should do, and what their customers and organisations like ISOGG or the FDA representing the interests of their customers should lobby them to do.

To a statistician, a sample is the set of data collected from the random experiments on the basis of which a hypothesis is tested. So a DNA sample comprises either the strings of letters returned by a DNA company or the cells collected from its customers from which those letters are observed. The relevant random experiment is not the collection of cells and observation of letters (which is deterministic, apart from some measurement error) but the act of reproduction many years earlier in which the random processes of mutation and recombination produced the child's DNA from the parents'.

The various competing DNA companies market various products which comprise both the collection of cells, the raw data returned in the form of strings of letters and the interpretation of both the genealogical and medical implications of those raw data.

Dispelling myths

Genetic genealogy has been very poorly explained, or even mis-explained, to the public. See, for example, Blaine Bettinger's well-reasoned post on genetic exceptionalism.

The results of DNA analysis are frequently combined with the history and mythology of human migration. The connection between genetics and the history of human migration is generally extremely poorly explained. Is it based on DNA extracted from prehistoric human remains, on other evidence from excavation of prehistoric settlements, or on pure guesswork based on the geographical spread of DNA in today's living people?

Analysis of DNA can provide estimates of the probability that an individual currently living in place A and an individual currently living in place B had a common ancestor, either at any time, or within a specified number of generations. DNA from living people on its own cannot provide any information as to whether any such common ancestor lived in place A, lived in place B or lived in some other place C, or moved between places A, B and C.

Consider the extreme example of a family of two brothers, one of whom continued to live in his birthplace and fathered 10 daughters and no sons, the other of whom emigrated and fathered 10 sons. Their shared Y-DNA (passed from father to son) disappeared in one generation from their birthplace, but increased and multiplied in the emigrant's destination. The present location of the Y-DNA is therefore far away from the location where the common ancestor lived. (The initial brothers could of course have had male line cousins who passed on the same Y-DNA, perhaps in yet another different location.)

The units in which DNA testing (Y-DNA testing in particular) measures the genetic distance between two individuals are numbers of mutations, i.e. rare (small probability) differences in DNA between a child and the parent from whom the child inherits the DNA. By studying the frequency distribution of mutations per reproduction (or recombinations per reproduction for autosomal DNA), we can begin to understand the significance of this genetic distance. With some knowledge of the number of reproductions per generation (i.e. the average number of children fathered by each male) and its variation over centuries and millennia, estimates of the average number of mutations per generation or recombinations per generation can be derived. These can then be used to provide further estimates of the number of generations between the two individuals. By studying the frequency distribution of the age of parents at reproduction (i.e. years per generation) and its variation over centuries and millennia, estimated numbers of years for variables like the time to the most recent common ancestor can be derived. As stated by Dan Bradley of Trinity College Dublin at BTOP, the error bars for such time estimates are typically of the order of +/-50% of the point estimate. (I presume that "error bar" is geneticists' jargon for what statisticians' jargon calls "confidence interval".)

Genetics is a branch of applied probability and statistics in exactly the same way as insurance, gambling, investment, lots of sports, medicine and many other aspects of everyday life are. The highly educated population of the 21st century are well capable of understanding it, provided that it is defined precisely and explained clearly in this context. Indeed, as Kelly Wheaton says, "a statistics course is more important than a genetics one for genetic genealogists".

Genetic genealogy is a branch of genealogy which likewise has its place alongside traditional genealogical methods. Statistics prove nothing and likewise genetic genealogy alone proves nothing. Both, however, can be of great help in telling researchers where to look for the desired proof, and in rejecting wrong hypotheses.

Annelies van den Belt, chief executive of DC Thomson Family History, told the Oireachtas Joint Committee on Environment, Culture and the Gaeltacht on 12 December 2013 that her company's DNA products are tools to allow casual users to discover their roots without in-depth research. This sounds like "dumbing down" rather than education. The intended audience of this page does not include such casual users. Genealogy is not possible without in-depth research.

Many of my doubts about aspects of what is passed off as genetic genealogy are reinforced by the Genetic Astrology page of the Molecular and Cultural Evolution Lab at University College London. Another good source is Elliot Aguilar's article Selling Roots.

The IBD v. IBS debate: where to draw the line?

After looking at lists of autosomal DNA matches for some time, most people realise that some are close enough to be of genealogical interest and others are distant enough to be a waste of time. Somehow the vague and poorly defined terms IBD and IBS have come to be used to describe respectively the half-identical regions which are of genealogical interest and those which are not. Debate rages as to where one should draw the line between the two categories and as to what terms should be used to describe each category.

In my case, the first new relative that I discovered through DNA testing was a ninth cousin twice removed whom I found through GEDmatch.com and facebook.com; he was not deemed an FTDNA-overall-match to either myself or any of my known relatives. The first new relative that I discovered through FamilyTreeDNA.com was not an FTDNA-overall-match to myself, but was second to me among my paternal first cousin's FTDNA-overall-matches, hiding behind an e-mail address from the other side of the Atlantic, with a longest half-identical region of 32.41cM. So I certainly wont be dismissing anything shorter than 32.41 as "IBS".

The question one must really ask here is what length of half-identical region suggests that someone in a DNA database is more closely related than the average person one might pass walking down the street? We all have millions of distant cousins. We all share descent from anyone who lived in the same geographical area a thousand years ago. We all have a billion slots to fill on the 30th generation of our family tree. If two people can document that they are 10th or 15th cousins, it is quite likely that they are equally closely or more closely related on other lines that they have not yet documented. At that distance, DNA does not add anything to our knowledge of relationships that pure mathematics has not already told us.

I was asked to look at the ADSA output for two full-siblings and noticed a remarkable difference. On Chromosome 6, they are half-identical (and possibly fully identical) from location 148,878 to location 75,903,756 and from location 165,993,090 to location 170,761,395.

Between location 34,600,991 and location 67,897,582 the brother has only one match, namely the sister. However, the sister has no less than 115 matching segments (including the brother) in this region. It is probably safe to conclude that the siblings inherited both their paternal chromosomes and their maternal chromosomes from opposite grandparents in this region.

ADSA really makes this hidden conundrum jump out like a sore thumb.

The lengths of these 115 matching segments range from 6,300 SNPs to 9,100 SNPs and from 7.09cM to 9.46cM. This is clearly an area where the SNP/cM ratio is unusually high.

Many of the sister's 115 matches in this area are not FTDNA-overall-matches to each other, presumably because they don't meet FTDNA's 20cM threshold for overall matches.

The term "IBS" is ambiguous and widely misused. It seems to be used to describe both half-identical regions which are small on the centiMorgan scale and half-identical regions which are small on the SNP scale.

Half-identical regions which are small on the SNP scale (no matter what their size on the centiMorgan scale) are quite likely to be half-identical-by-chance, i.e. to be comprised of sequences of alternating small compound segments, representing paternal/paternal, paternal/maternal, maternal/paternal and/or maternal/maternal matches lined up together.

Half-identical regions which are small on the centiMorgan scale (but possibly very large on the SNP scale, as in the present example) are most unlikely to be merely half-identical-by-chance. However, they may come from a very distant MRCA and consequently (as in the present case) be shared by a very large group of descendants.

Throwing away the half-identical-by-chance regions makes perfect sense, but throwing away the others with them is definitely a case of throwing away the baby with the bathwater.

We know that anyone who was alive 1000 years ago and has living descendants today must statistically be an ancestor of practically everyone living today, at least within a defined geographical region such as Ireland. Our example is Brian Boru, a High King of Ireland, the millennium of whose death at the Battle of Clontarf in 1014 was celebrated recently.

I like to think of the region on Chromosome 6 where the sister in this example is half-identical to 115 other people as coming from a MRCA of some time around Brian Boru's generation.

If we plotted half-identical regions on a scatter plot with the length in SNPs on the X-axis and the length in cM on the Y-axis, everyone would agree that those which fall near the axes are of little genealogical value and those that fall far out to the north-east of the diagram are of great genealogical value. The question remains of where to draw the boundary between the valuable ones (which a lot of people call IBD) and the others (which a lot of people call IBS). The general convention seems to be to draw a right-angled boundary and throw out everything below a particular cM threshold AND everything below a particular SNP threshold.

The quadrant northwest of the threshold point contains the regions that are half-identical-by-chance; the quadrant southeast of the the threshold point contains the segments from very distant MRCAs; the quadrant southwest of the threshold point contains regions failing on both criteria; and the quadrant northeast of the threshold point contains the good matches.

Why don't we use a diagonal boundary rather than a right-angled boundary? And why don't we set a different boundary for matches where there is additional evidence of a possible close relationship? E.g., in the present example, people who match the reference person's full-sibling and are just outside the chosen boundary should be considered better matches than people who don't match the reference person's full-sibling but are just inside the chosen boundary.

Ethnicity

The word 'ethnicity' is widely used in the marketing of DNA products. I have not even attempted to research how this word is defined. While the word is not used in Mark Thomas's Guardian article, I suspect that it is one of the concepts which he says 'are better thought of as genetic astrology'.

Nevertheless, the estimated ethnicity percentages derived from DNA and peddled by many DNA companies seem to be a key selling point, prompting many people with no interest in genealogy to end up on the DNA comparison websites.

FamilyTreeDNA's concepts of ethnicity long relegated all those of Irish ancestry to "British Isles" ethnicity, which many Irish people consider at best objectionable and at worst plain wrong. This finally changed with the release of myOrigins 3.0 starting on 22 September 2020.

All estimated ethnicity percentages that I have seen are displayed without any estimated margin of error. Until I can see solid statistical evidence that they are significantly different from zero, I will work on the assumption that all small percentages are essentially zero.

Large estimated ethnicity percentages are sometimes useful geographical clues in unknown parentage searches.  An estimated percentage of over 25 is probably worth investigating.

There are many good articles on the mis-selling of estimated ethnicity percentages, such as this one by John Grenham in 2016 and this one in WIRED magazine in 2020.

Jargon busting

Some DNA companies (ancestry.com in particular) have employed marketing people to sell their products by promising not to use jargon. In other words, they admit that they want to sell only to people who don't know what they are buying. Consumer protection authorities should look into this: the better regulated financial sector would never be allowed to get away with it! See Roberta Estes's blog and Heather Collins's blog for further critique of the ancestry.com product.

Any new science requires a new vocabulary to explain it. However, an attempt to reconcile the geneticists' vocabulary, the genealogists' vocabulary and the statisticians' vocabulary is urgently required. Scientists and marketers should agree on the vocabulary, minimise the number of different synonyms used for each concept, avoid mentioning concepts which are not directly relevant to their audience, and define any new words which are necessary clearly and precisely, with whatever diagrams and mathematical models are necessary to help the understanding of those who prefer verbal, spatial or quantitative approaches respectively. The problem is epitomised both by the looseness of FTDNA's glossary and by AncestryDNA's refusal to even use what it terms "jargon" to make its statements intelligible to multiple audiences.

For example, as noted above, at FamilyTreeDNA.com, the simple words "block" and "segment" appear to mean exactly the same thing and to be used interchangeably on the same page, unnecessarily confusing the company's customers. (If there is a subtle difference that I have missed, please let me know.)

As genetics is a branch of applied probability and statistics, it cannot be explained clearly without using the basic vocabulary of those subjects, i.e. words and phrases like probability, estimate, confidence interval and hypothesis test. Beware of anyone who tries to persuade you otherwise.

The FamilyTreeDNA.com website

Like any sophisticated and rapidly developing website, FamilyTreeDNA.com is bound to take some getting used to.

It appears that every visit has to start with a login screen even if one ticks the apparently useless 'Remember me' checkbox. One must also remember to click the small dark "LOG IN" button towards the middle left, not the larger and brighter "Login" button or plain text "Login" at the top right, which merely reloads the login screen. There are regular annoying pop-ups saying things like: 'You have been idle for 120 minutes. Your session may have timed out. The page will be reloaded and you may need to log in again.' or 'Your session will expire on Sun Nov 17 2013 13:19:52 GMT+0000 (GMT Standard Time). You have 5 minutes remaining until your session times out. Click OK to keep this session.' If facebook.com can keep its billions of users permanently logged in, there is no excuse for any smaller website such as FamilyTreeDNA.com not to provide this option. At least the timeout was increased from 30 minutes to 120 minutes soon after I started to use the website.

Those managing DNA samples from multiple family members must become project administrators in order to use a single login for all the kits. Even then, up to 2016 there was no way to use the known relationships between the kits of family members in more appropriately targeted searching for matches.

If you are a project administrator and wish to scan multiple kits simultaneously for new matches, then I recommend the following strategy:

• Open a new browser window and go to the Kit Authorization page, which may involve diverting first to the GAP 2.0 Sign In page, where you can log in with your project administrator username and password.
• For each of your kits, in the order in which you would like them to permanently appear, enter the kit number and passwords in the respective fields and click the Submit button.
• This produces a table of kit numbers (hyperlinked to open the kit home page in a new tab), names and delete buttons; right-click each kit number in turn and select Open Link in New Tab to open each of these simultaneously in separate tabs.
• For each of the tabs that you have opened, under Family Finder, select Matches, then select Match Date to sort by most recent match first.
• If you shut down your computer with the first (Kit Authorization) tab in this window active, and then when you re-start your browser session you log in again with your project administrator username and password, and reload all tabs in this window, you will see the most recent Family Finder matches for all of your kits by Ctrl-<tab>bing through these tabs, without having to log in or log out of each individual kit.
• In some versions of some browsers, you will still have to sort by most recent match first and click the "Show Full View" link for each kit for each session.

• For those deemed FTDNA-overall-matches, it implies spurious accuracy by giving the Total cM to five decimal places (seven, if one remembers that centiMorgans are already percentages).  Then it pads out the results with another five zeroes.
• For those not deemed FTDNA-overall matches, it round everything below 19.9999900000 down to 0.0000000000!!
• There is an unqualified "Relationship (Generations)" option, based on the Suggested Relationship column of the results spreadsheet, but there is no "Known relationship" option on the dropdown menu!
  

The GEDmatch.com website

I have already mentioned GEDmatch.comin passing a few times, and noted that my own GEDmatch.com kit can still be found using the original kit number F310654. However, I now appear in other people's match lists as T205074 (based on a FamilyTreeDNA data file) and A931453 (based on an AncestryDNA data file). There are only minor differences between these files as the samples were submitted when the two companies were using essentially the same set of SNPs. More recently, they have used very different sets of SNPs and the same person's data files from samples submitted more recently will give very different results at GEDmatch.

As with all DNA comparison websites, paranoia leads to some potential users expressing reservations from what some describe as a "security" point of view. Personally, I am far more comfortable with GEDmatch.com having my DNA data than I am with AncestryDNA having it!  The people running GEDmatch.com clearly want to help me to find my relatives; the people running AncestryDNA clearly are solely interested in separating me from my money.

As of 6 February 2015, my 664 FTDNA-overall-matches yield 622 distinct e-mail addresses and my top-1500 GEDmatch one-to-many matches yielded 1144 distinct e-mail addresses. The overlap was only 96 e-mail addresses, or just over 15% of the researchers that I could contact via FTDNA. On the one hand, that means that GEDmatch.com allows me to contact 1048 researchers who either are not customers of FTDNA at all or are customers of FTDNA but don't meet the thresholds required to be deemed FTDNA-overall-matches to me. Of my GEDmatch list, 614 came from ancestry.com, 449 directly from FTDNA, 45 from other sources via FTDNA, 391 from 23AndMe, and one was a phased kit. My conclusion is that, despite the great promise of GEDmatch, sending DNA samples to the other two companies will vastly increase the size of the pool in which I can fish for possible relatives.

One huge disadvantage of GEDmatch.com is that it doesn't operate according to the basic principles underlying the vast majority of websites, such as recognising logins for a fixed time or permitting hyperlinking and bookmarking of individual web pages within the website.

For example, if you go to http://www.gedmatch.com/ in one browser tab and login, and immediately open a new tab and go to the same URL, you will again be presented with the login screen. If you wish to look at several GEDmatch.com reports at the same time, then login and open the main menu in one browser tab. Every time you want to look at a new report, go back to that tab, right-click on the link to the form for whichever report you want next, and select Open Link in New Tab or equivalent.

Getting your DNA data from FTDNA to GEDmatch

Getting your DNA data from AncestryDNA to GEDmatch

Getting your GEDCOM file to GEDmatch and linking DNA kits to individuals in the GEDCOM

As with any DNA comparison website, in order to be of maximum assistance to DNA matches, all DNA kits at GEDmatch.com must be associated with GEDCOM files giving the known direct ancestors of the DNA subject.

Full details of how to do this are here.

My GEDmatch.com kit number

If you think that you may be related to me, then you will also want to compare your GEDmatch kit with those of my other close known relatives, which you will find at the top of the one-to-many match list for my own combined kit VA864386C1.

It is possible to download raw data from FamilyTreeDNA.com, ancestry.com, MyHeritage.com, 23andMe.com and some other websites and upload it to GEDmatch.com, which provides alternative and generally superior tools for analysis of the DNA data.

Another huge disadvantage of GEDmatch.com is that it is was long run by part-time amateurs and funded by voluntary donations, so that there has been a constant struggle to match the facilities offered to the demand for those facilities. Service improved since the months around February 2015, when the following message was displayed on the login page:

Due to increased usage we are experiencing slow or non response for GEDmatch programs.
We apologize and suggest logging on during off hours if you experience slow response.

The 'Gen' column by which GEDmatch.com sorts one-to-many matches by default is confusing. If a parent and child are both in the database, then GEDmatch.com finds that they are half-identical everywhere, and estimates 'Gen' as 1. However, if an individual submits samples to two DNA companies and uploads the data from both companies, then GEDmatch.com finds that the two kits are half-identical everywhere, and again estimates 'Gen' as 1. The matching algorithm fails to check for full matches everywhere, which would distinguish the parent-child relationship from the duplicate (or identical twin) relationship. If it did so, then it would presumably set 'Gen' to 0 for the latter comparison.

Similarly, you can click through to 'One-to-one' compare form at http://ww2.gedmatch.com:8006/autosomal/u_compare1.php and fill in the form to go to http://ww2.gedmatch.com:8006/autosomal/u_compare2.fnx?kit1=F310654&kit2=FU2924&chart=0&resolution=1000&threshold=&shared=&noise=&win_size=&bunch_limit=&xsubmit=Submit, but if you follow that link directly, you will get a different error message: (500) Internal Server Error. At least it is accompanied by a statement of the bizarre GEDmatch policy:

One common cause is trying to link to this page from a forum or an email. Most GEDmatch pages do not allow this, and require that you log-in to the site directly. Other than the main page, pages on this site should not be accessed from your browser history, or from links posted in forums, Google, etc.

The 'one-to-one' results show "Estimated number of generations to MRCA"; however, the algorithm used to arrive at this estimate depens on the parameters selected when submitting the form, so I have chosen to ignore all "Gen" figures generated by GEDmatch. I find the centiMorgan estimates much easier to get my head around than the Gen estimates, which, as already noted, don't seem to distinguish at the most basic level between self/identical-twin matches (Gen=1.0) and parent/child matches (also Gen=1.0). Attempting to distinguish between Gen=4.8 and Gen=4.9 can only convey a false and spurious sense of accuracy about estimates which have huge margins of error associated with them.

For example, Comparing Kit A475217 and A370395 with the default settings as of 3 Nov 2018 (Minimum threshold size to be included in total = 500 SNPs; Minimum segment cM to be included in total = 7.0 cM) produces an estimate of 3.5 Gen; changing to Minimum threshold size to be included in total = 400 SNPs and Minimum segment cM to be included in total = 6.0 cM produces no estimate. Thresholds of 1000 SNPs and 10cM give a more distant relationship estimate of 3.7 Gen. The default settings for the one-to-many comparison appear to produce the same estimates as the default settings for the one-to-one comparison.

As of 27 January 2014, the Find people who match with you on a specified segment page at http://ww2.gedmatch.com:8006/autosomal/seg_compare1.php behaved more normally. Following that link often produced ERROR(49) Not Logged in. Filling in the form brought one to http://ww2.gedmatch.com:8006/autosomal/seg_compare2.fnx?kit1=F310654&chrom=X&start=23955089&end=36111764&shared=7&chart=0&resolution=1000&xsubmit=Submit but if you follow that link directly, you will again be redirected to the error message: (500) Internal Server Error. The GEDmatch.Com Chromosome Segment Comparison took a very long time to complete (this one reported: "Comparison took 2714.723849 seconds"), so one had to make sure to start it at a time when one would not need to shut down one's computer shortly! Because of the load it was imposing on the GEDmatch servers, this analysis tool was withdrawn around February 2014.

On most of the GEDmatch.com forms, if you navigate back to the form using the browser back button or Ctrl-LeftArrow, the last values that you filled in will often be wiped out and you need to start from scratch. This behavious is not consistent: I have managed to open the same form in two tabs in the same window, and found that in one tab I could repeatedly navigate back and find the values still filled in, while in the other tab no matter how often I navigated back the values were wiped out. The usual workaround for that is to edit the URL in the navigation toolbar of your browser, but that is also disabled at GEDmatch.com!

Finally, if you close and re-open your browser with GEDmatch.com output visible in several open tabs, you will find the above error messages in each tab and have to re-enter the data in every form.

On 24 Mar 2014, I posted the following query in the GEDmatch Forums/DNA Utilities/Triangulation:

Subject: How can I find people who match two kits on a segment where those two match each other?

I have some known relatives who have uploaded their data to GEDmatch, such as my fifth cousin Cindy.

Our longest half-identical region is 4.6cM and our Estimated number of generations to MRCA = 6.9. Hence we don't appear on each other's top 1500 'One-to-many' matches even if we set minimum Autosomal largest segment to 4.5cM. Both of our top 1500 lists stop at 6.5 generations to MRCA.

There are 64 kits in common between my top 1500 and Cindy's top 1500.

The next thing I would like to do is to go through these 64 kits and find the people who match both of us and also each other on the same regions. Any such people are the most likely to be descended from our common GGGGgrandparents.

It seems that there should be a form where I can enter my kit number and my fifth cousin's kit number and get a list of the 64 kits who are common to our top 1500 along with some indication of which ones are half-identical to either or both of us on the regions where we are half-identical to each other.

The current Triangulation and Segment Triangulation utilities each ask for a single kit number, and look for pairs of kits which match the selected kit and match each other.

I would prefer a triangulation utility which asks for two kit numbers (obviously of known relatives who match each other) and looks for other kits which match both selected kits on the same regions where they match each other.

How can I do this without using Excel to find the 64 common matches between the two top-1500 lists and then manually doing 128 'One-to-one' compares between each of the 64 with me and my known relative?

The 'People who match one or both of 2 kits' utility does not appear to check whether the matches are in the same regions (suggesting a single common ancestor for all three) or in different regions (allowing the possibility that the third person is connected to the first two through different common ancestors).

GEDmatch.com continually tweaks its matching algorithm. On 29 Sep 2014, I looked at the top-1500 cut-off point in Gen for 11 kits and found the following range of values:

F303343 Donna: 6.6
F318138 Cindy: 6.8
FU2924 Anthea: 6.8
F310654 Paddy: 6.9
F335377 Antoin: 7.4
F325507 Colm: 7.4
F325763 Dara: 7.4
M090954 Sean: 7.4
M081357 Joanne: 7.5
F325501 Aileen: 7.5
F335391 Mary: 7.5

Anthea appears on Joanne's top-1500 at 6.9 Gen, but Joanne doesn't make Anthea's top-1500 which stops at 6.8 Gen.

The chapters which follow on interpreting the different types of DNA results will all eventually contain reviews and what I hope will be some constructive criticism of the relevant parts of the FamilyTreeDNA.com and GEDmatch.com websites.

The dna.ancestry.com website

AncestryDNA custom groups

1. Some people like to associate each match with the most recent common ancestral couple shared with the match.
2. Other people like to associate each match with the most distant individual ancestor related to the match.

• click the Add to group link
• if you have custom groups for parents, grandparents and greatgrandparents, tick the box for each greatgrandparent from whom the starred match is descended, or to whom the starred match is related, if he or she is not descended from any of your greatgrandparents; or
• if you have custom groups for greatgrandparents and greatgreatgrandparents, tick the box for each greatgreatgrandparent from whom the starred match is descended, or to whom the starred match is related, if he or she is not descended from any of your greatgreatgrandparents.

• if you have custom groups for greatgrandparents and greatgreatgrandparents, then
• descendants of your parents (siblings, etc.) will each have 16 coloured dots;
• other descendants of your grandparents (first cousins, etc.) will each have 8 coloured dots;
• other descendants of your greatgrandparents (second cousins, etc.) will each have 4 coloured dots;
• other descendants of your GGgrandparents (third cousins, etc.) will each have 2 coloured dots; and
• other descendants of your GGGgrandparents (fourth cousins, etc.) and more distant relatives will each have 1 coloured dot;
• if you have custom groups for parents, grandparents and greatgrandparents, then
• descendants of your parents (siblings, etc.) will each have 8 coloured dots;
• other descendants of your grandparents (first cousins, etc.) will each have 4 coloured dots;
• other descendants of your greatgrandparents (second cousins, etc.) will each have 2 coloured dots; and
• other descendants of your GGgrandparents (third cousins, etc.) and more distant relatives will each have 1 coloured dot; and
• individuals who are doubly related to you may have odd numbers of coloured dots.

• for each starred match with just one coloured dot:

• note the ancestor corresponding to the single coloured dot
• right-click on the match name and Open Link in New Tab, and switch to that tab
• click the "Shared Matches" tab
• for any shared match who is not a known relative and not already in the group corresponding to the ancestor noted above, add the match to the group
• close the shared matches tab

• for each starred match with two coloured dots:

• note the ancestor whose parents correspond to the two coloured dots
• right-click on the match name and Open Link in New Tab, and switch to that tab
• click the "Shared Matches" tab
• for any shared match who is not a known relative and not already in the group corresponding to the ancestor noted above, or in either or both of the groups corresponding to that ancestor's parents, add the match to the first-mentioned group
• close the shared matches tab

• for each starred match with more than two coloured dots:

• note the most distant single ancestor (parent or grandparent) through whom you are related to the match
• right-click on the match name and Open Link in New Tab, and switch to that tab
• click the "Shared Matches" link
• for any shared match who is not already in a group corresponding to an ancestor of the relevant parent or grandparent, add a note identifying the relevant parent or grandparent
• close the shared matches tab

• if a match has two coloured dots corresponding to two of your ancestors who were married to each other, and shares sufficient centiMorgans with you, then the match may be a descendant of that ancestral couple;
• if a match has two coloured dots corresponding to two unrelated ancestors, then the match may be related to one of your known relatives, but through a common ancestor different from the common ancestor that you share with the known relative; or
• the match with two coloured dots may be doubly related to you.

• right-click on the shared match's name and Open Link in New Tab;
• click the Shared Matches tab;
• click the Groups dropdown;
• click Starred matches and click Apply;
• note from which sides of your ancestry the shared starred matches come; and
• click the "Add note" link near the top of the new tab and add a note explanining the potentially ambiguous shared matches.

Using the AncestryDNA search button

The DNAGedcom.com website

This is another independent DNA tools website, featuring the Autosomal DNA Segment Analyzer amongst other tools.

You can register here.

Then bookmark the login page. There is a "Keep me logged in" tickbox, but it seems unreliable.

While you transfer of your raw DNA data from FTDNA, AncestryDNA or 23andMe to GEDmatch.com is a one-off procedure, you will want to periodically transfer your match data from FamilyTreeDNA.com to DNAGedcom.com as new matches appear.

As with GEDmatch.com, you can manage multiple DNA kits within a single DNAGedcom.com account.

You will also need to bookmark the download page.

Note that your web browser may automatically prompt you to use your DNAGedcom.com password as the password for each new FTDNA kit from which you wish to download match data. Remember to type the appropriate password for the relevant FTDNA Kit Number over the suggested password before hitting the "Get Data" button. Your web browser should then remember the relevant passwords whenever you want to refresh the match data for existing FTDNA kits.

If your download fails, the error message (in red on black) may not be easy to read or scroll through. You can copy and paste the entire error message to a text editor where it will be easier to read, if not easier to understand.

FTDNA frequently changes its website without warning, which often knocks out the DNAGedcom.com download procedure.

If you have an autosomal transfer kit at FTDNA, you can download your match data to DNAGedcom.com without paying the USD19 fee to unlock the chromosome browser etc.

There is a DNAGedcom User Group on Facebook which you should also join.

I will return to the Autosomal DNA Segment Analyzer later.

Chapter 2:

Interpreting autosomal DNA results

What is a match?

There are four different levels at which one can compare autosomal DNA and look for matches or potential relatives:

Lists of names

A black box algorithm can be used to list the names or pseudonyms of those in a database whose autosomal DNA is closest to yours. The various DNA companies and third party sites each have their own different algorithms. As well as looking at the names of the people whose DNA has been compared with yours, you can look at their ancestral surnames, ancestral placenames and family trees, if they have made these available. Anybody can do this.

Lengths of half-identical regions

To get full value from one's investment in DNA analysis, one should move on from the purely qualitative approach of looking at names and take a more quantitative approach. The first step is to look at the percentages of the length of the genome on which one is half-identical with a potential relative. The higher this percentage, the closer the relationship is likely to be. Some basic arithmetic skills are required for this.

Locations of half-identical regions

If three or more people are all half-identical to the others on the same region, and if two or more of them are known relatives, then it becomes far more likely that they are all descended from a common ancestral couple. Furthermore, it can be inferred that the DNA in the half-identical region has been inherited from either the male or the female of that common ancestral couple. This leads on to the science (or art) of chromosome mapping, whereby one can assign various regions of the paternal autosomes and various regions of the maternal autosomes to ancestors from whom they have been inherited. This requires comparing DNA with second cousins or more distant relatives, which allows regions to be attributed to specific grandparents or more distant ancestors. This may exercise your brain cells a little more than the first two approaches.

Raw data

Sooner or later, the only answer to a particular DNA puzzle will be to look at one's raw data, in the form of long sequences of pairs of As, Cs, Gs and Ts, in order to work out exactly how and why something happened. This is for the specialist.

Lists of names

My initial autosomal DNA results were presented at FamilyTreeDNA.com in the form of 36 pages of matches, with 10 people per page; subsequently this was increased to 30 people per page. In an attempt to avoid ambiguity, I will call these people my FTDNA-overall-matches. The term autosomal or Family Finder is implicit in this definition, as those who have had their Y-DNA and/or mtDNA analysed by FamilyTreeDNA will have different (possibly overlapping) sets of matches from those analyses.

The silly mania for dividing everything into groups of 10 still applies (as of 11 June 2017) to the screen for entering Current Surnames, where the browser back and forward commands don't even work properly between the groups of 10.

I have yet to find any formal definition of what the word "match" means in this context or of what matching algorithm is used at FamilyTreeDNA.com. The nearest to a definition that I can find in the FTDNA FAQs is:

The Family Finder program has calculated all of your matches to be your relatives within the relationship range. Family Tree DNA uses stringent standards for the relationship range and for the degree of relatedness. Thus, only those determined with high confidence to be your actual genetic relatives are included.

Where are the "stringent standards" published? How high is "high" confidence? What statistical principles lie behind this secret definition? Are user-entered known relationships used within the matching algorithm, as appears to be the case for ancestry.com's DNA matching algorithm?

At GEDmatch.com, the One-to-many DNA comparison page at least allows the user to tweak the parameters used to define a match. Note, however, that the GEDmatch.com 'One-to-one' compare page by default once looked for segments > 3cM in FTDNA data but only for segments > 5cM in 23AndMe data.

Who might match you?

After you have spent a while looking at your autosomal DNA matches, you will inevitably begin to question both to what extent the people on the long lists of matches thrown up by autosomal DNA comparison are any more likely to be related to you than the people that you might pass walking down the street in a place where your ancestors lived for a couple of generations, and to what extent you will be able to prove this using traditional genealogical methods.

I have estimated that in somewhere like Ireland, where the population is small and there was little inward migration in recent centuries, it is unlikely that any two randomly selected people with no tradition of recent immigrant ancestors are more distantly related than about twelfth cousins. Mark Humphrys argues that we Irish are all descended from Brian Ború, the High King of Ireland who was killed in battle in 1014.

This simple observation has profound implications:

• if your parents came from the same population, then they were probably twelfth cousins or closer;
• if your match's parents came from the same population, then they too were probably twelfth cousins or closer;
• so you and your match are probably related in at least four different ways: paternal/paternal, paternal/maternal, maternal/paternal, maternal/maternal;
• extending the analysis backwards, you and your match are probably related in many more ways;
• if you and your match have a known recent common ancestral couple, then one of that couple is probably the source of any large half-identical region that you share with your match;
• the source of a small half-identical region that you share with your match could be a more distant common ancestor of whom you are currently unaware;
• if you and your match have a known recent shared ancestral surname (e.g. Waldron), then a Mr. or Mrs. Waldron is probably the source of any large half-identical region that you share with your match;
• if your shared ancestral surname is common (e.g. Brown or Kelly or Smith) or if your shared ancestral surname has multiple genetic origins or if the half-identical region that you share with your match is small, then you should be less confident that a Mr. or Mrs. Brown (or whatever) is the source of that half-identical region;
• if your shared ancestral surname is uncommon (e.g. Blackall or Kett or Marrinan) or if your shared ancestral surname has only one known genetic origin, then you can be more confident that a Mr. or Mrs. Blackall (or whatever) is the source of the half-identical region that you share with your match.

On the other hand, there are documented cases of people who found each other because they were deemed to be autosomal DNA matches discovering a paper trail which shows that they are more distantly related than twelfth cousins. I personally have found a documented ninth cousin twice removed because we were deemed (by GEDmatch.com) to be autosomal DNA matches. It is of course possible, if not probable, that there is a closer but less well documented relationship between such distant cousins.

Lists of matches based purely on one-to-one autosomal DNA comparisons will undoubtedly include some people whose genealogical relationship cannot be established and omit some true genealogical relatives. The extent to which you will be able to filter the true genealogical relatives from the others depends not only on the closeness of the DNA match, but also on the answers to many questions which can not be considered by these pure one-to-one autosomal DNA comparisons:

• Do any known relatives of either match also match the other person? If so, how strong are these matches?
• Do the two people have ancestral surnames in common?
• Do the two people have ancestral places in common?
• Do any probable relatives of either match, based on common ancestral surnames or ancestral places, also match the other person?
• Do three or more known, probable or possible relatives all match each other on the same regions, i.e. share segments that all may have inherited from a single common ancestral couple?
• How long are those shared segments?

At this stage, some basic ideas about false positives (matches with no known relationship to you) and false negatives (known relatives who are not deemed to be matches) may be helpful.

False positives and false negatives

Every statistical inference is subject to two types of error. For no particular reason, they are known as Type I and Type II errors:

• A Type II error is a false negative; in the context of genetic genealogy, it means failing to list a known relative from the relevant database of test subjects on my match list. This could be either
  • because the two known relatives have not inherited any common segment from their known shared ancestors; or
  • because the two known relatives have inherited at least one common segment from their known shared ancestors but measurement error causes it to be missed; or
  • because the two known relatives have inherited at least one common segment from their known shared ancestors but the matching algorithm does not recognise its significance.
• While these three causes may appear quite different to the geneticist, they are essentially the same from the statistician's or the genealogist's point of view. The geneticist probably thinks of the hypothesis being tested as that the subjects' shared DNA is identical by descent (true positive) and not just identical by state (false positive), whereas the genealogist thinks of the hypothesis being tested as that the two subjects have a common ancestor.
• The FTDNA FAQs (now moved here) give these surprisingly small probabilities, at least beyond third cousins, of not making Type II errors (i.e., in statistical jargon, this table shows that the power or sensitivity of the tests is surprisingly low):

  Probability that relatives share a half-identical region:

  Relationship	Match Probability
  2nd cousins or closer	> 99%
  3rd cousin	> 90%
  4th cousin	> 50%
  5th cousin	> 10%
  6th cousin and more distant	Remote (typically less than 2%)

  23andMe has a similar table:

  Cousin relationship	Probability of detecting
  1st Cousin or closer	~100%
  2nd Cousin	>99%
  3rd Cousin	~90%
  4th Cousin	~45%
  5th Cousin	~15%
  6th Cousin and beyond	<5%

• The first thing to note from these tables is that when you are ready to persuade known relatives to provide DNA samples, you should start with your third cousins. For more distant cousins, the probability that at least one of you has not inherited any autosomal DNA from your most recent common ancestral couple is high, diminishing the value of the test. For less distant cousins, most of what you learn will probably not be new information, also diminishing the value of the test. I will return to this point later.
• It is not clear to me whether FTDNA's lower bounds come from some mathematical (probabilistic) model or from experimental sample data. Neither is it clear why lower bounds rather than point estimates are given. (We will see later that in other contexts FamilyTreeDNA likes to give point estimates where confidence intervals are more appropriate.) Nor is it clear what other unspecified factors might cause the power of the test to be greater than the given lower bounds.
• Since the power of the test is so low for those who are not closely related, my first idea when trying to place someone I don't know who shows up as a close match would be to look at all of his or her matches (not just our "in common with" matches) to see if I recognise any of them as a known distant relative who by chance matches the other person but doesn't match me. Under present access rules for some of the DNA websites, this would ideally require my close match to share his or her password, or as a next best alternative to download and forward to me the entire spreadsheet of all of his or her matches. GEDmatch.com does allow users to view all the matches of a match (just click the kit identifier in the first column of the relevant line of the basic One-To-Many DNA Comparison Results).
• A Type I error is a false positive; in the context of genetic genealogy, it means listing as a match someone who can be proven not to be a relative within the specified Relationship Range. I have so far not found any statement of the probability of Type I errors. This probability is the significance level used for the hypothesis test, so should be set to the industry standard 5%. I am extremely sceptical that this is what the FTDNA algorithm does and I believe that the proportion of false positives returned is vastly greater than 5%. In other words, the specificity is much lower than the standard 95%. The probability that two people are related is, of course, much larger than the probability that that relationship can be traced and proven by conventional genealogical means. Having reviewed my own first 36 FTDNA-overall-matches for which the Relationship Range does not include "Remote Cousin", my genealogist's instinct is that the proportion to whom I have any hope of proving a relationship is far less than the theoretical 95%, or that the true relationships are very likely to be more distant that the outer limit of the estimated Relationship Range..
• We need a table showing the opposite calculations: to ensure that, say, 80% of relationships are detected, what cM threshold for half-identical regions should be used to determine which such regions should be included in calculations?  For example, we might find that 80% of first cousins share a half-identical region of 80cM or more; 80% of second cousins share a half-identical region of 40cM or more; 80% of third cousins share a half-identical region of 15cM or more; 80% of fourth cousins share a half-identical region of 10cM or more; 80% of fifth cousins share a half-identical region of 4cM or more.  These figures are pure conjecture. If you have access to a relevant data set, please consider doing some calculations.

Setting thresholds and designing matching algorithms

As with any hypothesis test, there is a tradeoff between sensitivity and specificity when using DNA to test whether two individuals are related. In the language of the preceding section, reducing the probability of a Type I error will increase the probability of a Type II error.

Choosing where to set the threshold is more of an art than a science. The various DNA companies have all developed their own matching algorithms, which can give very different results.

Here is an extreme example involving myself (VA864386C1) and a man (A831973) who shares his surname with at least four of my 16 GGgrandparents, and shares one reasonably large half-identical region with me:

• GEDMATCH: 7    131,376,672    150,778,055    27.9cM    2,741 SNPs
• FTDNA: 7    131515632    150764204    29.09cM    2807 SNPs
• ANCESTRYDNA: no match

In this case, I have more confidence in the conclusions by FTDNA and GEDmatch than in those by AncestryDNA, as our ancestors not only shared a surname but lived near each other.

In another case, with no common ancestral surnames and no common ancestral locations, I might have more confidence in the DNA company which does not deem there to be a match.

The other DNA companies should follow the example of GEDmatch and allow their customers to choose where they would like to set the threshold. At the very least, they should state clearly and unambiguously where the threshold has actually been set.

The basic matching algorithms do not currently look at surnames or family trees.  Both AncestryDNA (ThruLines) and MyHeritage (Theory of Family Relativity) are trying to develop more sophisticated matching algorithms which combine DNA evidence and genealogical evidence.  In the future, the matching thresholds and ranking of matches used by the DNA companies may be revised to combine genealogical evidence with DNA evidence.

The Family Finder interface on the FamilyTreeDNA.com website

Major changes in the Family Finder interface were implemented on 6 Jul 2016. Parts of the following discussion may still need to be revised in the light of these changes.

The only URL for the Family Finder interface is https://my.familytreedna.com/family-finder/matches.aspx. There are various ways of customising the display, but in general no parameters are added to the URL and no cookies are set to remember your preferred view (if you are like me, this will probably be with newest matches first and with Expand, formerly referred to as Show Full View, turned on), so you cannot bookmark your customised display and you must repeat the customisation every time you go to the page.

Personally, I like to see my Family Finder matches ordered by descending Match Date, so I have to click the Match Date column header to resort the matches every time I visit my bookmark. For Y-DNA matches, I have to click twice, as the first click sorts with oldest first and the second click then sorts with newest first. I suspect that all customers will want quick access to the top 30 by Match Date, but this requires an additional point-and-click after selecting your bookmark. The number of  FTDNA-overall-matches is displayed at the top of the list of matches; if this has changed since your last visit, you will know that you have at least one new match.

After accidentally managing to add a parameter to the URL, I posted about this on 24 Mar 2015 at

https://www.facebook.com/groups/isogg/permalink/10153215548052922/

Each FamilyTreeDNA kit has an ekit identifier which is used in URLs to avoid confusion when you share your Family Tree or DNA results with project administrators or others.

To find your ekit identifier, go to your pedigree chart and select the "Share Tree" button which is the fourth item from the right on the white menu bar above your blank pedigree chart. This will display a URL in the form http://www.familytreedna.com/my/family-tree/share?k=j0XmKW8S87H%2Ffjy92CTXbQ%3D%3D
Whatever appears after the equals sign in the URL is your ekit identifier.

If you have access to multiple kits and want to bookmark pages for particular kits, you can generally add ?ekit= followed by the relevant ekit identifier to the end of any URL.This will be particular helpful when you have become a project administrator. 

To upload your GEDCOM file to FamilyTreeDNA.com, just select the "Upload GEDCOM" button which is the third item from the right on the white menu bar above your blank pedigree chart at, e.g., https://www.familytreedna.com/my/family-tree?ekit=AyxNwlRR9Y6t4mCCdnLA%2fw%3d%3d#mode=1

There seems to be no means of viewing all my hundreds of FTDNA-overall-matches in the same web browser window. I can, however, see them all, sortable by all fields, in a single Microsoft Excel window by clicking the Excel button at the bottom right of the browser window. This causes Mozilla Firefox to offer to open an XML Document in XML Editor. I am not familiar with either of these, but clicking OK then opens a normal Excel window. The file downloaded is not a properly formatted Excel file and is probably just a CSV file: column widths are not set to match the content width; panes are not frozen; autofilter is not turned on; dates are not in my preferred Microsoft Windows date format; e-mail addresses are not hyperlinked; long lists of surnames and placenames are not set to wrap in a readable manner; etc. As I will be re-downloading this file, I had to record this macro in order to make it usable in Excel 2010. Hopefully the macro will be of use to other FamilyTreeDNA customers. If you know how to use a macro in Excel, hopefully you know how to copy and paste someone else's macro into an appropriate place, and how to back up the macros which you want to access via your Excel Add-Ins menu, which Excel stupidly insists on storing in a fixed location in the directory hierarchy.

Nick Reddan has sent me some helpful additional information on Excel macros which I will be inserting here in due course.

For each FTDNA-overall-match, I can see the fields below either in the web browser window or in the Excel window or in both windows or somewhere else. The full (but invisible) list of matches is sortable in the web browser by clicking on any of three column headers (Match Date, Relationship Range or Shared cM); it is also sortable by four additional fields (Name (married surname), Longest Block, Y-DNA Haplogroup or mtDNA Haplogroup) by selecting from a dropdown Sort By menu and clicking an Apply button. These sorts in each case display the top 10 FTDNA-overall-matches by the chosen criterion. It is not possible to bookmark or hyperlink to the top 10 in any order bar the default Relationship Range order at https://my.familytreedna.com/family-finder/matches.aspx.

In Excel, FTDNA-overall-matches are naturally sortable by all 12 columns, including the following, by which it is not possible to sort on the website: first name, Suggested Relationship, Known Relationship, E-mail, first ancestral surname listed and Notes. Since married surnames are not a separate column in the spreadsheet, Excel cannot sort by them.

On the website, one can click on any match's Full Name or mugshot to bring up a Profile pop-up.

The following items of information are available for each FTDNA-overall-match:

Longest block [half-identical region] length:

This is the field by which results are sorted in Excel (Column F). Although to most experienced genetic genealogists it seems to be the most significant indicator of a relationship, it is not immediately visible in the web browser. It can be revealed for an individual FTDNA-overall-match by expanding a tiny, almost invisible, dropdown menu under each mugshot; or for all 10 visible FTDNA-overall-matches by pointing-and-clicking "Show Full View" in the very small print at the top-left corner of the FAMILY FINDER - MATCHES display.

I initially thought longest block was seven clicks away: click Family Finder, Chromosome Browser, Filter Matches By ..., Name, [type name, don't hit <Enter> key], Find, tick checkbox [don't click on the name], View this data in a table, scan the centiMorgans column for the largest value. See the section about the Chromosome Broswer below for more details and some examples.

I warn not to click on the name merely because this brings up an invitation to "Enter Notes About This Relative" even if the name is that of a complete stranger who merely shares a region which is half-identical by chance.

The average value of longest block length for my 354 initial FTDNA-overall-matches was 10.30cM.

Shared segments:

The number of shared segments (i.e. the number of half-identical regions of length 1cM or more) is not visible in either the web browser window or the Excel window, but appears after the sixth click in the above alternative path to the longest block.

Full Name:

The full name may include a title (Mr. or Mrs.) in the web browser, but not in Excel (Column A). In the case of Mrs., the Full Name does not clearly indicate the maiden surname, the only one of interest to the genealogist. Married women from different cultures may indicate their maiden surnames in different ways, for example as part of a double-barrelled surname or (in the U.S.) as a middle name. The Full Name column is sortable by first name in Excel, but not sortable by surname! One of my FTDNA-overall-matches (Mr. Robert M. Elliott) appears to have entered the "Mr." as part of his first names as it does appear in Excel.

Mugshot:

On a randomly selected page, 2 of the 10 people had uploaded mugshots. These are understandably not visible in Excel. If there is no mugshot, then there is a helpful colour-coded place-holder, blue for males and pink for females. The mugshots that I have encountered have all clearly indicated the person's gender, but one has to hope that FTDNA users (particularly those with ambiguous first names) do not start uploading the sort of gender-neutral profile pictures that have become commonplace at facebook.com. Sometimes the customer name and the colour-coding suggest different genders. I have even seen a customer first name of "Jennifer and Brian"; this one was coded blue. Where the gender is ambiguous to DNA matches, FTDNA should be able to confirm it by checking whether the raw data shows one or two X chromosomes. However, this error checking does not appear to be as rigorously implemented as it should be. I have come across cases where I am almost certain that a male's submitted DNA sample has been linked to a female's transferred autosomal DNA file, but have found no definitive way of either confirming or refuting this theory.

Profile:

Click on either the Full Name or the Mugshot to reveal a profile (not visible in Excel), which includes "Most Distant Ancestors", "About Me" and "Ancestral Surnames". Some people will have entered patrilineal and/or matrilineal Most Distant Ancestors (also sometimes referred to as most distant known ancestors or MDKA for short) but neither uploaded a GEDCOM nor entered Ancestral Surnames. This is different from the Family Finder Profile accessible from the chromosome browser.

E-mail address:

A hyperlinked icon in the web browser; not hyperlinked in Excel (Column H). It took a lot of googling to find this page which taught me how to add appropriate hyperlinks using my Excel macro!

On mouseover, the e-mail icon turns blue and, if the person can be contacted by e-mail, the cursor turns from an arrow into a finger.

There is an unexplained tickbox in front of the e-mail address(es) on each customer's Contact Information page. If one of these tickboxes is ticked, then the customer becomes contactable by e-mail by his or her FTDNA-overall-matches. If none of these tickboxes is ticked, then the customer remains uncontactable. I seem to have been inadvertently uncontactable for the first few months after my results became available. I figured out what I had done wrong on 11 January 2014, having been slightly puzzled that I hadn't heard from any of my FTDNA-overall-matches.

There are some simple rules of etiquette which it is imperative to follow when making contact with DNA matches by e-mail, whether by personalised e-mail or by bulk e-mail to many matches:

• Don't just start your e-mail with "Hello cousin". You could after all be dealing with a false positive match.
• A DNA match involves at least two people. The initial e-mail must identify both parties - yourself and the stranger you are approaching - clearly and unambiguously.
• Many customers use a single e-mail account for the DNA of multiple different people, for example the DNA of the owner of the e-mail address and the DNA of both of his or her parents or the DNA of several cousins. Some of these people may even be deceased, but their DNA data lives on. Thus when making contact by e-mail one must mention the name of the stranger whose DNA one matches. This rule applies to FTDNA, probably to all the other DNA companies, and certainly to meta-sites like GEDmatch.com.
• Similarly, many people use the same e-mail address for multiple DNA websites. Thus when making contact by e-mail one must mention on which website one found the e-mail address.
• The stranger being contacted will want to see the genetic information available about the DNA match that you manage. Thus, one must identify one's own side of the DNA match in the e-mail, by giving the matching person's name exactly as it appears at FamilyTreeDNA.com or whichever DNA company website is relevant and by giving one's GEDmatch kit number.
• The stranger being contacted will want to see the genealogical information available about the person initiating contact. Thus, one must state whether one is adopted or knows one's own genetic ancestry and, in the latter case, one must provide a hyperlink, and password if required, to a usable online family tree - at least until such time as FamilyTreeDNA.com or GEDmatch.com provides a usable interface for downloading or online viewing of GEDCOM files. Don't ask for access to someone else's family tree without first offering access to yours.
• Keep track of who you have written to and if you write to the same person a second time at least refer back to your initial attempt to make contact.
• One should also bear in mind general rules of etiquette for e-mail correspondence.

Note icon:

Allows notes to be added on the website. These are then included in Column L of the next Excel download.

Family tree icon:

A blue icon now indicates that the match has published a family tree including some details of his or her known ancestors and a grey icon in theory indicates that he or she has not (the affirmative icon was originally green). Initially, the family tree had to be prepared offline using conventional genealogy software and uploaded as a GEDCOM file; this remains the optimal method.
In mid-2014, FamilyTreeDNA destroyed its family tree system and replaced it with a new system which allowed the family tree to be directly entered on the website. This was presumably intended to cater for the tiny minority of customers whose interest in genealogy was sparked by DNA results rather than for the vast majority of customers whose interest in DNA was sparked by their genealogy results. It was the worst case of 're-inventing the wheel' that I can remember.
It took until October 2016 for FamilyTreeDNA to add a proper usable five-generation left-to-right pedigree chart to its GEDCOM viewer, but even then it did not make this the default view. Hopefully it will not take another three years to persuade them that this must be the default view.  It is at least possible to bookmark the pedigree chart view, e.g. https://www.familytreedna.com/my/family-tree?ekit=j0XmKW8S87H%2ffjy92CTXbQ%3d%3d#mode=1 (Just replace my ekit identifier with your own or with the one whose pedigree chart you want to see.)

The convention that the grey icon in place of the coloured icon indicates that the person has not either uploaded a GEDCOM or manually entered a family tree changed without explanation in 2016. It appears that the coloured icon may just indicate that there is some profile information available, not necessarily including even the DNA subject's parents' names. This is not part of the Excel download, where it would be extremely useful.

A surprisingly and disappointingly small proportion of users have published family trees - as few as one out of ten on a randomly selected page. This may reflect the high number of adoptees turning to autosomal DNA in the search for their biological families, as an adoptee will not have the information which should be included in the family tree.
Clicking on the family tree icon opens the family tree viewer in a new tab. The HTML title of the new tab is "myFTDNA - myFamilyTree" (previously "myFamilyTree" and before that again "Family Tree DNA - Family Tree Viewer (GEDC ..."), although it is generally not yours at all, but someone else's. Through three changes, this title has continued to make no reference at all to the name of the person whose family tree is displayed. Instead, one ends up with numerous tabs open simultaneously, all identically titled. A far more appropriate HTML page title would be "[Maiden surname], [Given names]: FTDNA family tree viewer".

The identifying part of the URL shown in the address bar for a family tree is equally uninformative, e.g. LzHMU7p8O9Y%3d. This should be (and could easily be) replaced with the person's name or kit number.

One tiny improvement brought in at the same time as the 2014 downgrade was the addition of the match's name above the top right corner of the family tree display; in the previous interface, horizontal scrolling hid the details of the person at the root of the pedigree, leaving the title bar and address bar as the only potential way of identifying the subject of the pedigree.
Since the introduction of computers for genealogy in the 1980s, using computers with keyboards with PageUp and PageDown keys, but no PageLeft or PageRight keys, genealogists have been conditioned to see family trees horizontally, with the root person as the left and ancestors to the right. Younger genealogists who have grown up with pointing devices (such as the mouse) and touchscreens have been conditioned differently. Thus modern family tree interfaces increasingly require the user to scroll right and left rather than up and down. This makes life increasingly difficult for those still using keyboards.
The original pre-2016 FamilyTreeDNA family tree viewer created a more serious information processing problem than this pure human-computer interface problem. It displayed the ancestors on each generation in a single row (vertical pedigree chart format) rather than a single column (horizontal pedigree chart format).
Which method of displaying my grandparents is easier to absorb:
John Waldron Mary Ann (Ciss) McNamara Thomas Durkan Bridget Durkan
or
John Waldron

Mary Ann (Ciss) McNamara

Thomas Durkan

Bridget Durkan
Which would be easier to absorb if, instead of looking at four grandparents, you were looking at 128 GGGGGgrandparents, as you need to do when looking for the common ancestor who may be the source of the DNA that you share with a predicted sixth cousin?
I practically gave up looking at or for family trees on sites like FamilyTreeDNA.com, while awaiting single-click access to standard multi-generation horizontal family trees. FamilyTreeDNA finally made progress in this direction in October 2016.

If I see the little coloured family tree icon beside a new match in my FTDNA Family Finder match list, I still tend to click on it, knowing that only frustration will result. I should remember that lists of ancestral surnames are now automatically populated by uploading GEDCOM files, so it is unlikely that there will be any family tree where there is no list of ancestral surnames. If the individual ancestral surnames were entered manually, there will probably still be no family tree. In the rare cases in which there is more than one person in the family tree, I then have to switch from Family View to Pedigree View in order to see the relevant information, and my eyesight is poor enough in relation to my screen size that I then have to switch my browser to full screen mode (with the F11 key). (Ancestry.com's conventional left-to-right layout with mouseover details long fitted four generations into a tiny fraction of the space used by FamilyTreeDNA.com's original bottom-to-top layout, and after many years of requests from users, FTDNA finally switched over in October 2016.) When I see an interesting name in a GGgrandparent box, there is nothing on the display to tell me whether or not there are further generations of that GGgrandparent's ancestry in the GEDCOM.
If someone reinvented the wheel and decided that it should be square rather than round, it wouldn't have looked as awful as the pre-2016 FamilyTreeDNA interface.

Linked Relationship:

The October 2016 changes to the interface introduced a Linked Relationship column to the match list.
These "linked relationships" replaced the "known relationships" in the previous versions of the user interface; older kits with known relationships are requested to add the relevant people to their family tree and link them to their DNA results.
In the FamilyTreeDNA family tree viewer (at least in some browsers), one can link known relatives in the Family Finder match list to the corresponding individuals already included in the family tree, or add them as parent, spouse, sibling or child to individuals already included. (I have found that this feature works in Opera, but not in Firefox, where it produces infinitely spinning timers or no reaction at all.)
There are two ways to use this feature:

1. The Linked Relationship feature can be used to assign some DNA matches to the paternal and maternal sides, i.e. those matches who triangulate with known paternal relatives or with known maternal relatives on regions of 9 centiMorgans or more..
   In the myFTDNA - myFamilyTree tab, there is a DNA Matches button at the left of the second menu from the top.
   This toggles a DNA Matches column at the left-hand side of the screen, which initially shows your top six Family Finder matches.
   It has a "Find your matches" search box at the top and a navigation bar at the bottom which can be used to locate more distant matches.
   When you find a match that you want to link to your family tree, just drag and drop from the DNA Matches column to the relevant individual in the tree, or to a parent, spouse, sibling or child if the individual is not yet included.
   After you drop, you will be asked to select the relationship between the DNA match and the family tree entry (father, mother, spouse, self, sibling, son or daughter).
   You are also asked whether to send an e-mail to the match announcing that you have created the linked relationship; I generally untick this box before clicking the Confirm button, as I think that FamilyTreeDNA already generates far too many unnecessary e-mails.
   When you return to the Family Finder match list after creating Linked Relationships, you will (usually only briefly) see a spinning timer and a blue "Calculating Family Matching" message to the right of the All/Paternal/Maternal/Both menu.
   After family matching completes, you will see the number of confirmed Paternal and Maternal (and Both) matches in brackets on the relevant tabs on this menu, and a blue icon for paternal or a red icon for maternal to the left of the mailto: link under the names of the relevant matches.
   Click on the relevant tab to view just Paternal, just Maternal, or just Both matches.
   In creating the two subsets, of paternal and maternal matches, the family matching process has of course also created as many as four further subsets for each grandparent (containing matches who triangulate with second cousins etc.) and eight further subsets for each greatgrandparent (containing matches who triangulate with third cousins etc.). It then merges the subsets for father, paternal grandparents and paternal greatgrandparents into the Paternal bucket; and merges the subsets for mother, maternal grandparents and maternal greatgrandparents into the Maternal bucket;
   Separating the maternal from the paternal is attempted only where (a) the customer has matches who are known relatives who are third cousins or closer, (b) the customer has uploaded a GEDCOM file or manually entered a family tree which includes these known relatives and (c) the customer has linked the DNA matches to the corresponding people in the family tree (in a browser in which this linking works). If you click on the paternal and maternal tabs without going through these three steps, then nothing happens. I have seen an example of a match list including Linked Relationships to two 3rd Cousins 1R and a 2nd Cousin 2R, who were the second, third and fourth closest matches at the time, but none of whom was assigned to either the paternal or maternal category; however, the top match, a 2nd Cousin 1R, is one of 31 matches in the Paternal bucket. [The hyperlink to this example will only work if you are logged in as an administrator of one of the projects to which the kit belongs, but the screenshot below shows everything.]
   
   In principle, for a customer who has one parent's DNA available for comparison, all the kits not identified as matching that parent (e.g. paternal) should be associated with the other parent (e.g. maternal). The fact that they are not automatically marked as such is apparently an admission that some may be merely half-identical by chance to the child. Where no parental DNA is available for comparison (as in my own case), parental phasing is still done based on more distant paternal and maternal relatives, but in this case there will almost always be matches who cannot be assigned to paternal or maternal categories because they match the customer in regions where no known relative matches him or her.The filtering of paternal and maternal categories leaves something to be desired - a customer with DNA from one parent, say a father, can view all the matches which ARE labelled paternal, but there is no equivalent filter to show all the matches which ARE NOT labelled paternal.
2. When I find a new match, I am usually anxious to see the matches that I share with the new match, which most of the DNA comparison websites allow me to do in some form or another.
   I would like to know further which of these shared matches are also triangulated matches.
   MyHeritage automatically marks the triangulated matches on the shared match list; AncestryDNA refuses to identify the triangulated matches; GEDmatch and other third party tools provide ways and means of finding the triangulated matches; but one has to be a little devious to find the triangulated matches directly at FTDNA.
   In fact, the Linked Relationship feature can alternatively be used to identify all the other matches who triangulate with a particular match of interest.
   To do this, you will want to have just one linked relationship at a time on one side, say Paternal. You can just link the match of interest temporarily as a new child to a paternal grandparent (or more distant paternal ancestor) in the family tree.You should mark this new child as living, to avoid any chances that your matches or project administrators interpret this device as proof of a relationship.
   Family matching will then put all the matches who triangulate with you and the match of interest in the Paternal bucket. You can still use the Maternal bucket in the normal way to collect your triangulated maternal matches (or you can use a maternal ancestor in this procedure and use the Paternal bucket in the normal way).
   When you have recorded the list of triangulated matches, you should probably reverse the process by returning to the myFTDNA - myFamilyTree tab and deleting the individual from the tree.
   Then you can repeat the process for any other match of interest.

If you want to use the Linked Relationships feature both for bucketing both Paternal and Maternal matches and for identifying triangulated matches with individual matches, and if your matches include known third cousins or closer on both paternal and maternal sides, then you may want to have two Family Finder kits, e.g. a kit based on swabs sent to FTDNA with a full pedigree chart for paternal/maternal phasing; and a kit based on an autosomal transfer from another laboratory with a minimal pedigree chart (including at least one grandparent) for identifying triangulated matches.
For more discussion of Linked Relationships, see the Analytic Genealogy blog and the facebook discussion which resulted.

Run Common Matches icon (formerly, but briefly, described as Run Triangulate):

When comparing the results of person W to those of person Z, with the objective of identifying their most recent common ancestral couple and proving their genealogical relationship, one must combine the evidence from traditional genealogy with that from genetic genealogy. Some pieces of the jigsaw puzzle will come from each of the two fields. Ancestral surnames and ancestral placenames (see below) are probably the most important clues. A further well-known technique for getting around brick walls is that of going sideways in order to go backwards in time. This means looking at evidence relating to siblings and cousins and mutual relatives for clues relating to shared ancestors. If the genetic evidence suggests a relationship between W and Z, four probably overlapping groups of possible mutual relatives will be of particular interest:

• those who are known relatives of both W and Z;
• those who are known relatives of W and FTDNA-overall-matches of Z;
• those who are known relatives of Z and FTDNA-overall-matches of W; and
• those who are FTDNA-overall-matches of both W and Z.

In an ideal world, all four groups will be identical. In practice, many pairs of known distant relatives will not be FTDNA-overall-matches as either or both of the pair will not have inherited sufficient autosomal DNA from their most recent common ancestral couple to be deemed FTDNA-overall-matches.

The FamilyTreeDNA.com website provides no obvious way of identifying people in the first three of these groups. However, the Run Common Matches icon allows one to filter FTDNA-overall-matches to see just those who are FTDNA-overall-matches of both W (the kit logged in) and Z (the kit on the current line). These are referred to as the "In Common With" FTDNA-overall-matches (ICWs) of the two kits.

These ICWs can then be downloaded into a smaller spreadsheet; for some bizarre reason this smaller spreadsheet does not include any information about either of the two people with whom those included are in common! For someone managing multiple kits, this can potentially become very confusing.

If one wishes to investigate possible relationships with two DNA matches (however defined) and if one knows that these two people are, say, second, third, fourth or more distant cousins of each other, then the number of ancestral lines requiring investigation is immediately reduced from 8, 16, 32 or more between the two matches to just a single common line, a vastly simpler and less time-consuming task. In other words, having access to known relationship between one's DNA matches is an essential element of the genetic genealogist's toolbox which FTDNA fails to provide to its paying customers.
Looking at ICW matches is effectively the first step in the techniques of phasing and triangulation to which I will return below.

Match Date:

One of the three fields on which the web results can be sorted. In North American all-numeric mm/dd/yyyy format on the web page. All genealogists know that the use of ambiguous all-numeric dates is a mortal sin, guaranteed to lead to the hell of confused months and days for events in the first 12 days of any month. My macro, inter alia, converts the Excel date (Column B) to my own preferred yyyy-mm-dd format.

Many Match Dates were inexplicably reset around 26 April 2014 to 4/26/2014.

Relationship Range:

This is the primary field by which results are sorted by default in the web browser, but not in the Excel download (Column C). Where is the algorithm explaining how it is calculated from the numeric results?
In my case, this range takes on one of five values:

• 1st Cousin, Half Siblings, Grandparent/ Grandchild, Aunt/ Uncle, Niece/ Nephew
• 2nd Cousin - 4th Cousin
• 3rd Cousin - 5th Cousin
• 4th Cousin - Remote Cousin
• 5th Cousin - Remote Cousin

Suggested Relationship:

Column D in the Excel spreadsheet, but not shown in web browser. This appears to be completely determined by the Relationship Range. In my case, the Suggested Relationships for the five observed Relationship Ranges are respectively:

• 1st cousin
• 3rd cousin
• 4th cousin
• -
• -

I have always found it counter-intuitive that the margin of error for the percentage share of the vote in an opinion poll is a fixed number of percentage points, whatever the actual estimated percentage share.

I find the relationship (no pun intended) between the Relationship Range (confidence interval?) and Suggested Relationship (point estimate?) in this case counter-intuitive for the opposite reason.

I would expect the Suggested Relationship to be near the mid-point on the Shared cM scale (see below) of the Relationship Range. For example, third cousins are expected to have Shared cM 16 times as large as fifth cousins. The mid-point on the Shared cM scale is 8.5 times, which is quite close to 8 times, which corresponds to third cousins once removed.
For some reason, the point estimates are the mid-points on the cousin scale, not the mid-points on the Shared cM scale. Why?

Does "Suggested" mean what statisticians call "Estimated"? If so, then is it a maximum likelihood estimate? I can't think of any other estimation method for a discrete parameter.
See further discussion of this point in the ISOGG facebook group.

Known Relationship, replaced by Linked Relationship on 19 October 2016:

This was a user-entered field, which must then be confirmed by the other relative. There is a limited dropdown menu of possibilities with the vague "Distant Cousin" hidden in the middle to cover any omitted relationships. "Distant Cousin" is NOT a "Known Relationship"!

There should be submenus or numeric fields to allow any degree of cousin and any degree of remove to be selected. What will I do if I find one of my 3rd Cousins 3R?

There should be a method for entering names, dates and places for all the ancestors between the two known relatives and their most recent common ancestral couple; perhaps this is the reason for introducing the horrible new family tree interface in 2014.

There should be a method for recording known distant relationships between two FTDNA customers who are not deemed to be FTDNA-overall-matches.

If and when I find and enter known relatives, this field will be downloaded as Column G in the Excel spreadsheet.

As mentioned above, there should be a way to identify those who are either FTDNA-overall-matches or known relatives of the kit logged in and also are either FTDNA-overall-matches or known relatives of the kit on the current line.

The absence of a quick route to this essential information is a major drawback of the website. If the two people who have agreed the Known Relationship have also both uploaded GEDCOMs, then it may be possible, if difficult, to work out the relationship.
Once the Known Relationship filled is filled in, the Relationship Range becomes blank in the web interface; however, it remains unchanged in the Excel spreadsheet.

Linked Relationship (introduced 19 October 2016):

Clicking on the icon in this column opens an `Add to Family Tree' tab.
The linked relationships out to 3rd cousins are used by the Family Matching tool.
There is a Linked Relationships Page.

Shared cM:

Presumably the sum in centiMorgans of the lengths of all half-identical regions longer than some unspecified minimum length, probably 1cM. Also represented by a graphical icon, which wastes a lot of valuable real estate in the web browser window, forcing other more important variables into the hidden dropdown underneath. For distant relatives, the graphical icons are so similar that they are much less informative than the numerical representation (in which trailing zeroes are properly included here). Column E in the Excel spreadsheet. Average value for my 354 initial FTDNA-overall-matches was 33.42cM.

Ancestral Surnames:

Ancestral Surnames are displayed in two places in the web interface: as part of the Profile accessed by clicking on Full Name or mugshot and by mouseover in the rightmost column.

In both places, the first few words are visible in the web browser window, and the remainder in a pop-up with a completely unnecessary nested scrollbar. (I absolutely hate nested scrollbars.) Clicking on the list allows the PageUp and PageDn keys to be used. The list cannot be dismissed with the <Esc> like most such pop-ups, so one has to point-and-click the X in the top right corner of each version.

Surnames and Locations can be entered by selecting the Surnames link at the end of about the sixth menu from the top of the myFTDNA - Genealogy page.

While Surnames and Locations are entered separately, they are combined for display purposes into a single long line of text. In the Profile version, locations are in []s and entries are separated by ", ". In the direct version, to avoid any appearance of consistency, locations are in ()s and entries are separated by " / ". The entry of ancestral surnames is possible without uploading a GEDCOM. The order of entries is unclear: should it be alphabetical, or ahnentafel order, or perhaps whatever random order the user entered the names in? Surnames shared with the person whose kit is logged in, and similar surnames, are bolded and moved to the front of the string of names. There appears to be no limit on the number of entries allowed. If known relationships are limited to 6th cousins, then should ancestral surnames not be limited to GGGGGgrandparents, or 128 surnames, not allowing for spelling changes or surnames not conventionally inherited? Even that is too many to be of use in free form unsortable text.

The Surnames and Locations should be displayed in two separate columns as they were originally entered, sortable by Surname, sortable by Location and sortable by whatever the mysterious default order is. I might even tolerate nested scrollbars if the content was made useable in this way!

In Excel 2010 (Column I), to find people using a particular word in this field, click the auto-filter dropdown in Cell I1, type F then A then the word of interest then <Enter>.

Ancestral Placenames:

Hidden in with ancestral surnames. This should surely be a separate field. It should be (but is not) possible to download this information into a spreadsheet with one line per ancestral surname and/or one line per ancestral placename for further analysis.

Y-DNA Haplogroup:

Shown, if applicable (i.e. for males) and available (i.e. customer has paid for it and order has come to the head of the queue) on the tiny, almost invisible, dropdown menu under each mugshot and in Column J of the Excel spreadsheet. N/A clearly means not-paid-for in the case of male matches but not-applicable in the case of female matches.

mtDNA Haplogroup:

Shown, if available (i.e. customer has paid for it and order has come to the head of the queue) on the tiny, almost invisible, dropdown menu under each mugshot and in Column K of the Excel spreadsheet. N/A clearly means not-paid-for in the case of all matches. Using different abbreviations for not-paid-for and not-applicable rather than using N/A for both would greatly help to reduce the potential for confusing beginners.

My autosomal results, or lack thereof

FamilyTreeDNA

• As of 6 Nov 2013, the offline version of my genealogy database contained 7,217 known relatives who were either my GGGGgrandparents or known to be descended from my GGGGgrandparents. All of these are my fifth cousins or more closely related (possibly some number of times removed). A lot of them are dead, but many of them are still alive. I did expect to find that at least one of them had done the autosomal test with FamilyTreeDNA and would show up as an FTDNA-overall-match, but no such luck.
• No known relative at all appeared among my initial 354 FTDNA-overall-matches.
• Until I found the table above, I didn't realise that I can't expect to find one of these 7,217 among my FTDNA-overall-matches until a lot more than one of them have tested with FTDNA.
• I have discussed DNA testing with a number of known relatives, but didn't feel that I could push them to test until I had done so myself. As you have probably read at the top of this page, I am now pushing as hard as I can (without picking up a bill which could run into hundreds of thousands of dollars if all my known relatives agreed!).
• My friends and relatives probably know by now that I hate Christmas. Not being a materialistic person and having a dread of shopping, I particularly hate being asked 'What do you want for Christmas?' and the pressure to reciprocate. As Christmas lights started to go up everywhere while I reflected on my newly received initial results in late November 2013, I suddenly for once had an answer for any relative who asked that dreaded question: 'I want you to sign up for the autosomal DNA Family Finder Testing at FamilyTreeDNA.com!' In return, I can hopefully at least give anyone who obliges a more complete family tree than would otherwise have been possible.
• I have a number of known fifth cousins and even sixth cousins with whom I have proven relationships using a wide variety of sources, ranging from the Registry of Deeds, to inheritance cases, to the combination of oral tradition and the writings of Sir Hal Blackall, to a little helpful note in the Kilkeedy burial register. However, surviving Irish church and civil and census records generally do not go back far enough to confirm most of these relationships. Additional DNA confirmation would be nice to have.
• In the long term, if all my known relatives test, it should be possible by chromosome mapping to reconstruct the DNA of all of our ancestors - possibly not exactly, but certainly in the form of some sort of posterior probability distribution. If I find someone who both has matching autosomal DNA and is a known relative, we can presumably deduce that our longest half-identical regions were almost certainly inherited from one of our most recent ancestral couple. Every such person will add another piece to the jigsaw puzzle.

What did I actually find?

• I should probably concentrate first on contacting the four closest FTDNA-overall-matches (Relationship Range 2nd Cousin - 4th Cousin; Suggested Relationship 3rd Cousin); then on the next 36 for whom the Relationship Range does not include "Remote Cousin"; and probably dismiss the other 314 for whom the Relationship Range does include "Remote Cousin". Some sort of colour coding (say green, amber and red) to distinguish between these three groups might have helped to highlight at first glance the significant differences between these groups.
• If one feels overwhelmed by the number of FTDNA-overall-matches, one can turn off the display of Speculative, Distant, Close and/or Immediate Family Finder matches on the Match and Email Settings page. This means both that you will not see people deemed to belong to the categories that you have switched off, and that they will not be able to see or contact you. If you wish to use Family Finder purely as a paternity test, you can do this by switching off everything except Immediate. On the other hand, if you learn of a known or suspected relative who has submitted a DNA sample to FamilyTreeDNA and are surprised that he or she does not show up in your match list, this may be because you have switched off the relevant category of matches.
• Only one of my four closest FTDNA-overall-matches has uploaded a GEDCOM.
• 124 of my initial 354 FTDNA-overall-matches have left the Ancestral Surnames column completely blank, frustratingly including the top three people in both the web browser and Excel orderings, and 13 of the 36 people for whom Relationship Range does not contain Remote Cousin.
• Only when I established contact with my closest FTDNA-overall-match did I realise that many of those with missing GEDCOMs and blank Ancestral Surnames columns could be adoptees. Could the percentage of adoptees testing be as high as implied by the above ratios? I will go into this example in more detail below.
• My own surname Waldron does not appear in the spreadsheet, per se. However, there are two people (same surname, same e-mail address, probably father and daughter) listing Waldronde, in Berkshire, England. My earliest known Waldron ancestor, my GGgrandfather, was born in County Roscommon, Ireland in the 1820s.
• My mother's surname Durkan/Durkin (which, as noted above, was the maiden surname of three of her four grandparents, so is potentially the source of up to 37.5% of my autosomal DNA) appears as the surname of one FTDNA-overall-match, but not among his ancestral surnames, or those of any other FTDNA-overall-match. There is one person with Durkee, a new variant to me, or more likely a completely different surname, among ancestral surnames.
• Despite this, there are at least two people that I know on the list:
  • Gerard Corcoran (4th Cousin - Remote Cousin), whose talks I attended at the afore-mentioned BTOP show: We both have Walsh ancestors, but they are in different parts of Ireland, and mine now has a big question mark as I suspect sloppy research by the cousin who gave me the information many years ago.
  • Terry Fitzgerald (it is actually her mother's DNA which suggests 5th Cousin - Remote Cousin): I will also go into this example in more detail below.
  • I once had a student named Carleen Doherty, and there is an e-mail address on the list (5th Cousin - Remote Cousin) with username carleendoherty. It's not the commonest combination of names in the world, but perhaps not unique.
• Terry's is just one of many e-mail addresses which are associated with multiple DNA samples of different family members.
• My top ten FTDNA-overall-matches, which are the same both by Relationship Range and Longest Block, include no less than five members of the Dengen family, sharing an e-mail address - a mother and four of her children. I will also go into this example in more detail below.
• My mother and all her known ancestors lived in County Mayo. Filtering the Ancestral Surnames column of the spreadsheet shows that 12 of my initial FTDNA-overall-matches use the word Mayo in the Ancestral Surnames field. For four of them it is a surname, for eight of them it is a placename.
• That got me wondering: how common is Mayo as a surname? Might I actually have relatives named Mayo? Is the surname derived relatively recently from the placename?
• Then I got wondering about other common surnames: 12 of my initial 354 FTDNA-overall-matches have Sullivan in the Ancestral Surnames field. Is that more or less than the proportion of the entire FamilyTreeDNA database who have Sullivan in the Ancestral Surnames field? How can I find the answer to that question? (I have no known Sullivan ancestor.)
• Another common Irish surname, which does appear among my ancestors, appears in the Ancestral Surnames column 13 times, variously rendered as oconnor, Connor, Connors or O'Connor. Are these 13 surname matches any more significant than the 12 Sullivan surname matches?
• I am clearly not alone in realising that the frequency of surnames among the ancestral surnames of my FTDNA-overall-matches is meaningless without information on the frequency of these surnames among the ancestral surnames of all FTDNA customers. 23andMe has a surname view in which surnames are sorted by enrichmentwhich is defined to be "how common a particular surname is among your DNA Relatives matches, compared to the entire 23andMe database". The surname view includes surnames listed by five or more of one's matches. This simple idea would add infinitely to the value of the FamilyTreeDNA database if adopted. Does AncestryDNA have a similar way of viewing relative surname frequencies?
• Around 2014, FTDNA did introduce lists of the three Most Common Surnames for each Family Finder subject.
  For six people in the O'Deas of Newtown project as of 15 Sep 2015, these were:
  Smith (7), Williams (6), White (4)
  Smith (6), Johnson (5), Murphy (5)
  Smith (9), Moore (7), Jones (6)
  Smith (11), Moore (8), Brown (8)
  Smith (11), Jones (8), Taylor (6)
  Brown (8), Smith (7), Cooper (6)
  Edward O'Dea, the most recent common ancestor of these six people, did have a granddaughter married to a Smith, but these statistics still appear to tell us more about the distribution of surnames in the entire FTDNA database than among the relatives of Edward O'Dea.
• Can the Ancestral Surnames column (and ancestral placenames, when separated) be populated automatically from an uploaded GEDCOM?
• I can filter by any specific Ancestral Surname, but how can I filter by the number of matching Ancestral Surnames?
• I had to do this to extract and analyse the Ancestral Surnames column:
  • copy it to a text editor
  • change every " / " to a line break
  • change every " (" to a tab
  • remove every ")"
  • paste into a new spreadsheet
  • insert a row of headers
  • Alt D P to create a pivot table
  • I managed to extract the (quite large) frequency table here from the pivot table
  • Apart from "Unknown", Parker with 10 occurrences is the most common of my own ancestral surnames; 15 of my ancestral surnames were not shared by any of my initial 354 FTDNA-overall-matches.
• This would work better if the characters used as delimiters between surnames and placenames (brackets) were not also allowed as parts of surnames or placenames!
• I ended up with 5,942 surname lines from 354 people, suggesting that FTDNA customers have entered an average of just over 16 ancestral surnames each.
• I've spotted only one Irish townland where I have known relatives (Barnacahoge, County Mayo), but most placenames are at county, country or state level only.
• On the Keas/Keyes side, I did find one person whose Keas ancestor I recognised as having lived in the same Catholic parish as mine (Patrickswell, County Limerick). However, fifteen years of conventional genealogical research have failed to prove the precise relationship between the two neighbouring Keas families, and the DNA evidence appears unlikely to advance the search for proof.
• There are two other people listing Keas/Keyes as an ancestral surname, one in Germany back to 1813 and the other in the USA back to 1671, surely just coincidence as my GGGGgrandfather John Keas lived in Ireland and was born in the 1770s.
• I have e-mailed a few people to see what happens, and my 5th cousin Cindy Wood, the Keas expert, has e-mailed a few others.
• I also persuaded Cindy to submit a sample of her DNA to FamilyTreeDNA but when her results came back on 14 January 2014 we were not deemed FTDNA-overall-matches and had precisely one FTDNA-overall-matches in common (Raphael Matthew Whelan). GEDmatch.com confirmed that Cindy and I have half-identical regions of 4.6cM (875 SNPs), 3.8cM (1177 SNPs), 3.5 cM (731 SNPs) and 3.2 cM (876 SNPs). Some or all of these are probably half-identical by descent from either our common GGGGgrandfather John Keas (d. 8 August 1845) or his unknown wife.
• As noted above, I did not realise until 11 January 2014 that I had switched off the facility for other people to e-mail me!
• On 21 March 2014, I made contact for the first time with someone with whom an initial DNA connection resulted (within hours) in establishing a known relationship (ninth cousin twice removed). We are not FTDNA-overall-matches, so our initial contact was via facebook.com and GEDmatch.com.
• My first real success arising from autosomal DNA matching came courtesy of my paternal first cousin's next closest match after myself by Relationship Range (2nd Cousin - 4th Cousin). As he had a completely blank Profile and blank Ancestral Surnames list and an e-mail address in Houston, Texas, I did not bother contacting him. Some months later, I met someone I knew with exactly the same name, and asked him if he had a namesake in Texas. It turned out that he was the same person and had been persuaded to give a DNA sample by a roots-hunting visitor from Texas who manages his DNA kit.
  We soon established that we were each descended from a woman with the maiden surname O'Dea who lived in the Catholic parish of Patrickswell, Lurriga and Ballybrown in County Limerick in 1821.
  Thinking about this situation gives rise to some general principles for such cases.
  If you find two people whose DNA is half-identical in a particular region and who have ancestors who shared the same surname and lived in the same area around the same time, then it is reasonably safe to conclude that the shared DNA is inherited from a most recent common ancestor with that surname (possibly a female, for whom it would then be her married surname).  Given this conclusion, one must consider the possibilities that the known contemporaneous ancestors are brothers, first cousins, second cousins, etc., or, equivalently, that the MRCA is the parent, grandparent, greatgrandparent, etc., of the known contemporaneous ancestors.
  If the MRCA is the parent, then the probability that the two siblings inherited the same segment in the region of interest is 1/2.
  If the MRCA is the grandparent, then the probability that the two grandchildren inherited the same segment in the region of interest is 1/8 (probability 1/2 that both parents inherited the same segment multiplied by probability 1/2 that the first grandchild inherited it multiplied by probability 1/2 that the other grandchild also inherited it).
  If the MRCA is the greatgrandparent, then the probability that the two greatgrandchildren inherited is 1/32, for GGgrandparents it is 1/128, and so on.
  If we assume that the two contemporaneous ancestors are from the same generation (and not, for example, uncle and nephew), then the conditional probability that they are siblings is 75%, first cousins 18.75%, second cousins 4.6875%, and so on.  The conventional 95% confidence interval encompasses the cases of siblings, first cousins and second cousins.  Evidence from conventional genealogical sources or from other types of DNA (mtDNA or Y-DNA or X-DNA) will be required to distinguish between these possibilities.
  In the O'Dea case, the DNA evidence first of all finally confirmed which of several candidates was the wife of my GGGGgrandfather John Keas, namely Maria O'Dea. 1821 was the year in which their last child was baptised, and the year in which the younger Bridget O'Dea married John Ryan. Comparing further family folklore confirmed that they were closely related. Each named one of her older sons Edward, so it appears possible that both were daughters of Edward O'Dea, who died on 19 December 1830 aged 74 and was buried in Kilkeedy Cemetery. If so, then the two FTDNA-overall-matches are fourth cousins twice removed, closer than suggested by my own match list (no relationship) but not as close as suggested by my first cousin's match list (2nd Cousin - 4th Cousin).
  Maria and Bridget may have belonged to the O'Dea family which continued to live in the townland of Newtown (in Kilkeedy civil parish) up to the mid-20th century. We are now trying to track down female line descendants of these two O'Dea women, in the hope that comparison of their mitochondrial DNA will confirm that they came from the same female line. In the meantime, I set up a Family Finder Project called O'Deas of Newtown on 24 November 2014. If you believe that you may be descended from Edward O'Dea and wish to join the project, log in to your own FamilyTreeDNA.com account and then go here and point-and-click the Join button. So far, there are four members with paper trails to either Maria or Bridget O'Dea, but only two of the six pairs are FTDNA-overall-matches.
• Another success story later resulted in a conundrum for the real autosomal DNA nerds:
  
  In the summer of 2015 via GEDmatch I found a fourth cousin (Dana) to whom I am half-identical for 44.6cM on Chromosome 12 (93,176,484 to 125,287,936).
  Later in 2015 via the Marrinan Family Reunion facebook group, I found another match (Bob) who is half-identical to both of us for 11.7cM within that region (116,665,672 to 125,064,434) and half-identical to me for a further 4.2cM up to 126,483,038.
  
  There appears to be a fuzzy boundary between 125,064,434 and 125,287,936 (0.5cM) where I am half-identical by chance to Dana but she is not half-identical to Bob.
  
  I am happy to deduce that the DNA shared by Bob, Dana and myself is also shared with either Hugh Clancy or Marcella Blackall, the common GGGgrandparents of Dana and myself.
  
  Now the complicated bit:
  
  My first cousin (Antoin, also a fourth cousin to Dana) is also half-identical to Bob, also on Chromsome 12, also between 112,242,549 and 116,643,188 (9.4cM, 1529 SNPs), but Antoin is not half-identical to either Dana or myself in this sub-region.  Hence, the DNA shared by Antoin and Bob cannot come from Hugh Clancy or Marcella Blackall.  It could have come from Antoin's father, or from our common grandfather.  However, for geographical reasons, it seems more likely to have come from our common grandmother, Ciss McNamara, as she alone was from the same part of County Clare as Bob's ancestors.
  
  If so, then Ciss must have passed on her maternal Clancy chromosome in this region to my father, and passed on different DNA, in other words her paternal McNamara chromosome, to Antoin's mother.
  
  So I deduce that Bob is probably doubly related to Antoin and myself, probably both through our McNamara greatgrandfather and through our Clancy greatgrandmother.
  
  That leaves the puzzle of the little gap from 116,643,188 to 116,665,672 where Bob is not half-identical to either Antoin or myself.
  
  My results are from FTDNA, which looks at only five SNPs in this gap:
  
  "rs11068648","12","116643188","CC"
  "rs7964607","12","116643307","GG"
  "rs975666","12","116646955","TT"
  "rs2174412","12","116657099","GG"
  "rs1976500","12","116657522","CC"
  "rs479810","12","116660573","TT"
  "rs17619048","12","116665672","TT"
  
  Bob's results are from Ancestry, and an Ancestry raw data file that I consulted has only one SNP in this gap, one that FTDNA doesn't look at:
  
  rs1818056    12    116645420    T    C
  
  So my conclusion is that somewhere in Bob's ancestry there was probably a crossover between what I will call McNamara DNA and Clancy DNA, somewhere within this little gap.
  
  It remains to find the paper trail to prove these two relationships!
• How fast are my match lists growing?
  
  • I started out with 354 matches all dated 15 November 2013.  By 2 January 2016, I had only 333 matches with this date. The other 21 must either have privatised their results or had the date changed due to a need for reprocessing.
  • My 666th match by date is dated 3 March 2015, suggesting that the FTDNA Family Finder database was doubling in size in just over 15 months.
  • My 960th and most recent match at the time of compiling these statistics was dated 26 December 2015 and my 480th was dated 21 Jul 2014. This suggests that the growth rate had slowed slightly, with the database now taking over 17 months to double.

AncestryDNA

• The first group of matches, headed "3RD COUSIN", contained a single match, Anthea Ring.  She was already my second top match at FTDNA and my top match at GEDmatch, in both cases ignoring close cousins for whose tests I had paid myself.  For Anthea, AncestryDNA says "Possible range: 3rd - 4th cousins" and "Confidence: Extremely High"; FTDNA says "2nd Cousin - 4th Cousin" and GEDmatch has Gen=3.4 (Total cM 133.3) for my FTDNA kit but Gen=3.6 (Total cM 98.9)  for my AncestryDNA kit.
• The second group of matches, headed "4TH COUSIN" contained 55 matches, all labelled "Possible range: 4th - 6th cousins".
  For the top 13, Confidence was Extremely High; for the other 42, Confidence was Very High.
• The third group of matches, headed "DISTANT COUSIN" contained the remaining 2991 initial matches, all with:
  Possible range: 5th - 8th cousins
  The first 143 had Confidence: High.
  The remainder had things like
  Confidence: Good
  and
  Confidence: Moderate.
  

• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/aa72b918-58bc-4c40-81bf-7934340ba07d
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/1bdd03bf-007a-4086-8438-18c7c0c1be38
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/fb9e0694-5ba9-4b49-be93-dfac12b2f25d
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/a710e867-8f97-4dc6-aade-de37255fd54e
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/275b2a80-9ec4-4105-9255-cf2787cc86f8
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/2519d6ed-ed87-464a-975b-ecdf6ad7936e
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/bdcfb467-0f3c-4f55-86a1-c09cbd88ef3a
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/79bcf59b-cab6-4bba-9655-54744ceedd9e
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/1d10db66-3e4b-48c0-a0d0-cfaee08f7541
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/7001ff3d-9ddb-4392-9006-d607441477df
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/135f55d8-9ce7-44e9-b67d-9ad0ce40d44a
• https://www.ancestry.com/discoveryui-matches/compare/d0f65c2d-194d-4ee6-b174-63b2b6b43e07/with/c294826e-d075-45fc-b9b4-3c9df4231d67

• One new match on AncestryDNA made the whole thing worthwhile. He is in second place on my list (39 centimorgans shared across 6 DNA segments), but not already at FTDNA or GEDmatch. I had seen his tree at Ancestry before, but had not contacted him as he had no information in his tree that I didn't have, and Ancestry does not indicate which of its users or which people in its user-submitted trees have submitted DNA samples.  We share a "great-aunt".  In his case, she is a well-documented great-aunt.  In my case, she was referred to by my mother as "Aunt Ellie", although she was not a real aunt, but some sort of cousin.  I've been trying for 40 years to establish the precise relationship.  This is one of the brick walls that I discuss in more detail in the introduction above. I had recently convinced myself that I had enough evidence to prove that my mother and her "Aunt Ellie" were actually second cousins. This would mean that I am a third cousin once removed of my DNA match. Ancestry says: Possible range: 4th - 6th cousins; Confidence: Extremely High; Predicted relationship: 4th Cousins; 39 centimorgans shared across 6 DNA segments.
  Numerous subsequent attempts to establish contact with this match have been unsuccessful. Watch this space to see whether the DNA comparison confirms or refutes my theory.
• In 20th place on the list was someone whose tree I had previously seen, with an ancestor from the same townland and with the same surname as my mother. I have now satisfied myself that we are fourth cousins.  Ancestry says: Possible range: 4th - 6th cousins; Confidence: Very High; Predicted relationship: 4th Cousins; 23.5 centimorgans shared across 2 DNA segments.
• My 4th closest match at GEDmatch, again ignoring close cousins for whose tests I had paid myself, has two Ancestry kits on the same account, namely herself and her sister.  They are confirmed 4th cousins to me.
  The sister who was my 4th closest match on GEDmatch is only 102nd on my ancestry match list (Possible range: 5th - 8th cousins; Confidence: High; 14.9 centimorgans shared across 2 DNA segments; dramatically different from 50.9 Total cM and 44.6 largest cM at GEDmatch).
  The other sister shows as my 43rd closest match at Ancestry (Possible range: 4th - 6th cousins; Confidence: Very High; 19.0 centimorgans shared across 3 DNA segments).
  I requested the sister that I am in touch with to upload the other sister's data to GEDmatch, which confirmed that I share more DNA with the other sister - I share exactly the same 44.6cM segment with both sisters, but a second segment of 17.4cM with the second sister in place of a second segment of 6.3cM with the first sister. When batch processing was completed, the new kit naturally leapfrogged over her sister on my one-to-many list to become the second closest match after the kits I paid for myself.
• In 611th place on the list was a known 5th cousin, already identifed with the help of FTDNA. I would not have recognised him by his initials or found him in search results at Ancestry if his son had not tipped me off. Ancestry says: Possible range: 5th - 8th cousins; Confidence: Good; Predicted relationship: Distant Cousins; 8.2 centimorgans shared across 1 DNA segment.
• In 752nd place on the list (Predicted relationship: Distant Cousins; Possible range: 5th - 8th cousins; Confidence: Good; 7.8 centimorgans shared across 2 DNA segments) was someone that I long suspected was a half fourth cousin.

• One represents a typical genealogical brick wall, where two families remained friendly through several generations, but the precise details of the relationship had been forgotten.
• Another represents another typical genealogical brick wall, where two families with the same surname lived on adjoining farms through several generations, but again the precise details of the relationship had been forgotten.
• Two involved a fostering, where the child fostered knew his birth parents' names and used his birth mother's surname, but had no further contact with his birth parents (who later married) after going to his foster parents.
• One involved a closed adoption, where the DNA trail identified the birth parents more quickly that the information provided by the adoption agency.
• One involved the mysterious, unsolved, and hushed up, mid-nineteenth century disappearance of a man that I have long thought of as `the wicked stepfather'.

• At the top of each page of matches, there is a "Search matches" box. It expands to two boxes, one for Search by surname, the other for Search by birth location. Using the surname box to search for my own suname, my ancestral surnames, surnames of my closest non-anonymous matches, etc., all returned "No matches found" for the first couple of weeks after my initial notification of results. Searching for birth locations produces a drop-down menu from which the birth location must be chosen. To get either Clare or Mayo, the two Irish counties where most of my ancestry lies, to appear on this menu, requires one to type Clare, Ireland or Mayo, Ireland in full, but typing Limerick alone is sufficient to get Limerick, Ireland to appear.  One can get nonsense locations like Kilrush, Kildare, Ireland (which is suggested to those trying to enter the much larger but missing Kilrush, Clare, Ireland).
• The search for O' surnames appeared to be broken: I copied and pasted the name O'Neil from my cousin (and match) mbrowntexasboatworldcom's tree to the search box, ticked "Include similar surnames" and got "No matches found". How can I be sure that I am finding all my matches with my ancestral surnames like O'Dea, O'Halloran, O'Neal, O'Neil or O'Neill in their family trees?
• Firefox (inevitably for the first few days) and Chrome (frequently) locked me into an infinite loop with this error message while I browsed through my matches:

  You must refresh your internet browser
  Uh-oh. It looks like you caught us just after we rolled a site upgrade. In order to continue, please refresh your internet browser. We apologize for the inconvenience.
  Refresh browser   Cancel
  

  So I was initially forced to struggle mostly with Safari and its horrendous ignorance of basic Windows keyboard shortcuts and clipboard practice.
• I had used Safari previously to log into a different Ancestry account; several times it spontaneously transferred me back from the account with my own results to the other account.

• There are seven results for Waldron, the first of them a third cousin once removed, with whom I had previously been in contact.  Ancestry underestimates the closeness of our relationship:
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: High
  13.1 centimorgans shared across 2 DNA segments
  
• When I moved on to my paternal grandmother's surname McNamara, I found a fourth cousin:
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: Moderate
  6.3 centimorgans shared across 1 DNA segment
• When I searched for variants of O'Neill, a surname which appears in both my paternal and maternal ancestry, the matches included an uncle and two nephews named O'Neill, but with a connection through a Butler ancestor that makes them my double half-tenth cousin and double half-tenth cousins once removed. This connection is based on the assumption that the William Massey named on the U.S. tombstone of his wife Ellen from Ballylanders in County Limerick is the William Massy who sold Glenville and died unmarried according to Burke's Irish Family Records. The family tree cites as its main source "Ancestry Family Trees", which always makes me highly suspicious that the real source is the shaky-leaf hint virus. Even if Burke is wrong, the shared DNA is likely to have come from some more recent unidentified common ancestor, possibly either O'Neill or Morley of Mayo.
• When I moved on to names which are common in my extended family but are not the names of direct ancestors, I had more success, and found another third cousin once removed:
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: Good
  7.9 centimorgans shared across 1 DNA segment

• 6 February 2016: A previously unknown fourth cousin, whose grandfather and greatgrandfather appear in both of our family trees.
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: Good
  9.1 centimorgans shared across 2 DNA segments
• 2 March 2016: A double third cousin once removed, whom I had encouraged to consider submitting her DNA over two years earlier; we discovered our second relationship only when comparing DNA results..
  Predicted relationship: 3rd Cousins
  Possible range: 3rd - 4th cousins
  Confidence: Extremely High
  90 centimorgans shared across 5 DNA segments
• 20 March 2016: A fourth cousin once removed, who may have seen my Facebook appeals for Clancy descendants to submit DNA samples.
  Predicted relationship: 4th Cousins
  Possible range: 4th - 6th cousins
  Confidence: Very High
  20.4 centimorgans shared across 1 DNA segment
• 14 May 2016: A fourth cousin, whose first cousin was one of my initial AncestryDNA discoveries:
  Predicted relationship: 4th Cousins
  Possible range: 4th - 6th cousins
  Confidence: High
  41 centimorgans shared across 4 DNA segments
• etc.

• A895750
  AncestryDNA says:
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: Moderate
  5.0 centimorgans shared across 1 DNA segment
  GEDmatch says:
  Largest segment = 0.0 cM
  Total of segments > 7 cM = 0.0 cM
  (2036) No shared DNA segments found
  
• A601367
  AncestryDNA says:
  Predicted relationship: Distant Cousins
  Possible range: 5th - 8th cousins
  Confidence: Moderate
  5.2 centimorgans shared across 1 DNA segment
  GEDmatch says:
  Largest segment = 0.0 cM
  Total of segments > 7 cM = 0.0 cM
  (2036) No shared DNA segments found

What does it all mean?

• It was probably evident from Chapter 1 that, as a mathematician, I have been looking, so far almost completely in vain, for a rigorous mathematical or statistical model to aid my understanding of the science of genetics and DNA.
• While possibly in danger of merely re-inventing the wheel, I have tried to develop a simple mathematical and statistical approach to the genealogical aspects that particularly interest me.
• The next best thing to a mathematical or statistical model is a graphical tool, and Family Tree DNA's chromosome browser is just such a (multicoloured) graphical tool.
• However, it initially was a hindrance rather than an aid to my understanding.
• And no sooner had I come to understand the chromosome browser that it was rendered obsolete by the ADSA.
• So I have written the following sections to explain how the light dawned for me.

Transitive relations in general

Before looking at the chromosome browser, we need a tiny bit of basic mathematics.

The mathematical relation R is said to be transitive if VRW and WRZ imply VRZ.

For example, equals (=) is a transitive relation, since V=W and W=Z imply V=Z.

Other simple mathematical examples of transitive relations are is greater than (>), is less than (<) and is a subset of.

A mathematical example of a relation which is not transitive is is not equal to. For example, 1 is not equal to 2 and 2 is not equal to 1, but 1 is equal to 1.

More generally — verbally — is identical to is a transitive relation, since V is identical to W and W is identical to Z imply that V is identical to Z.

In genealogy, is related to is not a transitive relation, since Tom is related to Dick and Dick is related to Harry do not necessarily imply that Tom is related to Harry. Tom could be related to Dick on Dick's paternal side and Dick related to Harry on Dick's maternal side, in which case Tom is not related to Harry. Or Tom, Dick and Harry could have a common ancestor (more likely, a common ancestral couple, depending on whether they are full-cousins or half-cousins) in which case Tom is related to Harry. Or Dick could have some more remote ancestral couple for whom one spouse is related to Tom and the other spouse is related to Harry in which case again Tom is not related to Harry. I think that takes care of all the possibilities. Some genealogists like to talk about the concept of is connected to, which is a transitive relation. (If X is related to Y and Y is related to Z, then we say that X is connected to Z, regardless of whether X is related to Z.)

Other simple genealogical examples of transitive relations are is an ancestor of and is a descendant of.

As an aside, and speaking of ancestors versus ancestral couples, it is surprising how much more common the former phrase is than the latter in what I have read about DNA. If two cousins find a significant half-identical region in their autosomal DNA, then they can, with a bit of co-operation, work out which is the most recent ancestral couple from whom they have both inherited the relevant segment. At that stage, it is generally equally likely that the segment was inherited from the husband in that couple as from the wife. (Political correctness probably means that I should call them male partner and female partner rather than husband and wife!) Eventually, a more distant cousin sharing the same segment may show up and reveal whether the segment came from the husband or from the wife in the most recent ancestral couple of the first two cousins. This only pushes the conundrum back another generation or more, to the most recent ancestral couple shared by all three cousins.

Transitive relations in genetic genealogy

The advantage of mathematics over the English language is its lack of ambiguity.

Is matches a transitive relation? It depends on the sense in which the word is used.

In many uses of the word matches, if V matches W and W matches Z, then V matches Z, and so matches is (sometimes) a transitive relation.

For example, if matches is used in the sense of is identical to, then we have already seen that it is a transitive relation.

However, Family Tree DNA uses the word matches in the sense of is related to, and we have already seen that then matches is clearly NOT a transitive relation (even without the added complication that in this case the relationship is probable rather than known).

Further confusion can arise, and certainly arose initially for me, from the multiple uses of the verb match, with different connotations, by Family Tree DNA and its users:

• explicitly, with the meaning that I have dubbed FTDNA-overall-matches, on the Family Finder - Matches web page, where it clearly means is (probably) related to, and is NOT a transitive relation; and
• implicitly, with the meaning that I have dubbed region-matches, on the Family Finder - Chromosome Browser web page.

Equivalence relations in genetic genealogy

Genealogists are familiar with the extension of an is-related-to type of relation to an is-connected-to type of relation.

Mathematicians in exactly the same way frequently extend a mathematical relation to the equivalence relation generated by the underlying mathematical relation.

Any equivalence relation divides the set of objects which it compares into equivalence classes.

We can define such an is-related-to type of relation on the set of all my FTDNA-overall-matches. Let's call this relation P (for Paddy). We will say that WPZ if (a) W FTDNA-overall-matches both Z and me and (b) Z FTDNA-overall-matches both W and me. This just means that there is DNA evidence that W and Z may be related to each other and to me.

Two people are in the same equivalence class of the corresponding is-connected-to type of relation if it is possible to trace a path from one to the other, but without going through me.

So if my siblings are not in the FTDNA database and my parents are not related to each other and my parents have no relatives in common who have tested, then my paternal relatives and my maternal relatives will not end up in the same equivalence class.

Similarly, if none of my first cousins or their descendants are in the FTDNA database and similar assumptions hold, then people related to me through each of my four grandparents will end up in four (or more) equivalence classes.

Many people believe that there are no more than six degrees of separation between any two human beings, but I don't. I think the world is much smaller than that. As one of my friends says, "there are only 200 people in the world and the rest are an illusion created with mirrors". It took me several decades of doing genealogy to come up with a path from my father to my mother: a cousin of my father and a cousin of my mother whose spouses were uncle and niece. Within a couple of years, I had found a second such path. There may well be such paths between your paternal relatives and your maternal relatives in the FTDNA database, so you may find that your FTDNA-overall-matches do not divide naturally into equivalence classes like this at all.

DNAGEDCOM.com allows me to download an ??????_ICW.csv file (where ?????? represents my kit number) defining the is-related-to pairs by which the relation P is generated. If I open this .csv file in Microsoft Excel, then I can use the PivotTable tool to start generating the is-connected-to relation which breaks my FTDNA-overall-matches up into the equivalence classes of interest. The next step is to use a few matrix multiplications to calculate for each of my FTDNA-overall-matches how many of my other FTDNA-overall-matches are within one, two, three, etc., degrees of separation. Unfortunately, as I feared, having tried to use it back around 2001 for handicapping racehorses, the MMULT function in Microsoft Excel is still incredibly slow and inefficient in the current version, even on my top-of-the-range 2012 laptop, so the details will have to wait until I install some real software like SciLab to do the job.

What I have discovered is that as of 10 Jan 2014 my 381 FTDNA-overall-matches included eight people each in equivalence classes on their own, in other words eight people with whom I have no ICW matches.

FTDNA's chromosome browser

To users of FamilyTreeDNA.com, the word "matches" can also sometimes mean region-matches.

Here's an example of what the FTDNA chromosome browser looks like when comparing the logged-in kit to two other kits:

A maximum of five kits can be viewed simultaneously in the chromosome browser. These can be selected by ticking boxes in one of the worst designed selectors imaginable. To preserve the anonymity of my FTDNA-overall-matches and to avoid shaming the designer, I don't show it here. It is about 7.5 lines tall, but shows one's FTDNA-overall-matches 10 at a time, ordered by surname, necessitating a vertical scrollbar. It runs along to the left of chromosomes 8 to 18, with plenty of blank white space to the left of chromosomes 19 to X. Instead of showing the usual colour-coded place-holders where no mugshots are available, it shows grey mugshots for both males and females. My first FTDNA-overall-match by surname is identified only by his or her initials "N A". I have to go to another tab and search for his or her colour-coded mugshot to determine whether this is a male or a female, which is very significant when looking at the X chromosome.

Someone I know through genealogy sent me the screenshot above (taken before FTDNA added the X chromosome), generated while logged in to her mother's FTDNA kit. Let's call her Terry. There are lots more similar examples on the ISOGG Wiki.

Terry and her mother have both tested with FTDNA and therefore are, of course, FTDNA-overall-matches.

Terry's mother and I are also FTDNA-overall-matches. As discussed on the FTDNA facebook page, we region-match on 14 regions of 1cM or more. Our number of shared segments, longest block shared (8.93) and total shared cM (38.24) combine to bring us in above the secret threshold for FTDNA-overall-matches.

Terry and I are not FTDNA-overall-matches. For reasons that I will come to later, we cannot see in the FTDNA data how much, or which segments, Terry has inherited from her mother of the autosomal DNA that her mother and I share, but we obviously expect it to be about half. What matters for now is that Terry and I come in below the threshold for FTDNA-overall-matches.

The blue regions in the image above are the 14 segments of 1cM or more on which Terry's mother and I region-match; the original default image showed only the 1 segment of 5cM or more on which we region-match, but there is a dropdown menu which can be used to reduce the threshold and display the smaller regions.

The orange regions in the image are those on which Terry and her mother match: pretty much everywhere.

For my first couple of days looking at these pretty pictures in the chromosome browser, I made the false assumption that region-matches was a transitive relation, but this example shows that it clearly isn't. If Terry region-matched me everywhere that she region-matches her mother and that her mother region-matches me, i.e. in all the blue segments in the chromosome browser, then Terry would have to FTDNA-overall-match me, which she doesn't.

The next clue that I had misunderstood something was the fact that Terry's DNA and her mother's DNA seem to match in 100% of locations, but we expect to find that Terry inherited only 50% of her DNA from her mother (one chromosome in each pair), and the other 50% (the other chromosome in each pair) from her father. The parent-child example in the ISOGG wiki looks just the same as Terry's example, so I knew there had to be a rational explanation.

I turned to Google in search of this explanation, and eventually found a reference to half-identical regions. Thinking that I might be on the right track, I googled that phrase, which brought me to Lesson 9 of the Beginners Guide To Genetic Genealogy on the Wheaton Surname Resources website, at which stage a light-bulb finally went off in my head! I hope I have explained the concept of half-identical region clearly above.

My initial confusion comes from the fact that there are 22 pairs of chromosomes, but the chromosome browser appears to show only 22 single chromosomes.

Don Worth's Autosomal DNA Segment Analyzer (ADSA)

Why ADSA is great

ADSA provides a nice graphical overview of your matches and allows you to identify groups of people related to each other, and in some areas to separate your paternal and maternal matches.

The FTDNA chromosome browser allows comparison of the logged-in kit with up to five FTDNA-overall-matches. The ADSA automatically compares all those with half-identical regions longer than the selected cM threshold on each chromosome. I recommend thresholds of 10cM and 1000 SNPs for beginners, but you will eventually want to drop these thresholds to check whether relevant individuals appear on particular chromosomes.

The FTDNA matrix tool allows comparison of a selected group of up to ten of the logged-in kit's FTDNA-overall-matches and shows which of the selected group FTDNA-overall-match each other. The ADSA automatically displays the equivalent matrix for 22 naturally defined groups, one for each chromosome, comprising all my FTDNA-overall-matches with half-identical regions longer than the selected cM threshold on the relevant chromosome.

The FTDNA chromosome browser and matrix tool sort the people being compared according to the probably arbitrary order in which the user selected them. The ADSA very helpfully sorts the people being compared by the starting location of the shared half-identical region.

The pretty FTDNA chromosome browser pictures can only be shared as screen-grabs. The even more colourful ADSA output is just a single clever self-contained (admittedly large) HTML file, which can be saved to disk and even shared as an e-mail attachment.

The FTDNA website breaks my FTDNA-overall-matches up into dozens of web pages with 10 people on each. The ADSA displays all of them on a single web page.

The FTDNA website displays ancestral surnames and locations with horrible nested scroll bars. The ADSA displays the full string on mouseover with no need for additional clicking (if your screen is wide enough).

The ADSA uses data transferred by the user from FTDNA, so cannot be used to view matches from the perspective of anyone other than the kit owner.

Note that the ADSA displays anyone who region-matches the kit-owner in more than one region of the same chromosome as if he or she is two separate people (who sometimes appear not to even FTDNA-overall-match each other).

How to use ADSA

1. If you are not logged in at DNAgedcom.com, go to the login page and enter your DNAgedcom Username and Password (which may not be the same as those for the FamilyTreeDNA kit that you wish to analyse).
2. Go to the download pageand enter the FamilyTreeDNA Kit Number and Password for the kit that you wish to analyse, hit the Get Data button, and wait. (Note that FTDNA turned off download of ICW files around February 2017, so you may see zeroes in the ICW Count column. This greatly reduces the usefulness of the ADSA report as you will have to go to other websites to check whether two kits which match the kit of interest in the same region also match each other there, or alternatively one matches the kit of interest on the paternal side and the other matches it on the maternal side.)
3. Go to the ADSA page, select whichever of your kits you wish to analyse from the Kit number dropdown menu, and hit the GET REPORT button.

My raw autosomal results: homozygosity and heterozygosity

A chromosome, as shown in the chromosome browser, is essentially an array of pairs of the four letters A, C, G and T.

This table shows the distribution of the paternal/maternal unordered pairs in my raw autosomal results:

Lots of interesting things can be seen from this table:

• At 70.40% of all SNPs, I am homozygous, in other words the letters observed from my paternal and maternal chromosomes are the same (CC, GG, AA or TT).
• At 0.50% of all SNPs, no letters are observed and a missing value code of -- is returned. Is this a form of measurement error?
• The letters which pair together on the forward and reverse strands of a single chromosome (AT or CG) almost never pair together on the paternal and maternal chromosomes of a single cell: at only 0.08% of SNPs are such pairs observed. Is this another form of measurement error?
• At the remaining 29.01% of SNPs I am heterozygous, in other words the letters observed from my paternal and maternal chromosomes are different (TC, AG, AC or TG).
• Since the data is unphased, these four pairs are never reported in the opposite order (no CT, GA, CA or GT).
• The letters which pair together on the forward and reverse strands of a single chromosome are reported roughly equally often in each order (GC and CG are both observed; TA and AT are both observed). Is this also measurement error?
• The variation between people (at least between my parents) at a SNP is almost never simply the reversal of the Watson-Crick base pair between strands (e.g. GC for one person and CG for the other), but usually involves different base pairs for each person (e.g. GC or CG for one person and TA or AT for the other person).
• While there are only 696,752 SNPs in my raw autosomal data, there are 707,269 SNPs in the raw autosomal data for the second person whose raw data I examined. Why the difference?

Note that at a typical (biallelic) SNP where I am heterozygous, I am half-identical to everyone. For example, TC is half-identical to CC, TT and TC. Hence, biallelic SNPs where I am heterozygous provide no information in the search for half-identical regions. On the other hand, at a biallelic SNP where I am homozygous, I am not half-identical to anyone who is homozygous with the other possible letter, i.e. where we are opposite homozygous. For example, if I am AA, I am half-identical to those who are AG or AA, but not to those who are GG. Thus the significance of a region where I am half-identical to a stranger is determined not by the total number of SNPs in the region, but by the number of SNPs in the region at which I am homozygous. The more heterozygous SNPs I have in a region, the more false positives will be expected to appear among those with whom I am half-identical on that region.

The prevalence of homozygous SNPs varies markedly throughout my genome. I have a spreadsheet in which I have compiled details of 281 regions on which I am half-identical to various people. The proportion of SNPs at which I am homozygous in 280 of these regions varies between 51.3% to 86.3%, with one small outlier where I am homozygous at 74 of 75 SNPs. The mean proportion is 72.8%, which surprised me. I am homozygous at only 70.4% of all SNPs, and expected homozygous SNPs to be under-represented in regions where I am half-identical to others. The standard deviation of the proportion is 6.6 percentage points.

Surprisingly, I have not yet found any comparison tool which automatically reports either the number or percentage of informative homozygous SNPs in a region of interest. For a region on which two individuals are half-identical, any such comparison tool should report the number of homozygous SNPs for each of the two individuals. A comparison tool which does this is urgently needed by all genetic genealogists.

genesis.GEDmatch.com began to address this problem by introducing the concept of slimming, which remains poorly documented, but has been discussed on a Facebook thread.

David Pike's utilities report, inter alia, on runs or sequences of consecutive homozygous and heterozygous SNPs. Here are summaries for the first four kits to which I had access:

The extraordinary thing about this table is the difference between the lengths of the longest sequences of heterozygous SNPs and the longest sequence of homozygous SNPs. As there are more homozygous SNPs than heterozygous SNPs, one would certainly expect the longest homozygous sequence to be longer than the longest heterozygous SNPs, but not more than ten times longer. Why is this?

The data for my relatives does not appear to be unusual, as the default settings for the two utilities are 20 SNPs and 200 SNPs respectively.

Back to transitivity

Several words and phrases suggest themselves to describe the two relations shown in the coloured regions in the FTDNA chromosome browser:

1. the relation between the reference person and the person represented by one of the colours (an is-related-to type of relation); and
2. the relation between the people represented by two different colours (an is-connected-to type of relation).

The words and phrases which spring to mind include:

• matches;
• shares a segment with;
• overlaps with; and
• is half-identical with.

For the first relation (that between the reference person and the person represented by one of the colours) let's stick to the last of these to make it completely unambiguous what we mean.

The first and most important thing to note is that, just like - and for exactly the same reasons as - is related to, is half-identical with is NOT a transitive relation. The person represented by the orange segments may not be half-identical with the person represented by the blue segments, even if the segments overlap.

Suppose V and W share a half-identical region on, say, chromosome 11, and W and Z share a half-identical region starting at the same location on chromosome 11. It does not follow that V and Z share a half-identical region here. For example, V's first pair could be AC, W's first pair could be CT, and Z's first pair could be GT (which is not half-identical with AC). The same could be the case at many other locations within the region.

In practice, this means that W inherited this segment of his (or her) paternal chromosome from an ancestor shared with V but inherited the corresponding segment of his maternal chromosome from an ancestor shared with Z (or vice versa, maternal shared with V and paternal shared with Z).

When W looks at V and Z together in the chromosome browser, there will be an overlap of coloured regions in the relevant part of chromosome 11.

When V looks at W and Z together in the chromosome browser, there will be just one coloured region in the relevant part of chromosome 11.

And when Z looks at V and W together in the chromosome browser, there will be just one coloured region in the relevant part of chromosome 11.

This assumes that each of the three individuals FTDNA-overall-matches both of the other two; otherwise FamilyTreeDNA.com does not allow them to do the comparisons in the chromosome browser.

If V, W and Z in this example want to research effectively, it appears that they will have to share their FamilyTreeDNA.com passwords, so that each can compare the other two in the chromosome browser. In Chapter 1, I have already pointed out other circumstances in which sharing passwords seems to be necessary for effective and productive research. It would be nice if there were two levels of access to kits - read-only guest access to allow this sort of chromosome browsing; and full write access to allow changing of passwords, editing of GEDCOMs, ancestral surnames, known relationships, etc., in much the same way as online family trees published using systems such as TNG and even the much-maligned ancestry.com allow different levels of access to different people.

On the FTDNA website, there are lots of routes from the Matches page to the Chromosome Browser page and to some of the data which the chromosome browser displays.

For example, find the person you want to compare with on the Matches page. Click the tiny dropdown just below his or her mugshot (or missing mugshot icon). The Longest Block figure is immediately revealed. Click the "Compare in Chromosome Browser" link. (Repeat for up to five individuals.) Click the large blue "compare" arrow. Now the number of Shared Segments between you and each selected person is revealed along with the lovely colour diagram.

I first found the following more circuitous alternative route: click Family Finder, Chromosome Browser, Filter Matches By ..., Name, [type name, don't hit <Enter> key], Find, checkbox. Not yet having found the quick route to the Longest Block figure, I thought I then had to View this data in a table and scan the centiMorgans column for the largest value. The centiMorgans data is shown to two decimal places in the table, but for some strange reason trailing zeroes are omitted and the numbers are centred instead of aligning on the decimal point, which doesn't make it any easier to find the maximum by eyeballing the column.

A strange policy

Now it is time for a discussion of an important flaw in Family Tree DNA's policy:

I can not use the Chromosome Browser to compare my DNA with that of someone who is not one of my FTDNA-overall-matches, not even with someone like Terry, who is the daughter of a match, and even uses the same e-mail address for her own kit and for her mother's kit. Likewise, I can not use the Chromosome Browser to compare my DNA with that of a known relative who has tested but has not shown up as an FTDNA-overall-match.

I don't see why any two consenting adult customers of Family Tree DNA should not be allowed to compare their autosomal DNA in the chromosome browser, but the company thinks differently, citing unexplained "compliance with our matching and privacy policies" when I raised this question on the company's facebook page.

Such comparisons must be done on third party websites, such as GEDmatch.com.

Example I: Dengen

The next two chapters will each deal in some detail with a single initial FTDNA-overall-match with whom I have had extensive correspondence. In this chapter, I will include brief reviews of two other groups of FTDNA-overall-matches whom I have not yet contacted directly.

As already mentioned, my initial top ten FTDNA-overall-matches, which are the same both by Relationship Range and by Longest Block, include no less than five members of the Dengen family, sharing an e-mail address - a mother and four of her children. (I was bemused when I first looked at this in the small hours of the morning and thought one of the sons was his father, with whom he shares his name! I am still bemused that the father has two Buckley lines, apparently from Cork and Tipperary, while I have one Buckley line, from Kerry; I don't seem to have any surnames in common with the mother, with whom I share DNA!) This is where the Chromosome Browser seemed to come into its own. All five Dengens are half-identical with me on the same large segment on chromosome 20 (27.96cM for the mother; 20.11cM or greater for the children). As explained above, I cannot compare two of the siblings to each other or compare mother and child in the chromosome browser, so I cannot tell whether any pair of them are half-identical in this segment. But because I know their relationships to each other from their posted family trees, I know that mother and each child must be half-identical in this segment. Ex ante, I cannot tell whether any pair of siblings are half-identical in this segment, but (I think) because all four are half-identical with me, the chances that any two of them are half-identical with each other become larger.

My Shared cM with the children is between 49% and 73% of my Shared cM with the mother. The four siblings somehow have slightly different lists of ancestral surnames - probably because FamilyTreeDNA hasn't thought of allowing, or forcing, siblings who share an e-mail address (and even those who don't) to also automatically share their list of ancestral surnames. My understanding is that the genetic process is an example of what statisticians call a Markov process: whether or not any or all of the four children have inherited this block of DNA from their mother adds nothing further to what can be inferred about my relation to the mother from the overlap between my DNA and hers.

Lengths of half-identical regions

So far, I have not discussed the crucial relationship between the lengths of half-identical regions, sometimes expressed as percentages of autosomal DNA shared by two individuals, and their genealogical relationship.

This relationship provides a crude way of estimating the genealogical relationship between two people whose autosomal DNA has half-identical regions.

Everyone inherits exactly half of his or her autosomal DNA from his or her father (22 paternal chromosomes) and the other half (22 maternal chromosomes) from his or her mother.

We have already seen that this implies that the regions where a parent and a child are half-identical cover the whole of the 22 autosomal chromosomes.

Because recombination is random in nature, the proportion of DNA inherited from grandparents and more distant ancestors becomes random.

On average, we each inherit 25% of our autosomal DNA from each of our four grandparents. Random variation means that some people, for example, inherit 24% from their paternal grandfather and 26% from their paternal grandmother; or 27.1% from maternal grandfather and 22.9% from maternal grandmother; or even 32% from paternal grandfather and only 18% from paternal grandmother. The latter is a real example from GEDmatch, where the grandson is A260081, the grandfather is A237206 and the grandmother is A329975.

On average, siblings are fully identical on 25% of their autosomal DNA (where they have inherited the same DNA from both parents); they are half-identical on 50% of their autosomal DNA (where they have inherited the same DNA from one parent, but different DNA from the other parent); and they do not match at all on 25% of their autosomal DNA (where they have inherited DNA from different grandparents on both maternal and paternal sides).

The sibling relationship is special because siblings are related on both the paternal and the maternal side.

The calculations are much easier for those who are related on just one side.

Siblings are expected to share 50%, uncle-or-aunt/nephew-or-niece 25%, first cousins or greatuncle--or-greataunt/greatnephew-or-greatniece 12.5% and so on.

There are some nice pictures and tables which illustrate the shared percentages, such as this one from the FTDNA website:

This graph from 23AndMe shows why it is easy to exactly identify close relationships but more difficult to be precise about relationships beyond first cousins:

On 24 October 2015, Robert James Ligouri announced his Autosomal (atDNA) Prediction Grid.  For a given value of Total Shared cMs, this shows the range of plausible full relationships (not considering the additional possibility of a half-relationship).

This 50% principle can be quite difficult to grasp, as illustrated by Roberta Estes's blog. The sort of loose language that Roberta occasionally uses can lead to confusion. Thus she appears surprised to find that almost 50% of short (in cM) segments of maternal (say) DNA are inherited in their entirety by a child from a parent, and almost 50% are not inherited at all by the child (who instead inherits the corresponding paternal segment). In the limit, this is like a coin toss, where almost 50% of the time the coin lands head up, almost 50% of the time the coin lands tails up, and there is a miniscule probability that the coin lands standing on its edge.

At the opposite extreme, when results are aggregated over the entire genome, the proportions of a child's maternal autosomes that come from the maternal grandmother and from the maternal grandfather are each expected to be 50%, and the standard deviation around this figure is small.

For a large collection of short segments, it is of course expected that half of the segments will be passed on to the child and half will not. It is NOT expected that half of each individual segment will be passed on. By definition of a centiMorgan, it is expected that a 100cM segment will experience one crossover and thus be passed on in two parts. In this sense, we could say that segments longer than 100cM are expected break into more than two parts, but segments shorter than 100cM are expected (on average) to break into less than two parts.

When checking whether a small segment has been partially passed on by a parent to a child or not passed on at all, it is important to set both the cM and SNP filters low enough to pick up even smaller segments. See Example III below.

If the percentage of autosomal DNA shared by two people is 12.5%, then other variables like age differences need to be considered in working out the most likely relationship between them. Two men of similar age sharing 12.5% are most likely first cousins, but if their ages are a couple of generations apart they are more likely to greatuncle and greatnephew.

How can we estimate the shared percentages from the observed data?

The standard procedure appears to be to do this on the cM scale, by adding up the lengths of any half-identical regions longer than 1cM. This overestimates the shared percentage by including half-identical regions which are not half-identical by descent, but underestimates the shared percentage by excluding half-identical regions which are shorter than 1cM but are half-identical by descent. It seems that these two biases cancel each other out quite effectively.

If we have an unbiased estimate of the shared percentage between W and Z and want to estimate the shared percentage between W and one of Z's parents whose DNA is unavailable, say V (the one on whose side the relationship is), what can we do? Since Z got half of her DNA from V, we just double the estimate. But what about half-identical regions between 0.5cM and 1cM which are not counted when comparing W and Z, but which are expected to come from half-identical regions of between 1cM and 2cM shared by W and V? Do we need to use a factor slightly greater than 2.0 to take account of these regions?

Similarly, if we have separate estimates of the shared percentages between B and the siblings D, E and F, we can get a more precise estimate of the shared percentage between B and the parent of the sibling group who is related to B, say H, by doubling the figures for D, E and F and then taking the average of the three results.

The method of doubling the shared percentage appears to work fine until the result is greater than 50% or even 100%. By the time that stage is reached, in theory the analysis has gone back beyond the common ancestor, possibly by taking a wrong turn somewhere along the road. In practice, however, the shared segments that are detected are precisely those that are longer than expected, so implied shared percentages greater than 50% or even 100% are likely to be encountered even in a correct lineage.

In fact, beyond a common ancestor, a halving principle replaces the doubling principle. Suppose I share 23% of my DNA with one of my grandfathers (slightly less than the expected 25%). Given this information, I am expected to share 11.5% of my DNA with each of his parents (slightly less than the prior expectation of 12.5%).

Establishing parentage

If you are an adoptee, or even a foundling, or for some other reason have doubts about your parentage or paternity, then DNA can be a big help. In summary:

If you are male, then:

• you have Y-DNA which you definitely share in its entirety with your patrilineal ancestors (father, father's father, etc.) and with anyone else with the same patrilineal ancestors;
• you have X-DNA which you potentially share with some of your maternal ancestors (mother, both of mother's parents, three of mother's grandparents, etc.) and with anyone else with the same X ancestors;
• you have mitochondrial DNA which you definitely share in its entirety with your matrilineal ancestors (mother, mother's mother, etc.) and with anyone else with the same matrilineal ancestors; and
• you have autosomal DNA which you potentially share with all of your maternal and paternal ancestors and all of your cousins.

Also:

• anyone with whom you share Y-DNA is related to you through your father;
• anyone with whom you share X-DNA is related to you through your mother;
• anyone with whom you share mitochondrial DNA is related to you through your mother; but
• it is impossible to tell on which side (your paternal or maternal sides) someone with whom you share autosomal DNA only is related to you.

If you are female, then:

• you have X-DNA which you potentially share with some of your maternal ancestors (mother, both of mother's parents, three of mother's grandparents, etc.) and with some (but fewer) of your paternal ancestors (father, paternal grandmother, father's maternal grandparents, etc.) and with anyone else with the same X ancestors;
• you have mitochondrial DNA which you definitely share in its entirety with your matrilineal ancestors (mother, mother's mother, etc.) and with anyone else with the same matrilineal ancestors; and
• you have autosomal DNA which you potentially share with all of your maternal and paternal ancestors and all of your cousins.

Also:

• anyone with whom you share mitochondrial DNA is related to you through your mother; but
• it is impossible to tell on which side (your paternal or maternal sides) someone with whom you share autosomal DNA only or X-DNA is related to you.

If you know who your mother is, but don't know who your father is, then DNA can also help, particularly if your mother has other children who are willing to provide DNA samples. Your mother's other children will be either:

• your full-siblings, in which case you can expect to be half-identical to them on 75% of the length of the autosomes or approximately 2538cM; or
• your half-siblings, in which case you can expect to be half-identical to them on 50% of the length of the autosomes or approximately 1692cM.

These are just expected values; actual values will be distributed around these averages. The standard deviations are poorly documented but there is an online spreadsheet showing a small sample of comparisons. The percentages seem to be calculated differently in this spreadsheet (can someone please explain?), but the maximum shared percentage observed for half-siblings is much smaller than the minimum shared percentage observed for full-siblings. In other words, this test can unambiguously distinguish between half-siblings and full-siblings.

Anyone who shares half-identical regions of autosomal DNA (particularly overlapping regions) with two half-siblings (or two groups of half-siblings) with the same mother is unlikely to be related to the father of either group.

Example II: Choate

My FTDNA-overall-matches include two people whose GEDCOMs suggest, with various caveats, that they may be sixth cousins, namely Charles (with whom I share 38.19cM) and Janice (27.90cM), and also Janice's nephew Walter (29.39cM).

Note that I share more with the nephew than with the aunt! Walter's father must have inherited much more than expected and Janice inherited much less than expected from their mother. My implied shared cM with Walter's father, calculated by doubling my shared cM with Walter, is 58.78. Similarly, my shared cM with Janice's mother, calculated by adding (averaging, then doubling) the shared cM figures for two of her children (one figure directly observed, the other inferred from his father's figure) is 86.68. Ultimately, my implied shared cM with their common ancestral couple, Christopher Choate and his wife, calculated by doubling the shared cM figures back to the common ancestor and then averaging, and subject to the aforementioned caveats, is 5217.92cM or 77.1%, which is implausible. One of my five closest FTDNA-overall-matches (who submitted his DNA after I did and whose shared cM with me 49.36) is also a Choate and shares an e-mail address with Walter. Unfortunately Walter has not yet uploaded a GEDCOM for this latest member of his immediate family to give a DNA sample, so I have no idea where to incorporate the new person into this calculation. He has listed the new person's Most Distant Paternal Ancestors as "James Choate b.1813 TN m. Elmira Farmer b.1816 MO".

I was not surprised when I checked the chromosome browser and found that I share the same half-identical region on Chromosome 9 with all four of these people. The half-identical region which I share with Janice is 9.76Mb or 12.69cM or 2477 SNPs long, and is contained within the even longer half-identical regions which I share with the other three. There seems little doubt, given the additional genealogical evidence, that all four of them have inherited this segment from Christopher Choate or his wife.

Christopher is said to have been born in Maryland in 1720, so at first seemed very unlikely to have descendants in Ireland, where all my known ancestors back to 1720 have lived. There is certainly no mention of Ireland in the extensive Choate pedigree on genforum. However, another Choate pedigree says that Thomas Choate, one of Christopher's many American-born sons, married in Ireland. In the complete absence of genealogical evidence to link me to his descendants, it could of course be that I am merely half-identical by chance with Christopher or his wife in the relevant region of chromosome 9, and thus that I am also half-identical by chance with many of their descendants who have inherited the relevant segment from one of them, including these four FTDNA customers. Or perhaps the caveats in the GEDCOMs are correct, and all these people are descended from their daughter-in-law, the woman whom Thomas Choate married in Ireland.

Two more people FTDNA-overall-match myself and the four Choate descendants and share half-identical regions with me overlapping with that on chromosome 9 that I share with Janice and the others. GEDmatch.com has no less than 17 kits with which I am half-identical on the same segment as with Janice, including Janice herself and Walter again, three other FTDNA kits and twelve 23AndMe kits. I have not yet tried to trace any of them back to Christopher Choate and his wife. Some of them may be half-identical with the Choate descendants, some of them may be related to me on the opposite side from the Choates (paternal or maternal), and some of them may again be half-identical purely by chance.

Phasing and Triangulation

Triangulation and phasing are really opposite sides of the same coin.  If V is half-identical on the same region with W and Z, then there are two possibilities:

1. W and Z are half-identical to each other on this region, in which case V, W and Z probably inherited an identical segment in this region from a single common ancestor and the relationship can be described as triangulated; or
2. W and Z are not half-identical to each other on this region, in which case V is probably related to W on V's paternal side and V is probably related to Z on V's maternal side, or vice versa, and V's autosomal DNA in this region can be phased.

1. because it is always possible than one or more of the pairs are merely half-identical by chance, particularly if the number of SNPs observed in the region at which the parties are mutually homozygous is small; and
2. because each may share an identical segment with one of the other two on the paternal side and with the third person on the maternal side.
   To give a concrete example, when I think of a triangular relationship, I always think about my GGGgrandfather Parker's brother and my GGGgrandmother Keas's sister who married the two Smith siblings. They produced three families, each of which were first cousins to the other two, but who didn't have a single common ancestral couple! If one took DNA from one member of each of these three families, two Parkers and a Smith, then each of them as first cousins would share many half-identical regions with both of the others. There would be some regions in which the two Parkers had an identical segment from a Parker grandparent, one of the Parkers and the Smith would have an identical segment from a Smith grandparent, and the other Parker and the Smith would have an identical segment from a Keas grandparent. In this example, the three cousins will all "match" each other genetically, but on closer examination it will be found that there is no common ancestral couple of all three.
   This is the very opposite to what "triangulate" usually means to genetic genealogists and thus, possibly for these purely personal reasons, I dislike the word triangulate.

I further dislike the word triangulate because it is used ambiguously, often being used also in the context of FTDNA-overall-matches as well as in this context of region-matches. In the case of FTDNA-overall-matches, the logic is also that if three people each FTDNA-overall-match the other two, then it is more likely that all three share a common ancestor. While this triangulation argument makes a common ancestor more likely, it does not definitively prove that one exists, as each pair may share completely different half-identical regions coming from three different common ancestral couples.

Furthermore, a triangle has three sides, but in the case of region-matches FTDNA continues to effectively insist on displaying just two sides of the triangle - I can see my half-identical regions with two of my FTDNA-overall-matches, but without asking one of them to look in the chromosome browser or ADSA or GEDmatch or to join a project which I administer, I cannot tell whether they are half-identical with each other in a region where both are half-identical with me, or alternatively appear to be related to me on opposite sides (one paternal, the other maternal).

While the word triangulation suggests that inferences can be drawn and even that proofs can be established based on groups of three people, who may only be FTDNA-overall-matches, in fact one needs to look at groups of four people, who must region-match on the same region, to draw truly valuable inferences. If three people region-match you on the same region, then either all three share your paternal segment on that region, or all three share your maternal segment on that region, or two share one segment and one shares the other. In other words, at least three of the four people have an identical segment. Now it will be much easier to make progress.

This all assumes that the half-identical regions in question contain enough SNPs that they are not merely half-identical by chance. If you find two people with whom you are half-identical on the same region, there are really three possible explanations:

1. the other two people are half-identical to each other on the region and all three share a common ancestral couple;
2. the other two people are not half-identical to each other on the region, one shares a common ancestral couple with you on your father's side and the other shares a common ancestral couple with you on your mother's side; or
3. the other two people are not half-identical to each other on the region, and at least one of them is only half-identical by chance to you on the region.

In the second of these cases, it can be deduced that at any biallelic SNP where the other two people don't match (i.e. are opposite homozygous), you are heterozygous (since you match both). Furthermore, if you know which is the paternal match and which is the maternal match, then you can deduce which letter came from your father and which from your mother at that SNP. For example, if you are AG, the paternal match is AA and the maternal match is GG, then your A must have come from your father and your G from your mother. Even if you don't know which is the paternal match and which is the maternal match (e.g. if you are an adoptee), you can still draw valuable inferences. For example, if both matches have ancestral surnames and/or ancestral places which crop up repeatedly among your matches, then you can phase the surnames and places into two groups, one associated with each parent. Such an analysis between Anthea (an adoptee) and myself and Michael (who both match Anthea on the same region on Chromosome 4 but don't match each other) provided strong evidence that Anthea's many matches from Connemara are probably through the parent related to Michael, and that her many matches from east Mayo are probably through her other parent, the one related to me.

Another word of caution (which still applies to this last example): if the region in question is shorter than 20cM, then it is not sufficient to check whether the two people are FTDNA-overall-matches or even to check whether ADSA shows that they match in the region of interest. It could be that they are half-identical on the region of interest, but don't meet the 20cM overall Shared cM criterion to be deemed FTDNA-overall-matches. It is essential to copy both parties' raw data to GEDmatch.com and to run a one-to-one comparison between them there. This has not yet been done in this example. It is also advisable to set the cM threshold for the one-to-one comparison at GEDmatch.com much lower than the length of the region of interest, since it is well-known that half-identical regions have fuzzy boundaries. Many people argue that the word 'triangulate' should never be used when discussing ICW matches unless all three have been shown to be half-identical to one another on the same region of a particular chromosome.

Here is another interesting example combining triangulation and phasing:

The above table shows six half-identical regions between four individuals: each is half-identical to the other three, at a minimum at 4,338 consecutive SNPs between locations 29,194,808 and 32,795,951 on Chromosome 6. Note that this example deals with a region with a very high SNP/cM ratio. (Ann Turner has written a paper about this strange region on chromosome 6.) As the cM lengths of the half-identical regions are small, the most recent common ancestors (apart from for the known first cousins with a half-identical region of 35.8cM) are probably very distant.

F310654 and F335391 in the first row are known first cousins on F310654's maternal side. M090954 is half-identical to both of them between locations 29,194,808 and 32,795,951, so must also match F310654's maternal chromosome between these locations, and the same applies to F310841. So we can claim successful triangulation (or even quadrangulation) in this region.

However, between locations 25,988,473 and 29,194,808 both M090954 and F310841 are half-identical to F310654, but not to F335391. Now we can claim successful phasing in this region: it is safe to assume that F335391 matches F310654's maternal chromosome in this region, since they are known first cousins. Hence, M090954 and F310841 must match F310654's paternal chromosome in this region.

Now the question arises as to whether M090954 and F310841 also match F310654's paternal chromosome in the adjoining region between locations 29,194,808 and 32,795,951. One way of checking this is to look at the colour-coded graphic bars in the GEDmatch.Com Autosomal Comparison:

The following table shows the output for F310654 and M090954:

The following table shows the output for F310654 and F310841:

In both cases, the output makes it clear that there are subregions (coloured green) where each of the other parties match both F310654's paternal chromosome and F310654's maternal chromosome. It would be necessary to inspect raw data to identify the overlapping segments more precisely.

F310654 and M090954 are believed to be fourth cousins twice removed on F310654's paternal side, but the half-identical region of 3.5cM considered here may be from a more distant common ancestor than this known relationship.

Triangulation groups

The ultimate objective is to collect DNA matches into triangulation groups. A triangulation group is a set of three or more people who are all half-identical to each of the other group members on overlapping regions.

Here is an example from Chromosome 9:

9 106,881,785 124,347,952 24.0 4,938 Hincken/Morrissey
9 114,714,102 132,034,981 24.4 4,397 Quinn/Hincken
9 114,714,102 125,890,734 15.7 2,999 Morrissey/Quinn

All three members of the triangulation group are half-identical to each other from 114,714,102 to 124,347,952. The interpolator can be used to confirm that the (sex-averaged) length of this overlap region is approximately 13.7cM:

This region is long enough that it almost certainly contains a DNA segment inherited by all the members of the triangulation group from a relatively recent single common ancestor.

A triangulation group including at least one subgroup who are known relatives is of particular use. In the above example, Hincken and Quinn are known third cousins, with most recent common ancestral couple Denis O'Connell (died 1887 aged 90) and Kate O'Dea (died 1889 aged 78). It can then be concluded that the other members of the triangulation group are related to one of the most recent common ancestral couple of the known relatives, or even descended from both. In this case, we can infer that Morrissey is related to either Denis O'Connell or Kate O'Dea. The total amount of shared DNA will indicate whether the most recent common ancestor of the entire triangulation group is upstream or downstream from the known most common ancestral couple of the known relatives. In this case, Morrissey has known ancestry from the same townland as the others, so geographic evidence added to genetic evidence points in a very specific direction.

If a triangulation group contains two subgroups of known relatives, then it can be concluded that one of the most recent common ancestral couple of the first subgroup is related to one of the most recent common ancestral couple of the second subgroup

This question from IGP's County Clare Ireland Genealogy Group on Facebook illustrates some of the factors to bear in mind when looking at possible triangulation groups:

This is the diagram of chromosome 14 for five of my DNA matches. The first two are first cousins to one another and my third cousins. We three are descended from our ggg grandparents from Clare or Galway. The last match shares their surname. Are we all likely to be related through that line?

In theory, some of these five FTDNA-overall-matches could match the questioner's paternal chromosome 14 and others match her maternal chromosome 14. In practice, something like this usually does turn out to be a genuine triangulation group. It is necessary to look at all 15 one-to-one comparisons between the six people in order to confirm that each is half-identical to the other five on the overlap, and thus that there is a DNA segment which all six have inherited from a shared common ancestor. The easiest way to do this is to have all six people at GEDmatch. If five of the six can be seen at FTDNA, either by having the passwords or by administering a project to which they belong, then one can check that way. One can also get a good indicator from the ADSA which will show which of these kits are FTDNA-overall-matches to each other. This does not prove that they are half-identical to each other on this particular region: one could be related to the questioner's father but have a second relationship through a different common ancestral couple to those who are related to her mother. The DNA match still doesn't prove who the common ancestor was, but one can be virtually certain in this case that the shared DNA came through one of the known shared GGgrandparents of three members of the triangulation group.

The likelihood that it came through a common ancestor with the shared surname depends on various other factors:

• how common is the surname?
• did the most distant ancestors with the same surname live near each other?
• is there any other shared surname between members of the triangulation group?
• does the total shared DNA indicate that the person sharing the surname is a third cousin or closer?
• can you add a known relative of the person sharing the surname to the triangulation group?

Pile-up regions and pile-up groups

• the centiMorgan scale may have been badly estimated and may exaggerate the length of these regions;
• these may be regions where the DNA subject has long runs of heterozygosity, which result in him or her matching almost everyone else;
• many of the SNPs observed in these regions may exhibit very little variation, with the vast majority of humans having the more common letter;
• the members of the apparent pile-up group may actually include many close relatives, or even duplicate kits;
• etc.

• have a shared DNA segment inherited from a very distant common ancestor, much further back in time than would normally be inferred from the centiMorgan length of the shared segment alone; or
• be merely half-identical by chance to each other.

• the more members the triangulation group has (in other words if it appears to be a pile-up group);
• the more distant the known relationship;
• the less complete the known pedigree charts of the DNA matches; and
• the shorter the centiMorgan length of the apparent shared DNA segment.

• Jack's father is related to JJ's father (doubly so, as JJ's relevant paternal greatgrandparents were cousins);
• Paddy's father's mother is related to Mary's mother; and
• Mary's father is related to Tom's father.

• there are 36 locations out of the 1,016 where all five subjects are heterozygous and the letter inherited in the common segment cannot be inferred;
• there are 55 locations out of the 1,016 where one or more of the five subjects has a missing observation;
• Tom (CC) is opposite homozygous to Jack and JJ (AA) at the terminal location 11,072,818, but all five kits are mutually half-identical at the initial location 8,654,894 (i.e. the two endpoints are treated differently when GEDmatch reports half-identical regions - the subjects are half-identical at the start location, but are not half-identical at the end location);
• at the remaining 924 locations out of the 1,016, the letter inherited from the common ancestor can be inferred uniquely (as GEDmatch does for Lazarus kits);
• there are 311 locations out of the 1,016 where all five individuals are homozygous (i.e. monoallelic locations within the group of five);
• there are 650 biallelic locations;
• there is no triallelic location; and
• of the remaining 55 partially missing locations, 22 are biallelic, 32 are monoallelic and 1 is missing for all five individuals.

Three-generation studies

Chapter 3:

Example III - Paddy and Terry

Terry and I got to know each other through the County Clare Ireland Genealogy group and the Kilrush Local History Group page on facebook.com. We discovered that we both have ancestors named McNamara who lived in the adjoining townlands of Breaghva and Moveen West in the civil parish of Moyarta on the Loop Head peninsula in the west of County Clare. Terry's cousin Michael McNamara still lives in Breaghva and my cousin Michael McNamara still lives in Moveen West. When necessary, they are distinguished by the age-old Irish tradition of using patronymics rather than surnames: Michael "Anthony" and Michael "Pádraig" respectively. In any case, the surname is invariably shortened to "Mack" in that part of County Clare, where "Mack" is almost always short for McNamara (although I did know a Tommy Mack, whose full name was Tommy McInerney).

Terry and I became facebook friends in January 2013 and met when she returned to her mother's native Kilrush for the National Famine Commemoration in May 2013. We have a lot in common besides our McNamara roots. She is an excellent genealogist. When she couldn't find Breaghva in the Tithe Applotment Book of 1827 for Moyarta parish, she converted the acreages of all the townlands from Irish acres to statute acres, compared them with the corresponding acreages from the Ordnance Survey, and discovered that Breaghva was originally considered as part of the adjoining townland of Moyarta West, where she found what is surely her McNamara ancestor living as early as 1827. My McNamara relatives, on the other hand, are mere blow-ins, and didn't come to Moveen West until my greatgrandfather Old Johnnie McNamara arrived from a townland about 26km away on his marriage in 1876. The two families have known each other since then, but I have heard it explained many times that they are not closely related.

Terry is also a technical expert in many areas. Her TNG site was among those that inspired me to switch in August 2013 from tribalpages.com to TNG for my (password-protected) online family tree. The fact that she had sent DNA samples for herself to all three companies (FTDNA, 23andMe and ancestry.com) and for both of her parents to both FTDNA and 23andMe was among the triggers that finally persuaded me to send mine to FTDNA.

The Loop Head peninsula, where our ancestors lived, is bounded on the south by the Shannon Estuary and on the north by the Atlantic Ocean. A peninsular popluation by definition is not quite an island population, but it is still a population group with a limited number of founders and a certain lack of mobility when it comes to finding marriage partners. So I was not too surprised to find Terry's mother among my initial FTDNA-overall-matches. Sadly she was gravely ill at the time and died a few weeks later (RIP).

Terry's first thought was that we are probably related on the McNamara side after all, and that we should probably get our respective cousins, the two Michael Macks, to submit DNA samples, for both Y-DNA and autosomal DNA comparisons. But as Terry's mother and my paternal grandmother come from the Loop Head peninsula and all of their known ancestors lived there, the common ancestor from whom the shared segments (or some of them) derive might not be a McNamara at all.

[Example details moved here.]

Here I should probably give a counter-example. Joseph and Paul (father and son) caught my attention among my FTDNA-overall-matches because their ancestral names and places include surnames and townlands in County Mayo which also appear in my mother's family tree. My longest block with each of them is the same 8.07cM block on chromosome 19. In this case, there is no doubt that this block was inherited by the son in its entirety from the father. I would not be in the least surprised to find that both of them and myself all inherited it from a common ancestor. The first surprise in this case was to find that Terry's mother (from County Clare) also FTDNA-overall-matched Paul (with roots in County Mayo), but not his father. This is another spurious match. The second surprise was to find that my total Shared cM with the son (33.64cM) was greater than my total Shared cM with the father (26.53cM), even though the mother is of German ancestry.

How long is "long" and how close is "close"?

The many anomalies already noted in the relative lengths of half-identical regions make it clear that short half-identical regions are often merely half-identical by chance and are not indicative of a close genealogical relationship. This gives rise to the related questions of "how long is 'long'?" and "how close is 'close'?

Peter Ralph and Graham Coop, who have a far better grasp of the relevant mathematics and statistics than most of those writing about genetic genealogy, have written about the identification of genomic regions shared between distant relatives and conclude that "sharing a single long block doesn’t imply a particularly close genealogical relationship". While the words "long" and "close" are left open to different interpretations, this is a good principle to bear in mind.

The ultimate answers to these questions depend on what supplementary evidence is available:

• Are the people being compared known relatives?
• How strong is the traditional genealogical evidence linking them?
• Equivalently, how good is the paper trail linking them?
• Is there evidence that one person may have inherited the relevant (paternal or maternal) segment in the shared half-identical region from an ancestral couple not shared with the other person?
• Could there be a closer but undocumented relationship between the two people?
• Is there a tradition of a relationship, but no matching paper trail?
• How many known relatives of one person share the same half-identical region with how many known relatives of the second person?
• How many known relatives of one person share any half-identical region with how many known relatives of the second person?
• Is there a common ancestral surname?
• Is there a common ancestral place?
• Is the common ancestral place a townland, a parish, a county or merely a country?
• Are regions being measured in cMs, in SNPs or in base pairs?
• How many other half-identical regions are there between the people being compared?
• Is the objective to determine whether two people are related, or whether a given half-identical region contains an identical segment from a known common ancestral couple?
• How much of his or her genome has each person already mapped to specific ancestral couples?
• How much time is available to correspond with potential relatives and to research the potential relationships?
• How many people share longer half-identical regions with each person?
• Is one of the people being compared an adoptee?
• Are the people being compared complete strangers?

No matter what the answers to the above supplementary questions, the answers to the initial questions remain subjective.

I started out innocently assuming that I could prove my relationship to all my FTDNA-overall-matches. Then I found the spurious 9.1cM half-identical region in the previous example, and began to dismiss anything below that. Finbar O'Mahony then advised me that he does not normally contact anyone (presumably apart from a known relative) whose longest half-identical region is less than 15 cMs, and I began to think about increasing my threshold further. In other words, in the case of complete strangers, the guidance is that anything under 15cM is short.

As the threshold for FTDNA-overall-matches is 20cM, one is left wondering in the case of half-identical regions under 20cM whether those who are not FTDNA-overall-matches are not half-identical on the relevant region, or are half-identical on the relevant region but lack enough small additional half-identical regions to make up the 20cM threshold. This soon convinced me that it's probably not worth the effort of investigating possible relationships with those sharing longest half-identical regions under 20cM.

It was stated above that autosomal DNA contains a few hundred segments of genealogical value per individual; this estimate is based on dividing the total length of autosomal DNA (3587.1cM) by a reasonable cut-off value for the length of a half-identical region of genealogical interest, say 20cM.

As time has gone on, I have wondered whether the threshold should be even higher than 20cM.

As of 17 March 2015:

• I have 18 individuals at FamilyTreeDNA.com with whom I share half-identical regions of 20cM or longer. Of these:
  • three are known relatives for whose kits I have paid (first cousins at 89.47cM and 70.44cM and a first cousin once removed at 85.14cM);
  • one is a relative who submitted her DNA sample independently; there was some doubt as to our relationship, which the matching DNA has now eliminated (fourth cousin twice removed at 24.77cM);
  • one is an adoptee (30.45cM);
  • my relationships to the other fifteen (including a family of five, comprising a mother, her daughter and three of her sons) have still to be determined.
• I have 22 kits at GEDmatch.com with whom I share half-identical regions of 20cM or longer. Of these:
  • two are the known first cousins from FamilyTreeDNA.com;
  • one is the known fourth cousin twice removed from FamilyTreeDNA.com;
  • one is the adoptee from FamilyTreeDNA.com;
  • four are accounted for by the mother (3 kits) and daughter (1 kit) in the extended family at FamilyTreeDNA.com, but the three sons come in just below the 20cM threshold at GEDmatch.com;
  • conversely, two are accounted for by an individual (2 23andMe kits) who comes in just below the 20cM threshold at FamilyTreeDNA.com;
  • two are among the other ten FTDNA-overall-matches to whom my relationship has still to be determined;
  • five are accounted for by kits from 23andMe (4 individuals plus 1 duplicate) to whom my relationship has still to be determined; and
  • five are accounted for by kits from Ancestry.com (4 individuals plus 1 duplicate) to whom my relationship has still to be determined.

In the case of known relatives, guidance as to the length of half-identical regions certain to come from the common ancestor is in short (no pun intended) supply, but 20cM is clearly quite long in this case. Indeed, this question did not arise in my own mind until I found that I shared half-identical regions with a ninth cousin twice removed. A half-identical region of 8.8cM/918SNPs with that ninth cousin twice removed seemed very long. With a known fifth cousin, my longest shared half-identical regions are 4.6cM/875SNPs and 3.8cM/1177SNPs, which seemed quite short in this context.

With both of these known relatives, there is a suspicion of a second relationship. My ninth cousin twice removed has Waldron cousins, who could be my ancestors. My fifth cousin and I both have O'Halloran ancestors as well as our known shared Keas ancestors. What is the likelihood that our shared half-identical regions contain shared segments from our known common ancestors (as opposed to shared segments from these other possible common ancestors)?

For now, I will have to leave these questions unanswered, but for known relatives I will certainly look at all half-identical regions greater than 1cM and greater than 500SNPs.

Among my 354 initial FTDNA-overall-matches, I had:

• 30 with Autosomal largest cM greater than or equal to Finbar's threshold of 15; and
• 182 with Autosomal largest cM greater than or equal to my own initial threshold of 9.1.

At GEDmatch.com as of 23 Dec 2013, I had:

• 19 matches with Autosomal largest cM greater than or equal to Finbar's threshold of 15 (5 from FTDNA, 10 from 23andMe and 4 from ancestry.com; only 11 different e-mail addresses, due either to multiple family members sharing an e-mail address or individuals testing with multiple companies);
• 188 matches with Autosomal largest cM greater than or equal to my own threshold of 9.1; and
• 1,311 matches with Autosomal largest cM greater than or equal to the default value of 7.

It can be seen from these figures that probably only around one in six FTDNA customers have copied their raw data to GEDmatch.com.

It can also be seen that GEDmatch.com's definition of a match (apparently based solely on largest cM) includes far more so-called matches than FTDNA's definition (apparently based on additional criteria such as number of shared segments and total shared cM).

I certainly suspect that the vast majority of the 1,311 matches for the default GEDmatch.com parameters are false positives. Besides, 11 e-mail addresses are much more manageable than 1,311!

For someone like me with a large database of confirmed blood relatives (9,531 people on my father's side, but only 813 people on my mother's side at Christmas 2013), 19 interested and interesting matches is a poor return.

For a foundling or any adoptee with no confirmed blood relatives, on the other hand, 19 interested and interesting matches would be a fantastic return.

Now back to myself and Terry and her mother: In the segments where my DNA is half-identical with Terry's mother, it could be the case that either:

1. Terry has inherited from her maternal grandfather, but I am related to her maternal grandmother; or
2. Terry has inherited from her maternal grandmother, but I am related to her maternal grandfather; or
3. something else is going on.

Until Terry and I can compare ourselves directly in the chromosome browser, we cannot rule out possibility 3. If we could compare ourselves directly, then we might find that we have smaller half-identical regions within the half-identical regions that I share with her mother.

While I had no known relative who had tested before me, perhaps Terry has others besides her parents and we can do some sort of further analysis to distinguish between possibilities 1 and 2 and thus see on which side I match her mother.

Chapter 4:

Example IV - Paddy and Anthea

After a wait of almost three days, I heard back from Anthea, the first FTDNA-overall-match that I attempted to contact when my initial results arrived. She has already featured in passing in some of my examples above.

Anthea told me a very interesting and totally unexpected story. She has given me permission completely to publish any details of her story, which in any case has been in the public domain for a very long time, wherever I want. However, the details of how she came to be adopted in Worthing in England in 1938 are of no relevance here.

By looking at my FTDNA-overall-matches in common with Anthea, it soon became apparent that we must be connected through my mother, as many of the ICW matches, like my mother, had roots in the triangle between Swinford, Charlestown and Kilkelly in County Mayo. When the Family Finder results for my paternal and maternal first cousins arrived, they confirmed that my relationship to Anthea is on my maternal side. However, the connection to the first of my maternal first cousins to submit a DNA sample (estimated by FTDNA as 4th Cousin - Remote Cousin) is not as strong as the connection to me (estimated by FTDNA as 2nd Cousin - 4th Cousin), implying that the relationship must be less close than was suggested by my own results alone. When another of my maternal first cousins later submitted a DNA sample, the estimated relationship had to be revised again, and it now appears to be closer to the initial estimate.

As of 29 July 2016, Anthea's closest match is an estimated second cousin at AncestryDNA. Initial analysis points very strongly at one pair of his greatgrandparents as direct ancestors of Anthea, so the puzzle may be 25% solved.

A lady whom I will call Anne is Anthea's top FTDNA-overall-match by the old default sort order (i.e. by longest block). It is surprising that Anne and I had not met before we discovered this DNA connection, as we have connections in the worlds of academia and local history and numerous mutual friends, and as her maternal ancestors and my paternal ancestors have roots in adjoining parishes in County Clare. All this is pure coincidence, however.

Anne subsequently obtained DNA samples from her full-brothers Garry and Terence and their first cousin Patricia (brothers' children). Neither brother is deemed an FTDNA-overall-match to Anthea at all, but Patricia is. This raises a number of questions.

First of all, it clearly implies on the one hand that FTDNA's estimated relationships between Anne and Anthea and between Anne and Patricia (2nd Cousin - 4th Cousin in both cases) must also be revised outwards but on the other hand that FTDNA's estimated relationship between Anne's brothers and Anthea (none at all) must be revised inwards. (Recall that FTDNA's estimated relationships consider solely the DNA of the two people being compared, and completely ignore the DNA of known relatives of either party.)

At the next level, the fact that one sibling can top someone else's match list and the other not appear on it at all suggests investigating the Shared Segments between the matches, in this case between Anne and Anthea and between Patricia and Anthea. Between Anne and Anthea, there is one Shared Segment of 43.53cM but there is no other longer than 4.14cM. Between Patricia and Anthea, there is one Shared Segment of 23.52cM but there is no other longer than 4.21cM.

In fact, on Chromosome 10, based on GEDmatch comparisons:

• Anthea and Anne are half-identical to each other but not to Patricia between 91,271,061 and 95,358,506;
• Anthea and Anne and Patricia are all half-identical to the other two between 95,358,506 and 97,190,034 (1.5cM, 580 SNPs), which may just be by chance;
• Anthea and Anne are half-identical to each other but not to Patricia between 97,190,034 and 114,482,888;
• Anthea and Anne and Patricia are all half-identical to the other two between 114,482,888 and 126,723,633; and
• Anthea and Patricia are half-identical to each other but not to Anthea between 126,723,633 and 135,297,961.

Given that Anne inherited this long 43.53cM segment from one of her parents, what is the probability that her full-sibling did not inherit it, or did not inherit enough of it to register as an FTDNA-overall-match with Anthea? Suppose this segment came from the, say, paternal chromosome of one of Anne's parents. There is a 50% probability that her brother inherited from the corresponding maternal chromosome at the relevant start location (91,205,789 on Chromosome 10), and a Poisson probability of 64.71% of no crossover throughout the relevant segment. Thus there is a probability of over 32% that the brother does not match Anthea anywhere in this region. If one allows for possible crossovers near the ends of the region, or multiple crossovers, so that Anne's brother and Anthea share small segments of DNA, but not enough to meet the FTDNA thresholds, the ex ante probability that Anthea and Anne's brother are not FTDNA-overall-matches is clearly somewhat more than 32%. With two brothers, since the events are independent, the probability can just be squared, but there is still an ex ante probability of over 10% that neither brother FTDNA-overall-matches Anthea.

Now suppose that Anne and Anthea were half-identical on two separate regions, on two different chromosomes, each half as long as the actual 43.53cM match, i.e. each 21.765cM long. The probability that Anne's brother and Anthea don't match in one of these regions is again the 50% probability that the brother inherited the opposite chromosome at the start of the region, multiplied by the relevant Poisson probability of no crossover in the shorter region, which is clearly much larger, in fact 80.44%, giving a result of 40.22%. However, inheritance on two differenct chromosomes is independent, so the probability that the brother and Anthea don't match on either of the two regions is 40.22% x 40.22% or just 16.18%.

This gives the slightly counter-intuitive result that if you have two FTDNA-overall-matches with the same Shared cM but different Longest Block, you are more likely to match a sibling (or any known relative) of the FTDNA-overall-match with the shorter Longest Block.

Like the diversification principle in investment (which essentially says "don't put all your eggs in one basket"), this is essentially just another application of the Law of Large Numbers.

With DNA samples from three siblings and a first cousin, we can try to divide their FTDNA-overall-matches into four subsets, one subset for each grandparent of the sibling group. I will consider the subset of FTDNA-overall-matches who are half-identical to Anthea or to one of the sibling group on the region where Anne and Anthea are half-identical to each other (Chromosome 10 between locations 91,205,789 and 126,559,193). The easiest way to do this is using the ADSA for each of the four people, with "Chromosome to graph" set to 10, "Base Pairs" set from 91205789 "to" 126559193 and "Minimum Segment Length in cM" set to 8. I ignored some half-identical regions which had only a tiny overlap with the start or end of the region where Anne and Anthea are half-identical.

Let us label the grandparents as follows:

1A

The paternal grandparent through whom Anthea is related to the sibling group.

1B

The other paternal grandparent (spouse of 1A).

2A

The maternal grandparent from whom Anne inherited on this region.

2B

The other maternal grandparent (spouse of 2A).

The autosomal DNA of the three siblings alone could not tell us whether 1A and 1B were the paternal grandparents and 2A and 2B the maternal grandparents or vice versa. However, the fact that a paternal cousin is half-identical to Anthea on the same region confirms that the relationship is through one of the paternal grandparents. Likewise, autosomal DNA alone still cannot tell us whether A is the grandfather and B the grandmother or vice versa on either side.

On side 1, Anne has inherited from grandparent 1A and, as Garry and Terence do not match Anthea, they must both have inherited from grandparent 1B.

Garry is half-identical to both of his siblings on this region, so he must have inherited from the same grandparent as Anne on the other side, i.e. from 2A.

Anne and Terence are not half-identical on this region, so they must have inherited from opposite grandparents on both sides; in other words, Terence inherited from 1B and 2B.

So we have the following pattern:

1A

Anne and Anthea and Patricia

1B

Garry and Terence

2A

Anne and Garry

2B

Terence

1. (s)he is half-identical by chance to one of the group; or
2. (s)he is half-identical to another member of the group in this region, but is not an FTDNA-overall-match to that member because their total Shared cM is less than the FTDNA threshold value of 20.

There is also an outside chance that either of these reasons could also result in a person being assigned to the wrong group, unless the lengths of the relevant half-identical regions are 20cM or greater.

The following table shows the matches and categories:

It is reassuring that the two people in grandparent group 1A, matching Anne and Anthea, namely Lewis and Likens, FTDNA-overall-match each other.
Of the eight people in group 2A, matching Anne and Garry, Smoyer and Johnson FTDNA-overall-match each other; Johnson, Murphy, the two Swansons and Bean FTDNA-overall-match each other; the Swansons, Bean and Fetherston FTDNA-overall-match each other; and Bean, Fetherson and Wellar FTDNA-overall-match each other. These subgroups arise from different subregions of the long region where Anne and Anthea are half-identical.
Of the four people in grandparent group 3, matching Anthea only, only Blake and Peneycad FTDNA-overall-match each other, leaving the possibility that the other two may be half-identical by chance to Anthea.

The next stop is to look for common ancestors of the three siblings and each of the four grandparent groups in the above table. If the common ancestor with group 2A can be identified, then we will know that Anthea is related through the other parent. If the common ancestor with group 1A or group 1B can be identified, then we will know which grandparent Anthea is related to.

There is a lot more work still to be done!

Update: Since I compiled the above table, two Kane samples have been submitted to FTDNA. In the region of interest, they are half-identical to Anne and Garry (12.94cM and 12.69cM for both siblings) but not to Anthea or Terence, so they must be related to grandparent 2A.

For another interesting example concerning my Kett GGGgrandfather, see facebook discussion.

Chapter 5:

Interpreting Y-DNA results

Y-DNA comparison is the best way to rule in or rule out distant relationships between men with the same or similar surnames. For closer relationships, autosomal DNA comparison gives more precise answers.

Only men have a Y chromosome for comparison.

A woman does not have a Y chromosome, so should find a male relative with the relevant surname to swab:

• a father, brother, nephew, cousin, etc., if her interest is in her maiden surname; or
• a husband, son, brother-in-law, father-in-law, etc., if her interest is in her married surname.

By far the most comprehensive Y-DNA service is provided by FamilyTreeDNA.com, but there are competitors like YFull.com and YSEQ.

If you have already sent cheek swabs to FamilyTreeDNA for Family Finder or mitochondrial analysis, then they are held in storage and will be re-used for Y-DNA analysis.

SNPs and STRs

Objectives

• to identify the original surname which was subject to a surname/DNA switch (SDS), whether known of from other sources (e.g. adoption) or first discovered through DNA comparisons;
• to identify the most recent SNP mutation in a man's lineage;
• to determine whether that most recent SNP is specific to the man's surname or occurred before the surname was adopted by his male line ancestors;
• to identify any STR mutations that have taken place in the man's lineage since the most recent SNP mutation and/or since the most distant known patrilineal ancestor;
• to estimate, using STR mutations, how close the relationship is between two men with the same surname and same most recent confirmed SNP but without a known common ancestor;
• to verify traditions relating to common origins of different modern surnames (see here);
• etc.

[surname] FTDNA project

• this modern SNP-based analysis provides far more accurate matching than the now outdated STR-based analysis provided by Y-37 etc.;
• it overlays SNP mutations and surnames on the Tree of Mankind;
• surname-specific SNP mutations are being discovered all the time, many of them not just surname-specific but even parish-specific;
• SNP mutations can not be formally recognised until they have been found in two different men;
• many project members still find themselves alone in a group on the Y-DNA Colorized Chart, and will remain alone there until another closely or distantly related man signs up for Big Y-700;
• SNP analysis can provide clearer evidence as to whether there have been surname/DNA switches within the surname era, or two unrelated founders adopting the same surname at the start of the surname era;
• etc.

• If your budget is limited, then the entry-level purchase is Y-DNA37, which examines 37 STR locations on the Y-chromosome. The Y-DNA37 results can still be used as a guide to the best subsequent purchases.
• The recommended top-of-the-range purchase is Big Y-700, which replaced Big Y-500 on 30 January 2019; Big Y-500 had replaced Big Y only in April 2018.
• If you just want to confirm that you have the same confirmed SNP mutation as a suspected relative with your surname, then you can start with Y-DNA 37 and order a single SNP test from YSEQ when the Y-DNA37 results are available (and have confirmed that your first 37 STRs match your suspected relative).

• your surname (or your male line beyond the adoption of your surname) may not be one of those which have proliferated due to many men of the surname (or male line) each having several sons;
• your surname (or male line) may be in danger of being "daughtered out", due to many men of the surname (or male line) not marrying or fathering only daughters;
• there may be no other man of your surname in the FTDNA database (e.g. no Geheran in February 2018);
• there may be only a few people of your surname in the FTDNA database (e.g. there were only 11 Dungans of either gender in February 2018);
• there may have been no concerted effort to recruit men of your surname to the FTDNA database;
• there may have been a concerted effort to recruit men of some genetically related surname to the FTDNA database;
• the men of your surname in the FTDNA database may not yet have ordered any Y-STR product;
• there may have been an above average number of STR mutations in your male line in recent generations, resulting in few matches of any surname;
• there may have been a below average number of STR mutations in your male line since the adoption of surnames, resulting in many matches with men whose common ancestry predates the use of surnames;
• there may have been an overt or covert surname/DNA switch in your male line since the adoption of surnames;
• your surname may have multiple independent genetic origins;
• etc., etc.

Preliminaries

New FamilyTreeDNA.com customers need to fill in the names of both their Direct Maternal (i.e. matrilineal) and Direct Paternal (i.e. patrilineal) Most Distant (i.e. most distant known) Ancestors here in order to help those looking for mitochondrial DNA matches and Y-DNA matches respectively. An extraordinarily high proportion of customers have failed to attempt this, or have attempted it but have filled in details of the wrong ancestors, often filling in details of ancestors of the wrong gender. It is particularly important for anyone who has ordered mtDNA analysis and for men who have ordered Y-DNA analysis to fill in details of these ancestors which then appear in the relevant project reports, but it's a good idea for all FTDNA customers to fill in the details, which then show on the basic customer profile shown to those who match any part of their DNA.

Most people squeeze in names, places and dates to the limited string length of 50 characters available for the names of the most distant ancestors, but FamilyTreeDNA really should provide separate fields and columns for name, birth date, death date, country, county, etc., to help those scanning this information in the tables in surname projects and mitochondrial projects.

As I have already noted, some people are actually confused by the simple concept that Y-DNA follows the male line, and even by the simpler concept that in most cultures the surname generally, but not always, follows the same male line. Even more people are confused by the related concept that in many cultures grants of arms generally, but not always, follow the male line and the surname. Y-DNA will identify relationships that go back much further than the adoption of surnames, which in most cultures was around or after the year 1000 AD. Other cultures, for example European royalty, still do not use surnames in the 21st century.

Surname/DNA switches

In practice, there are many exceptions to the foregoing cultural principles, which result in sons inheriting DNA from their genetic father, but not inheriting the exact surname used by their genetic father.

The spelling of surnames mutates over the generations in much the same way as DNA mutates. After many generations, the surnames used by two men from the same genetic male line may end up being unrecognisably different.

A surname/DNA switch is defined as the use of a surname different from that used by the genetic father, which may be:

• a surname inherited from someone else; or
• a surname translated in some way from the genetic father's surname.

When the surname does not follow the male line, some genetic genealogists once used the term non-paternity event (NPE), but most now prefer to refer to these occurences more precisely as surname/DNA switches. After all, every birth involves paternity, so NPE is now more usually expanded as "Not the Parent Expected" and used when the DNA results do not match the oral family tradition.

Among the myriad of, possibly one-off, circumstances causing surname/DNA switches (and other forms of NPE) are:

• adoption (including of foundlings), with the suname inherited from the adoptive father;
• foundlings given a surname based on where or by whom they were found;
• infidelity, with the surname inherited from the mother's husband;
• use of sperm donors, with the surname inherited from the man who raised the child;
• parents giving every second child the father's surname and the mother's surname, with some inheriting the surname from the mother;
• men using their mother's surname for other reasons;
• men using their stepfather's surname;
• a change of surname associated with inheritance of a family estate, with the surname inherited from the benefactor;
• men (possibly include this writer's own brother) going on the run for all sorts of reasons and changing their surname to avoid being traced, whether running away from the law, from political opponents, or from their families, perhaps even wishing to commit bigamy;
• men using their maternal grandmother's maiden surname (see example below);
• translation of a surname back and forth between languages in different ways (see Sir Robert Edwin Matheson's Varieties and synonymes of surnames and Christian names in Ireland: for the guidance of registration officers and the public in searching the indexes of births, deaths, and marriages);
• inconsistent standardisation of the spelling of a surname once the computer age put an end to spelling diversity;
• reverting to an ancient spelling of a surname discovered in the course of research;
• etc.

There are many examples of surname/DNA switches in the pedigrees of recent world leaders, including the following:

• The president of the United States of America from 1993 to 2001 had Blythe Y-DNA but was known as Bill Clinton. His father was killed in a car accident more than three months before he was born and he later took the surname of the first of his three stepfathers.
• The prime minister of the United Kingdom of Great Britain and Northern Ireland from 1990 to 1997 had Ball Y-DNA but was known as John Major. His father Abraham Thomas Ball was a music hall performer, who initially used Tom Major merely as a stage name.
• The prime minister of the United Kingdom of Great Britain and Northern Ireland from 2019 to 2022 had Kemal Y-DNA but was known as Boris Johnson.His paternal grandfather Osman Wilfred Kemal's mother died in childbirth in 1909 and the baby was brought up by his maternal grandmother Margaret Hannah Brun née Johnson and became known as Wilfred Johnson. While Prime Minister Johnson has Kemal Y-DNA, he has a surname that was not used by any of his eight greatgrandparents and that descended via a female GGgrandparent. See here.

Grants of arms have historically been associated with specific families and never with surnames; thus sharing a surname does not automatically confer the right to bear the same arms. Similarly, sharing a surname does not automatically mean that two men carry the same Y-DNA.

Genetic Distance

I was initially under the misapprehension that genetic distance was a simple count of the number of differences between the sequence of integers reported for two individuals. For example, two individuals who have purchased Y-DNA37 and are reported to have a genetic distance of 2/37 might be expected to have the same results in 35 positions in the sequence and different results in the other 2 positions in the sequence. The actual situation turns out to be much more complex than this. Some of the numbers reported are related. For example, the 10th and 12th numbers in the sequence both relate to DYS389. One mutation can cause both of these numbers to change. Similarly, the 22nd, 23rd, 24th and 25th numbers in the sequence are all related to DYS464. One mutation can cause more than one of these four numbers to change. For some men, Y-DNA37 results may contain more than 37 numbers. For example, most men have four numbers for DYS464, but some O'Deas have six numbers, as can be seen on the results page. For more details, see Deconstructing TMRCA & Genetic Distance by John Barrett Robb.

Y-DNA genetic distance is no more closely correlated with genealogical relationship than shared centiMorgans of autosomal DNA. Note also that lower genetic distance indicates a closer relationship, while higher shared centiMorgans indicates a closer relationship.

Terry Barton of WorldFamilies.net gives a nice example in his 2008 interview with Blaine Bettinger: "my Dad and I each started a mutation (his is at DYS388, while mine is at DYS452) So, I am 41/43 when compared to my Uncle. I use this example to explain how you can’t count mutations to determine how closely related you are to someone ... Dr. Richard Barton [and myself] have no paper trail connection [but] Rich is a 43/43 match to my Uncle."

Matching criteria

• a Genetic Distance (GD) of 0 at 12 markers;
• a GD of 2 at 25 markers;
• a GD of 4 at 37 markers;
• a GD of 7 at 67 markers; or
• a GD of 10 at 111 markers.

Finding actual and potential Y-DNA matches

Having made yourself findable by others who share your surname and potentially share your Y-DNA, the next step is to look for such men in the FamilyTreeDNA community.

On the Surname & Geographical Projects page, FamilyTreeDNA has a "Project Search" box (the search box at the top of the right-hand column). This actually functions as a Surname Search box. Whether or not one is logged in, one can enter a surname and see results like this:

The following names matched your search request:

The COUNT is apparently the number of FTDNA customers with the surname. It is not clear whether it is the number of male customers, the number of Y-DNA customers, the number of customers whose results are fully processed, the total number of customers who have ordered kits, or what. It can at least be used to give an upper bound on the number of men with the same surname with whom another male can potentially compare his Y-DNA.

FamilyTreeDNA provides the infrastructure for volunteer administrators to run projects, including surname projects and other types of Y-DNA projects.

Notifications

FamilyTreeDNA.com insists on sending e-mail notifications of what it deems Y-DNA "Test Matches"; the customer has little control over what is deemed worthy of generating an e-mail, so a "Test Match" may be somebody with a different surname, no online family tree, no Most Distant Ancestor recorded, and the sixth such match at a genetic distance of two steps on a 37-marker scale. One e-mail alerted me to an individual with a different surname for whom the data could not reject the null hypothesis that we did not share a common ancestor within the last 14 generations; he was still my closest Y-DNA match at the time. These probability calculations appear to be blind to the surnames of the men whose Y-DNA is being compared.

FamilyTreeDNA's e-mail notification policies are very inflexible: I don't want e-mails about distant Y-DNA matches with different surnames with whom I have no hope of establishing a genealogical relationship, but must receive them; I do want e-mails about possible distant cousins who are deemed to be my Family Finder matches, but the FAQs state that FamilyTreeDNA.com does "not send notifications for Family Finder matches that are more distant than 3rd cousins". This should presumably be interpreted as indicating a high likelihood of false positives amongst such matches.

• the new match has probably bought Y-DNA37 and been deemed to be more than genetic distance 4/37 from you (i.e. not a match); and
• on the Y-DNA - Matches page, you will need to select 25 or 12 as appropriate from the Markers: dropdown menu in order to see your new match.

An example: Waldron Y-DNA

In the case of Waldron, the COUNT of FTDNA customers with the surname Waldron was 29 when I first learned of this search facility on 26 October 2015; it had not increased as of 23 December 2015, but had grown to 60 by 23 Jul 2017.

Further down the search results, it was stated that there were 33 members in the Waldron project on 26 October 2015; this too had not increased as of 23 December 2015, but had increased to 49 by 23 Jul 2017.

1. Surname projects:
   The Waldron project is an example of a surname project. There are several pages of interest associated with each surname project, including:
   
   • the Y-DNA Colorized Chart;
   • the Description;
   • the Project Stats;
   • the Activity Feed;
   • the Group Members;
   • the project surnames;
   • etc.
   Some of these pages seem to exist only for projects "participating in the myGroups Beta".
   What you see on these pages depend on whether or not you are logged in as a member of the project.
   Of the first 33 Total Members in the Waldron project, three had purchased Y-DNA12, another ten had purchased Y-DNA37, another six had purchased Y-DNA67 and another two had purchased Y-DNA111,  so in theory 21 people should have appeared on the Y-DNA Colorized Chart as of 19 February 2016; in practice only 20 did to those logged in as project members, and only 17 appeared to those not logged in.
   The obvious inference is that there were a further 12 Waldron project members who either were female or were male and had not purchased any Y-DNA product.
   Of the first 20 on the Y-DNA Colorized Chart, 16 had surnames beginning with Wald-.
   I exactly match one of the three Y-DNA12 only project members: N41617. As there is no way of getting directly from the Waldron project page to his FTDNA profile, all that I could see for many months is that his name is WALDRON and that he has left his Paternal Ancestor Name blank.
2. The Y-DNA - Matches page:
   As of 7 Apr 2014, if I switch on e-mail notifications here, I can see 3483 12-marker matches via this page; none of them has "Last Name Starts With:" matching Waldron or WALDRON. I don't understand why N41617 appears on the surname project page, but not on the matches page. Perhaps he has turned off e-mail notifications, thereby hiding from his 12-marker matches. To avoid a flood of unwanted spam e-mails, I have turned off everything below 37-marker comparisons.
   On 7 Feb 2014, I was notified of my sixth Family Tree DNA Y-DNA37 Test Match having a genetic distance of 2 or less (roughly speaking, matching on 35 or more of 37 markers). I had one "36-of-37" match and five "35-of-37" matches as of 30 Nov 2015, but I had no 37-marker match at any reported distance with surname beginning with Wal-. I have two Walshes and two Walkers who are "23-of-25" matches, but have further differences in the next 12 markers.
   I have two theories as to why I have no Y-DNA matches sharing my surname:
   
   • I may descend from the well-documented Waldron family who came to Ireland with the Ulster Plantation of 1609; however, the documented male line of this family appears to have died out, and so cannot be represented in DNA databases; or
   • My Waldron greatgrandfather or my Waldron greatgreatgrandfather may not be genetically Waldrons; there is plenty of autosomal DNA evidence that my paper-trail Waldron greatgrandfather and his mother were my genetic ancestors, but I need to recruit further DNA donors to confirm my ancestry beyond this point.
   Of the six men at a genetic distance of 2 or less from me on the 37-marker test, one was initially predicted to be from haplogroup R-Z383, three from R-M269, one from R-U106, and one from R-L148. Only four of the six are willing to be contacted by e-mail by their Y-DNA37 matches and only two of the six give any information about their ancestry. By 30 Nov 2015, only one of the six was showing any ancestry information; one now had confirmed haplogroup R-Z383, and the other five were now all predicted R-M269.
3. The Advanced Matching page:
   Log in as a kit number, not as a project administrator, before following this link. Click the Select All box at the top left; select your surname project (or any other project that you have joined) from the "Show Matches For:" dropdown menu and set Results Per Page to whatever you prefer (I always set these to the maximum available, 500 in this case, so that I can use Ctrl-F to search as many of the results as allowed). Then point-and-click the Run Report button towards the bottom right.
   Over a year after I was matched with the mysterious N41617, I found a link to his profile here and discovered that he is my first cousin once removed, with whom I had discussed DNA testing away back in 2007. I then persuaded him to also order the Family Finder test.

My efforts, and those of the Waldron Clan Association in County Mayo organising the 2013 Waldron Clan Gathering, to communicate with the administrators of the Waldron project were slow to get off the ground, but we eventually made contact in December 2015.

I am advised every time I get an e-mail about a very distant Y-DNA match that "We recommend ordering the Y-DNA67 to narrow down your matches with more precision & confidence." It is not immediately obvious why this recommendation is of any relevance until such time as I have at least two people matching me on all of the 37 markers that I initially purchased. Apart from being a good marketing ploy, the principle seems to be that "65-of-67" or "64-of-67" matches are typically more closely related than "35-of-37" matches. Furthermore, all expert advice now is that identifying and ordering a relevant SNP pack is better value than an STR upgrade.

Haplotrees, haplotypes, terminal SNPs, most recent confirmed SNPs, predicted haplogroups and confirmed haplogroups

1. he may purchase additional SNP tests (single SNPs, SNP packs or Big Y-700) for SNPs which are descendants of his current most recent confirmed SNP; and
2. additional once-in-the-history-of-mankind SNPs (for which he is positive) may subsequently be identified.

Estimating the age of SNPs

• Go to YFull's SNP search page
• Enter a SNP identifier (e.g. L226, without the top-level haplogroup letter) and click the Search button
• A green hyperlink, labeled with a haplotree branch name (e.g., R-L226, with the top-level haplogroup letter), should be displayed. Click on it.
• You should now see a branch of the haplotree. Typically, this branch will have two dates:
• The "formed" date is an estimate of when this branch began to diverge from its surviving siblings. (Extinct siblings are unknowable and therefore ignored.)
• The "TMRCA" date is an estimate of when this branch's surviving children began to diverge from each other. (Again, extinct lineages are ignored.)

My own Y-DNA results

However, my known first cousin once removed has also done the Genographic Project test and that gives his paternal line as R-M343 (of which R-M269 is a subclade).

On 28 Nov 2015, I finally persuaded the Waldron project administrators to look again at the grouping of project members and to assign myself and my known first cousin once-removed to the same group, which they still describe in the old notation as R1b1a2. This was probably equivalent when the group name was assigned to R-M269, but, if so, two new SNPs upstream from M269 have since been discovered and R-M269 has become R1b1a1a2 on the 2017 ISOGG haplotree. The old-fashioned R1b1a1a2-type descriptors no longer appear on the FTDNA haplotree.

As of 8 Dec 2015, the Waldron project members had been arranged by the administrators into four groups: three Waldrons in I1 (all with predicted haplogroup I-M253); one Buso in J2 (predicted haplogroup J-M172); two ungrouped; and the remaining 14 in R1b1a2, including myself. 12 of these have predicted haplogroup R-M269, one has confirmed haplogroup R-L20 (which is a subgroup of the R-M269 group; see below) and I have confirmed haplogroup R-FGC29367. Note that project members can seem to disappear and later reappear from day to day depending on whether you look at the results when not logged in (or timed out), when logged in as a kit which is a project member, when logged in as a kit which is not a project member, when logged in as administrator of the project, or when logged in as administrator of another project. This is determined by each individual project member's selected privacy settings.

As of 8 December 2015, when my own Y-DNA haplogroup was confirmed, only two other members of the Waldron Surname DNA Project had a confirmed haplogroup, namely a Waldron in R-L20 and a Phillips in R-DF23.

It is possible to order individual SNP tests from FamilyTreeDNA at USD39 each (and more cheaply from YSEQ), but I had not been able to figure out from online sources which ones I should order when Joss Ar Gall of ISOGG at the FTDNA stand at Genetic Genealogy Ireland 2015 taught me more in a few minutes about my own Y-DNA than I had learned in several years of reading web pages and attending lectures.

Joss's advice was to look at my Y-DNA matches and sort them (twice) by Terminal SNP. This revealed nine matches with identified Terminal SNPs, one a "35/37" match, two "34/37" matches, and six "33/37" matches. The terminal SNPs were L148, L48, two M269s, U106, Z11, Z343, Z383 and Z8. My closest STR match ("35/37") of those with identified Terminal SNPs has terminal SNP Z383 which did not appear on the Haplogroup R page as of 18 Oct 2015. 

"looking at his 37 STRs, I think it's very likely that he's U106+ and just about as likely that he's Z8+, which is downstream from U106. I base that on his results for DYS390, DYS447, DYS464d and H4. His results for those markers match the clear modal values found in Z8. If Patrick hasn't ordered the new Z8 SNP pack yet, he should do so. (It just became available on Thursday.)"

After a lot of searching, I found the order form for SNP packs. The only pack that it offers me is the R1b-M343 Backbone SNP Pack.

So I sought further advice on where to find an order form for the Z8 SNP pack and got this from Mike:

"To order the Z8 SNP pack, log into your FTDNA account and click on the blue "Upgrade" button in the upper right corner of the page. On the page you're sent to, look for the box labeled "Advanced Tests" and click on the blue "Buy Now" button. You'll be sent to a page with a pull down menu on the left side labeled "Test Type" - choose "SNP Pack" from the menu that's revealed. You'll see the Z8 SNP pack as the last one on the list. Click on the "Add" link for that test and follow the directions for completing the purchase."

The Z8 SNP pack results were scheduled to arrive by 23 Dec 2015. I looked for them on 8 Dec 2015 and found that they had been waiting for me since 3 Dec 2015! The bottom line was "Your Confirmed Haplogroup is R-FGC12057. Haplogroup R-U106 is the descendant of the major R-P25 (aka R-M343) lineage and is found from Eastern Europe to its highest frequency in Central Europe and the British Isles."

FGC12057 is also known as Y30001. The 95% confidence interval for the time to the most recent common ancestor is from 1450 years ago to 3100 years ago (as of 2015).

My Big Y-700 results subsequently moved me town the haplotree from R-FGC12057 to the more recent R-FGC29367.

Having found a known relative at last via Y-DNA testing on 14 Dec 2014, I put out an appeal to the Waldron Clan facebook page and group for other Waldrons to order kits and join the project. I presume that the basic Y-DNA37 product is the best starting point for every Waldron at this stage, but would welcome advice on whether and when people should be advised to order individual SNP tests in addition to or in place of the Y-DNA37 product.

I was the second member of the Waldron Surname DNA Project to purchase a SNP product. The following table shows the subclades to which myself and my fellow pioneer belonged, with the defining SNPs for each subclade:

Note that the nomenclature of the subclades is subject to annual revisions as more SNPs are identified. The table above is based on the 2015 nomenclature.

My fellow Waldron pioneer and I belong to different subclades of R1b1a2a1a, also known as R-L151. According to YFull, the 95% confidence interval for the Time to Most Recent Common Ancestor (TMRCA) for two people who are L151 positive is from 4,400 to 5,300 years, long before the adoption of surnames.

The commonest Y-DNA haplotypes and terminal SNPs identified in Ireland are also from subclades of R1b1a2a1a and are listed in the following table:

One of the longest documented male line lineages in Ireland is that from Brian Boru (d. 1014), Dalcassian High King of Ireland, to the present Lord Inchiquin, Conor O'Brien, whose subclade of R-L226 is R1b1a2a1a2c1f2a1a1a or R-YFS231286 or R-Y6913. See kit 29355 at the O'Brien Y-Chromosome DNA Surname Project.

Surname projects are only one of three quite different ways of identifying close male-line relatives:

1. looking for people with the same surname or a similar surname, for example in the Waldron Surname DNA Project as I have done above or Walden Y-DNA Surname Project;
2. looking for people with similar STR markers and confirmed terminal SNPs, for example in your Y-DNA37 match list; and
3. looking for people with similar SNP markers, for example in the R U106 (R1b-U106) (and subclades) project.

1. my known first cousin once removed, who has bought only the old Y-DNA12 STR product and has bought no SNP product; and
2. the only other Waldron member of the Waldron project with a confirmed haplogroup.

• FTDNA lists three SNPs on the next generation, namely Z383, Z8175 and A5616.  I was once presumed negative for Z383 (and tested negative for L148 under that); tested positive for Z8175 (and tested positive for FGC12057 under that) and tested negative for A5616:
  
• The U106 Tree by the U106 project administrators lists only two of these three SNPs on the next generation, namely Z8175 and A5616.  The grouping in the U106 project appears to list Z383 two generations further down than FTDNA, under FGC12057 which is still under Z8175.  L148 is also two generations further down, still under Z383. The notes to the U106 Tree suggest that Z383 is of dubious quality and that families are getting mixed results (some positive/some negative).
• The ISOGG folks list only L148 under Z12 and don't mention Z383 or Z8175 or FGC12057 or A5616:
  

• upstream haplogroups: R-U106 (1 person), R-Z8 (1 person), R-Z12 (5 people);
• debateable haplogroups: R-Z383 (1 person), R-L148 (5 people);
• downstream haplogroups: R-S18890 (3 people), R-FGC12058 (3 people), R-A687 (2 people) and R-S7297 (1 person).

TiP Calculator

I am sceptical of the TiP calculator, which estimates the probability that the most recent common ancestor of two Y-DNA matches is within any number of generations.

These estimated probabilities depend on the genetic distance between the two men, the mutation rates of the particular markers at which they differ, and the number of known generations of male line ancestors of each man.

However, I don't think that the TiP calculator takes any account of the number of matches reported, of the surnames of the men being compared and of their matches, or of the locations where their known ancestors lived.

If the men being compared have similar surnames and known ancestors from the same location, then the most recent common ancestor is probably closer than suggested by the TiP calculator.

On the other hand, if the men being compared have different surnames and their known ancestors lived far apart, then the most recent common ancestor is probably further back than suggested by the TiP calculator.

Similarly, someone from a dynasty which has many more matches than average, with many more surnames than average amongst those matches, probably has many fewer mutations than average, so the most recent common ancestor of two people from that dynasty is probably more distant than predicted by a model that seems to ignore this information.

I tend to use the TiP calculator to come up with a 95% confidence interval for the number of generations to the most recent common ancestor; I know that others look at the 50% probability cut-off or median number of generations to MRCA.

Bearing all these caveats in mind, it is interesting to look at what perfect STR matches tell us about the number of generations back to the MRCA.

At 0/37, the upper bound of the 95% confidence interval is between 6 and 7 generations.
At 0/67, the upper bound of the 95% confidence interval is between 5 and 6 generations.
At 0/111, the upper bound of the 95% confidence interval is between 3 and 4 generations.

In these cases, an STR upgrade can be viewed as giving a more precise estimate of the number of generations to the MRCA. The 37-67 upgrade moves the MRCA one generation closer if no additional mutation is discovered (and can move the MRCA further back if additional mutations ARE discovered).The 67-111 upgrade moves the MRCA two generations closer if no additional mutation is discovered (and can also move the MRCA further back if additional mutations ARE discovered).

In one example that I have studied, one additional mutation in the last 44 STR markers left the upper bound of the 95% confidence interval between 5 and 6 generations.

Grouping Project Members

The main objective of analysing a man's Y chromosome is to find the lowest (i.e. most recent) SNP on the haplotree for which he is positive, or likely to be positive.

There are several ways of doing this:

• the big bang approach - buy the Big Y-700
• selective purchasing of SNP packs and individual SNPs, guided by STR results
• educated guesswork based on examining the confirmed SNPs of his closest STR matches

• Open the genetic distance report
• Login to my project administrator account if not already logged in
• Use Ctrl-F in my browser to find the word "ungrouped" if I am dealing with a member whom I have not yet assigned to a subgroup
• Copy the member's kit number and create a row for him in the offline spreadsheet in which I keep my notes on project members, including columns for the following:
• Kit no.
• Surname
• Y-DNA products purchased
• Terminal SNP according to FTDNA
• Most recent SNP predicted by myself
• Date analysed
• Number of STR matches visible to the member
• Number of intra-project matches visible to me as administrator
• Comments
• Right-click the kit number and open the member's dashboard page in a new tab, check how many STRs he has purchased (37, 67 or 111) and open his Y-DNA match list
• Go back to the genetic distance report and select the appropriate number of markers from the dropdown menu
• Click the arrow beside the member's kit number to start generating the report, which may take a few minutes
• While waiting:
• In a third tab, open the FTDNA haplotree: https://www.familytreedna.com/my/y-dna-haplotree?ekit=j0XmKW8S87H%2ffjy92CTXbQ%3d%3d
  (The ekit identifier at the end of the URL is for myself; when you bookmark this link, you will have to change it to the ekit identifier for a kit in a project that you administer, probably your own kit.)
• If the member's Terminal SNP is new to the project, copy and paste the SNP identifiers for his line of descent from the haplogroup root into a string, which in many cases will be the name of the subgroup to which he will be assigned, e.g.
  R-M269>L23>L51>L151>P312>Z290>L21>DF13>ZZ10_1>Z253>Z2534>FGC5618>L226>FGC5660>ZZ31_1>FGC5628
• Look at the man's STR matches and their terminal SNPs and type a brief summary in the comments column of the spreadsheet
• Look at the man's intra-project matches and the subgroups to which they have been assigned and again type a brief summary in the comments column of the spreadsheet
• Now I am in a position to make an educated guess as to which branch of the haplotree and which subgroup within my project the man may belong, using:
• his own confirmed SNPs, if any;
• the most recent common ancestor of the terminal SNPs of his own closest STR matches;
• the most recent common ancestor of the subgroups to which I have already assigned his closest intra-project matches; and
• the subgroups to which I have already assigned project members with the same or similar surnames.
• Open my project results page in a fourth tab and check whether I need to create a new subgroup or reassign existing project members to different subgroups
• Open the editor for member subgroups in a fifth tab and create the new subgroup and/or move members around as necessary

• FTDNA will never predict anything below R-M269 without the purchase of a SNP product, but it is often easy for project administrators to make more precise predictions with some confidence.
• The multi-part STRs in the first 37 form a good predictor for membership of R-L226 (Irish Type III), in which there are distinctive values of DYS459 (8-9) and DYS464 (13-13-15-17).
• The ISOGG Wiki suggests that if Y-DNA67 is available and R-M269 is predicted, then P312 and U106 (to which I belong) can be distinguished by the 66th marker, DYS492 (12 for 95.1% of P312; 13 for 96.0% of U106).
• STR comparisons do not really help to distinguish between subclades of R-FGC5660 (to which almost every member of R-L226 belongs) or R-M222.

• Each top-level haplogroup represented in the project has its own colour, so far comprising:
  • E (Lime)
  • G (Light Blue)
  • I (Beige)
  • J (Aqua Marine)
  • Q (White)
  • R (Light Grey)
• Within haplogroup R, there are also separate colours for sub-branches:
• R1a (Pink)
• the four main Irish sub-branches:
• R-M222 (Green Yellow) is North West Irish/Irish Type I and subclades
• R-CTS4466 (Plum) is South Irish/Irish Type II and subclades
• R-L226 (Coral) is Dalcassian/Irish Type III and subclades
• R-L362 (Orchid) is Munster Type I and subclades
• the rest of R-L21 (Yellow)
• R-U106 and subclades (Light Cyan).
  

New branches of the haplotree

What to do when your Big Y-700 results appear

Chapter 6:

Interpreting X-DNA results

Recombination

According to Jim Owston:

a man may inherit his X as one of his mother’s two X-chromosomes completely intact; however, it is more likely he will receive a recombined X that includes segments from each of his mother’s two Xs.

The same remark about recombination applies also to a woman's maternal X chromosome; her paternal X chromosome is a copy of her father's single X chromosome, so is not subject to any recombination.

As I am a male, my single X chromosome is a combination of my mother's two X chromosomes. Anywhere between 0% and 100% of that recombined X chromosome comes from my maternal grandfather and the remainder from my maternal grandmother.

Roberta Estes says, without linking to any source, that:

a complete X chromosome ... is comprised of 18092 SNPs and is 195.93cM in length, barring anomalies like read errors and such, which do periodically occur.

Taking this length in cM and assuming that recombination follows a Poisson process (i.e. that successive recombinations are independent events), the distribution of the number of crossovers on one X chromosome in one generation is:

In a small sample of five, using data from Matt Dexter, Roberta finds one instance of transmission without recombination. She expresses herself "staggered" that, in another study by Robert Paine with 21 people, 25% of participants show no recombination on the X chromosome. Five successes in 21 binomial trials with a success probability of 14.1% in each trial is not significantly different from the expected 2.96 successes. Perhaps I should express this result in terms of failures rather than successes, as those anticipating recombinations and not finding them may consider their absence to be a failure. On the other hand, those of us who want to know exactly where our X-DNA came from will probably get excited by the discovery that there was no recombination, eliminating a whole branch of our ancestry as a potential source of X-DNA, and consider this a success!

Roberta also shows a screenshot from the 23andMe chromosome browser, suggesting that the fact that individuals from different generations are half-identical throughout the X chromosome is evidence of transmission without recombination. As with the autosomal chromosomes, parent and child will always be half-identical throughout the X chromosome, regardless of recombination.

We have seen in an earlier table that only the first five autosomal chromosomes are longer in terms of cM than the X chromosome; thus the last 17 autosomal chromosomes have a probability higher than 14.1% of being transmitted without recombination (again making the assumption of independence so that the Poisson distribution applies). As can also be seen in the chromosome browser or the Wikipedia table, on the base pair scale the X chromosome is longer than all bar seven of the autosomal chromosomes.

Elsewhere, Roberta says

I really do suspect that [the X chromosome is] recombining less frequently than the ... autosomes.

She actually appears to suspect either that the accepted length in cM of the X chromosome is wrong, or that recombinations are not independent, so that the Poisson distribution misrepresents the distribution of crossovers.

While, as a male, my single X chromosome comes entirely from my mother, it includes a contribution from at least one ancestor in every generation beyond my mother, and parts of it almost certainly come from two or more ancestors in more remote generations. Only by comparing DNA test results can I figure out with whom I share all or part of my X chromosome. If enough potential X cousins, as they might be called, submit DNA samples for analysis and upload their data to gedmatch.com to permit X chromosome comparisons, and if there is enough diversity among their X chromosomes, then it may be possible to narrow down the potential sources of my own X chromosome to less than the theoretical maximum number of ancestors, in my grandparents' generation and beyond.

X Inheritance paths

For autosomal DNA, a segment of, say, 10cM, is equally likely to have come down unbroken from any of the ancestors in a given generation, say from each of my eight greatgrandparents. This does not apply to X-DNA, for which the number of opportunities for recombination in the inheritance path depends not on the number of generations in the path but on the number of females in the path.

If we let M denote male ancestors and F denote female ancestors, then the inheritance path to an ancestor can be described by a string of Ms and Fs, for example MFF for a man's maternal grandmother or FMFM for a woman's father's maternal grandfather.

The expected proportion of one's X-DNA inherited from a particular ancestor is 0 if there are two consecutive Ms in the inheritance path, and otherwise 2^-f, where f is the number of Fs in the path excluding the last letter.

From my father (MM), I (as a male) inherit no X-DNA.

From my mother (MF), I inherit 2⁰=1 or 100% of my X-DNA.

For any ancestor on my paternal side, the inheritance path begins MM... so I inherit no X-DNA.

From each of my maternal grandfather (MFM) and my maternal grandmother (MFF), I expect to inherit 1/2 of my X-DNA.

From my matrilineal greatgreatgrandmother (MFFFF), I expect to inherit 1/8 of my X-DNA, but I expect to inherit exactly the same percentage from a far more distant ancestor with inheritance path MFMFMFMF.

Conversely, the typical X-DNA segment of, say, 10cM, is equally likely to have come down unbroken from these two ancestors three generations apart with different inheritance paths.

Similarly, an X-DNA segment of, say, 10cM, is far more likely to have come down unbroken from an X-ancestor on a given distant generation than an autosomal DNA segment of the same length. The exception to this is the matrilineal X-ancestor in the given generation, whose X chromosomes are subject to recombination in every generation.

Finding the paper trail to explain the source of a shared X-DNA segment will therefore on average be more difficult than finding the paper trail to explain the source of a shared autosomal DNA segment of the same length.

In other words, the closeness of an X match cannot be thought of in standard cousin terms. A father passes on his X unchanged to his daughters, but a mother passes on a recombination of her two Xs to all her children. So the distribution of the amount of X shared by two people depends only on the number of females on the path between the two people in the family tree. For example, two male third cousins whose mothers' PATERNAL grandmothers were sisters are expected to share more X-DNA than two male third cousins whose mothers' MATERNAL grandmothers were sisters, because there is one less recombination on each side. In the first case, the path to the common greatgreatgrandmother for both third cousins is MFMFF and in the second case it is MFFFF. Draw yourself a little relationship diagram if you don't follow!

This difficulty is both exacerbated and simplified by the inheritance path of surnames: exacerbated because the surname follows the X-DNA for at most two generations (father's surname and daughter's maiden surname; or mother's married surname and daughter's maiden surname); but simplified if two people sharing X-DNA find that they also share an ancestral surname (there are only two generations where the surname inheritance path crosses the X-DNA inheritance path). For example, I share X-DNA with someone who has a Walsh ancestor. My own matrilineal greatgreatgrandmother may have been a Walsh (this remains unproven). If our shared X-DNA comes through these Walshes, then my "match" must descend from my possible GGGGgrandmother Mrs. Walsh. This is just too far back to be sure that we would also share autosomal DNA (which we don't).

These X inheritance paths have their advantages as well as their disadvantages.

For a mitochondrial or matrilineal ancestor, the proportion of her X-DNA which a descendant is expected to inherit is the same as the proportion of her autosomal DNA which the descendant is expected to inherit. Thus the ratio of expected cM of autosomal DNA inherited to expected cM of X-DNA inherited is the same as the ratio of the total cM length of the autosomes to the total cM length of an X chromosome: 3587.1/195.9 or approximately 18.3:1.

For an X ancestor with one male on the line of descent, the proportion of the ancestor's X-DNA inherited by a descendant (male or female) is twice the proportion of the same ancestor's autosomal DNA inherited by the same descendant; thus the ratio of expected cM inherited is half the figure for the matrilineal ancestor, or approximately 9.2:1. Similarly, with two males in the inheritance path, the autosomal:X ratio drops to 4.6:1, and so on, until with five males in the path the ratio becomes 0.6:1, and we can expect to find more X-DNA than autosomal DNA inherited from that particular ancestor.

This explains why GEDmatch.com often shows matches sharing substantial segments of X-DNA but no autosomal DNA. Unfortunately, the FTDNA matching algorithm ignores X-DNA, so does not report those who share large segments of X-DNA but not autosomal DNA. I have written about a great example of this here.

One can actually take advantage of this quirk when selecting descendants to provide DNA samples for particular research problems. For example, my GGGGgrandfather John Keas was one of three men of similar age with that unusual surname (now generally spelled Keyes) who held land in 1833 in Carrig in county Limerick. I would like to test the hypothesis that the three men were brothers. The first strategy that comes to mind is to find one descendant of each Keas man, from the closest living generation to the 1833 landholder in each case, and to look for half-identical regions of autosomal DNA. In two cases (John Keas and William Keas), there are many descendants from whom to choose; in the third case (Michael Keas), we are still struggling to find a single proven living descendant. Where there are many descendants to choose from, and when economic circumstances dictate that DNA samples from all of them cannot be submitted, then the possible use of the X chromosome should be considered. An X-descendant with an alternating male/female line of descent from one of the three Keas men is expected to have inherited a much larger proportion of the X-DNA of Mrs. Keas, the unknown hypothesised common mother of the three men, than a direct female line descendant or any descendant who is not an X descendant. So, when exploring the family tree in search of candidates from whom to collect DNA samples, concentrate on these alternating male/female lines.

For example, in the case of this Mrs. Keas, who was bearing children by the late 1780s, there is a living GGGGgrandchild with a FMFMFMF line of descent. She is expected to have inherited 1/8th of each of Mrs. Keas's two X chromosomes, or about 49cM, but only 1/64th of Mrs. Keas's 44 autosomes, or about 112cM.

More importantly, if there is shared autosomal DNA, it could have come from any of the 64 ancestors on Mrs. Keas's generation, but shared X-DNA can come from only 21 of those 64 ancestors.

Finally, if the two subjects whose X-DNA matches are both male, then it is certain that there is an identical segment, and not just a region which is half-identical by chance because it is made up of overlapping paternal and maternal segments.

Comparing X chromosomes

For men, matches on the X chromosome must come from the maternal side. For women, matches on the X chromosome can come from either the paternal or maternal side.

When comparing X-DNA results for two females, the same principles apply as when comparing autosomal DNA results for two individuals of any gender. Each female has two X chromosomes, and it is possible only to identify half-identical regions or half/half matches.

When comparing X-DNA results for two males, things are a lot easier, since each has just one X chromosome, and it is possible to unambiguously identify identical segments, or to find full/full matches.

When comparing X-DNA results for a male with those for a female, we are faced with a new complication, as the male has one X chromosome and the female has two, so one can observe only half/full matches.

Two individuals could share an identical segment on the X chromosome without sharing one on any of the autosomal chromosomes. Many autosomal comparisons show only one substantial half-identical region, so there is no reason why the only such region can not be on the X chromosome, particularly in the case of a female-to-female comparison.

In a male-to-male X-DNA comparison, there is no danger of finding half-identical by chance regions. In a female-to-female X-DNA comparison, half-identical by chance regions are very possible.

The simplest comparison is between the single X chromosome of two males. If matching segments are found, then there is a full/full match, which has definitely not arisen by chance and is most likely to have arisen by descent. For those males, like me, who remain unconvinced that half-identical regions of autosomal DNA are very likely to contain identical segments, male matches on the X chromosome are a good place to start looking hard for genealogical relationships with strangers.

Things get more complicated when comparing the single X chromosome of a male with the two X chromosomes of a female. The result may be a full/half match, in which the male's X chromosome matches at least one of the female's X chromosomes throughout some half-identical region. This may arise by chance or by descent.

Stronger conclusions can be drawn when comparing the single X chromosome of a male with the four X chromosomes of two known X-related females (who are not doubly related). If there is a segment where the two females have a half/half match, then, because there is evidence of a recent common X-ancestor, it is extremely likely that the two females have matching segments in that region. If the male has a full/half match with both females in the same region, then it is extremely likely that their common X-ancestor is also X-related to him.

Finally, comparisons can be made between two pairs of known X-related females. Any segments where one of the X-related pairs have a half/half match probably come from their most recent common X-ancestor. If all four females are half/half matches with each other on the same region, then it is extremely likely that the most recent common X-ancestors of each pair were related.

Suppose that two sisters look at the half-identical regions on the X chromosome that they share with a third person (male or female).

If the third person matches the sisters' shared paternal X chromosome, then both sets of half-identical regions will be the same (unless the third person is related to the sisters on both paternal and maternal sides).

The contrapositive of this statement is also true: if the two sets of half-identical regions are different, then the third person must be related to the sisters on their maternal side (or merely half-identical by chance). This is because the maternal X chromosomes inherited by the sisters from their mother are the result of recombination, so only 50% of them are expected to be the same. In other words, sisters' pairs of X chromosomes are expected to be full-identical on half of their length and half-identical everywhere they are not full-identical. Where they are full-identical, they come from the same grandparents (paternal grandmother and maternal grandfather or paternal grandmother and maternal grandmother). Where they are half-identical, the maternal X chromosomes come from opposite grandparents (one sister from maternal grandfather and the other sister from maternal grandmother).

Comparing autosomal DNA is just like comparing the X-DNA of two females, with the additional complication that the source of the shared DNA can be any ancestor, not just an X-ancestor.

Before any definitive conclusions can be drawn, both parties needs to have not only their own DNA analysed, but also the DNA of some half-related individuals - in other words, the DNA of any relative other than a full-sibling or a double cousin.

So really this X-DNA chapter should come before the autosomal DNA chapters.

FTDNA-X-Matches

As of 2 January 2014, FamilyTreeDNA added two new features:

1. the ability to filter the list of FTDNA-overall-matches to show only those which it terms X-Matches (for clarity, I will use the term FTDNA-X-match); and
2. the ability to see half-identical (or equivalent) regions of the X-chromosome in the chromosome browser.

I have not yet found FTDNA's definition of X-Match. As of 25 January 2014, the FAQs still report that:

the Family Finder test does not currently use X-chromosome DNA (X-DNA) test results. The X-chromosome follows a different inheritance pattern than your autosomal DNA. Therefore, it requires a different matching algorithm to be accurate and scientifically valid.

The Bioinformatics team is investigating the math and programing for an accurate X-chromosome program.

Roberta Estes says, without linking to any source:

The X matching criteria [sic] at Family Tree DNA is: 1cM/500SNPs.

All that I can report is the nature of my own first three FTDNA-X-matches (as of 25 January 2014), which comprise two males (6.93cM or 650SNP identical segment with one, 5.12cM or 575SNP identical segment with the other) and one female (4.98cM or 550SNP half-identical region, or full/half match, by some fluke almost totally overlapping the identical segment with the first male).

Not yet having any known relative among my FTDNA-overall-matches, these are the first confirmed segment matches of any sort that I have found via FTDNA.

FTDNA apparently allows comparison of the X chromosomes of two FTDNA-overall-matches, but not of those not deemed to be FTDNA-overall-matches based on the autosomes.

GEDmatch-X-Matches

How does GEDmatch.com deal with autosomal match v. X match?

For one-to-one comparisons, regardless of gender, GEDmatch.com presents a report beginning with a legend listing Base Pairs with Full Match (green), Base Pairs with Half Match (yellow) and Base Pairs with No Match (red). If both parties in the comparison are male, the only possible results are Full Match and No Match, so there will be no yellow regions.

Here's an example of a male v. male comparison, with a threshold of 3cM and one fully matching segment above that threshold, of 4.6cM. The images appear to be generated on a SNP scale rather than a cM or bp scale. Note the absence of yellow regions.

Here's an example of a male v. female comparison, again with a threshold of 3cM, this time with two half-identical regions above that threshold. Note the presence of yellow regions.

The thresholds to use for X comparisons depend on the genders involved. When comparing two females (with two X-chromosomes each), use the same thresholds as for autosomal comparisons. Use lower thresholds when comparing a male (with one X-chromosome) to a female (with two X-chromosomes). Then lower the thresholds again when comparing two males (with one X-chromosome each). Clearly, there is no way that an X match between two men can be half-identical by chance (i.e. made up of overlapping segments from maternal and paternal chromosomes), as frequently happens with half-identical regions on the X chromosome between two females and with half-identical regions between autosomal chromosomes for any combination of genders. For some bizarre reason, the GEDmatch one-to-one X comparison is set to use the same default of 7cM whatever the genders associated with the two kits being compared.

If you suspect that a kit has been uploaded to GEDmatch with the gender misreported, probably the easiest was of checking this is to look at the graphic for the one-to-one X comparison with a known male kit. If there is no yellow region in the graphic, then the suspect kit must be male; if there are yellow regions, then the suspect kit must be female.

The gender bias

Because women have two X-chromosomes and men have only one, it is inevitable that women have many more X-matches than men. Women have twice as much X-DNA available for comparison with the same database of potential matches, so one would expect a woman to have on average just twice as many X-matches in the same database as a man.

Roberta Estes says on her blog that the reason women have many more X-matches than men is because women have so many more ancestors in the “mix”. This statement strictly is not even true, let alone an explanation of the gender bias. Although most people believe that human history is finite, in any mathematical representation of that finite history that we might use, both men and women ultimately have an infinite number of X-ancestors. In each generation, the ratio of the number of X-ancestors that a female has on that generation to the number of X-ancestors that a male has on that generation approaches the golden ratio, approximately 1.6180339887... (the limit of the ratio between two consecutive Fibonacci numbers). The expected number of matches for a given amount of X-DNA found by searching a given database depends only on the amount of X-DNA (one or two X-chromosomes) and the size of the database, and not in any way on the number of ancestors from whom that X-DNA might have been inherited, whatever form of ancestor-counting is used.

The observed gender bias appears to be far larger than the 2:1 ratio that one would expect to find.

In my case, I have access to three FTDNA accounts, one male and two females. I am male and have only three FTDNA-X-Matches out of 398 FTDNA-overall-matches (as of 25 January 2014) but one female has 69 FTDNA-X-Matches out of 357 FTDNA-overall-matches and the other has 48 FTDNA-X-Matches out of 416 FTDNA-overall-matches.

Similar discrepancies can be seen at GEDmatch.com, which shows that in many cases two people can share more X-DNA than autosomal DNA (on the cM scale).

As of 22 January 2014, I have only 20 GEDmatch matches by X-DNA Total cM of longer than 9.1cM, of whom only 4 are male and with only 6 of whom I share autosomal half-identical regions longer than 7cM.

Anthea, on the other hand, based only on 23AndMe customers, has 20 GEDmatch matches by X-DNA Total cM of longer than 49.6cM, of whom none are male and none share an autosomal half-identical region longer than 7cM with her.

It is obvious from the X-DNA inheritance pattern that the majority of X-DNA matches will be female, but 20 out of 20 is still surprising.

The observed gender bias must arise instead from a preponderence of half-identical by chance regions.

An example

At GEDmatch.com, I recommend that males go to the 'One-to-many' matches page and enter their kit number. In the X-DNA group of columns, click the blue arrow in the largest cM column to sort by that column. Look down the Sex column and note the Kit Nbr for any M that you find. These are the men with whom you have identical segments on the X chromosome and are worth investigating further.

In my own case, by using this approach I found five males including myself who have identical segments of various lengths in the region of the X chromosome between locations 23,955,089 and 36,111,764. Two are from FTDNA, two from 23andMe and one from Ancestry. Of the other four, only the other FTDNA customer has published an e-mail address, enabling us to establish contact. However, his X ancestors cannot be traced out of the USA and mine cannot be traced out of Ireland, so we have failed to establish our precise relationship. I would love to hear from the other three anonymous X matches whose GEDmatch Kit Numbers appear in the table below.

As these are identical segments and not just half-identical regions, all five men are very likely to share a common X ancestor.

Here's a table showing the ten one-on-one matching segments between these five men, identified by their GEDmatch kit numbers:

This table identifies eight crossover locations, viewing 32,493,780 and 32,496,045 as the same crossover for two reasons:

1. there is 0cM between them; and
2. between these locations, F310654 matches M223101 and F310654 matches M391301, but M223101 does not match M391301.

As the latter is impossible (since male/male X matching is transitive - unlike male/female or female/female X matching), there must be some form of measurement error in this tiny segment.

I needed this hand-drawn diagram in order to figure out what was going on:

All five men are identical on the segments up to the crossover at 32,387,789, so these segments appear to descend from a common X ancestor of all five men.

Beyond that crossover, the five men break into two subgroups: A241230 and F156355 are identical to each other; and M223101, F310654 and M391301 are all identical to one another. For one or other subgroup, these segments appear to descend from a more recent common X ancestor of the subgroup.

These small shared segments probably come from a very distant common X ancestor, but, with at least five people known to be identical on the same segment, the chances of finding a common X ancestor for at least two of the five men are increased. If all of them were willing to provide a means of contact and to discuss their possible common X ancestors, the chances would be even greater.

For further reading on X-DNA, see Louise Coakley's blog post.

Chapter 7:

Interpreting mtDNA results

Who shares mtDNA with you?

In practice, however, if you look at the relationship diagram connecting you to a distant mitochondrial cousin, everyone included will (typically) have a different surname, apart from the most recent common male ancestor and his two daughters.

Just as some surnames proliferate, due to many men of the surname having several sons, and other surnames get "daughtered out", due to men of the surname not marrying or fathering only daughters, so some mitochondrial DNA signatures are more prolific than others. For example, as of 31 January 2016, I had managed to document only 101 people (living and deceased) sharing my own mitochondrial DNA, but no less than 449 sharing my father's mitochondrial DNA.

Indeed, my grandmothers' mitochondrial DNA is doomed, as each of them had only one daughter, and each of those daughters in turn had only sons. Once we are gone, our respective grandmothers will never again have mitochondrial descendants.

My greatgrandmothers' mitochondrial DNA is in safer hands. Greatgrandmother Waldron née Nolan has a female mitochondrial descendant born in 2005; greatgrandmother McNamara née Clancy has a female mitochondrial descendant born in 2013; greatgrandmother Durkan née Durkan has several female mitochondrial descendants born since the 1980s; and my other greatgrandmother Durkan née O'Neil also has a female mitochondrial descendant born in the new millennium.

In genetic genealogy, mitochondrial DNA is useful for situations like these:

• In your ancestral research, you may come across two women with the same maiden surname, who were of the same generation, and lived in the same area, and you may want to know whether they were full-sisters, the alternatives being that they were half-sisters with the same father, or cousins of some sort. If you can find a matrilineal (i.e. mitochondrial) descendant of each woman and find that their mtDNA doesn't match, then you have proven that the original women were not full-sisters; if the mtDNA of the descendants does match, then it is very likely that the original women were full-sisters and that the mtDNA came from their mother. It may still be coincidence, as the two mothers could be different women from the same matrilineal line. In my own case, I am looking for a matrilineal descendant of Bridget O'Dea who married John Ryan in Patrickswell parish on 21 February 1821, and hoping that her mtDNA will match that of Maria O'Dea who married some years earlier and lived in the same parish, further confirming the evidence that suggests that the two O'Deas may have been sisters.
• You may have a marriage record for, say, Margaret Keas, and several birth or baptism records for girls named Margaret Keas from the same area around 20 or 30 years earlier, but you may be unsure which birth or baptism record matches the marriage record, which may not include the names of the parents of bride and groom. If you can find a matrilineal descendant of the Margaret in the marriage record, and matrilineal descendants of the mothers of the Margarets in the birth or baptismal records, and if there is just one mtDNA match, then you have ruled out all bar one of the birth or baptismal records as a match for the marriage record.

My mtDNA experience

When I submitted my own DNA sample, I was advised to defer purchase of mtDNA analysis for various reasons, which may have included:

• It is currently overpriced.
• Its price is expected to fall soon.
• The very slow mutation rates of mtDNA make it difficult to identify precise relationships.
• One type of DNA result at a time is hard enough to get to grips with.
• Examples such as those given above are rare, and those where mitochondrial descendants of all relevant parties can be traced are even rarer.

I eventually purchased the mtFull Sequence (FMS) product for myself and received my results on 24 February 2015. My first and only FMS match at a genetic distance of 0 at that stage was an adoptee. Three more perfect matches appeared subsequently, one each in 2015, 2016 and 2017, but we have been unable to find a common ancestor between any two of us.

My most distant known mitochondrial ancestor is my GGgrandmother Mrs. Mary O'Neil, who died in Barnalyra in County Mayo on 6 June 1887.

I also ordered mtFull Sequence for my paternal first cousin (who shares my father's mtDNA) on 10 February 2016, because there was a good chance that it could prove or disprove my hunch that two early nineteenth century West Clare matriarchs are closely related, namely:

• his most distant known mitochondrial ancestor Mary Conors/Connors/oConnor of Glascloon in Killard civil parish (wife of firstly Timothy Galvin and secondly Thomas Kelly, and also one of my GGGgrandmothers); and
• Catherine Crotty of Breaghva in Moyarta civil parish (wife of a McNamara, probably the Patt McNamara listed in Moyarta East in the Tithe Applotment Book of 17 Nov 1827, when Breaghva appears to be subsumed into Moyarta East).

• Both are listed, apparently widowed, as occupiers in Griffith's Valuation of Kilrush Poor Law Union, dated 20 August 1855; each occupied a house and offices with rateable annual valuation of 15 shillings; Catherine McNamara was the only female occupier listed in Breaghva and Mary Kelly was one of only two female occupiers listed in Glascloon.
• Catherine's known children have implied birth dates between 1830 and 1835; Mary had a daughter married in 1846 and a youngest child born in 1838; so their child-bearing years overlapped, and both appear to have been born within a decade of 1800 and they appear much more likely to have been of the same generation, rather than anything like aunt and niece.
• Family tradition is that Catherine's maiden surname was Crotty, but no primary evidence to verify this has yet been located; two greatnephews of a son-in-law of Mrs. Mary Kelly told me in the 1980s that Mary's maiden surname was also Crotty, but her first husband's tombstone and her last child's baptismal record confirm that this is incorrect. Possible causes of the incorrect oral tradition are that Mary came from a house that subsequently became a Crotty house, or perhaps she exchanged visits with a Crotty relative.
• Two of Mary's granddaughters by her first marriage in turn married the same John McNamara and lived in the townland of Moveen West, adjoining Breaghva. The McNamara families in Breaghva and Moveen West claim not to be related in the male line, but could they be related in a female line?
• Oral tradition is that both Catherine and Mary were from "The West", a sort of moveable feast in County Clare, referring to anywhere between the speaker's current location and Loop Head.
• One of the Mrs. John McNamaras is described in a letter from about 1911 as a "cousin" of Mrs. Anne Eustace N.T., née Crotty, from Ross in Kilballyowen civil parish.
• Both Catherine and Mary were prolific, in their own ways, in terms of the number of descendants inheriting their mitochondrial DNA, as shown in the following table, showing the number of mitochondrial descendants of each of them (and of my own most distant known mitochondrial ancestor) whom I had documented as of February 2016:

If Catherine and Mary were first cousins, with different maiden surnames, then there is one chance in three that their mothers were sisters, and that they shared mitochondrial DNA.

Catherine has two GGgrandchildren (descended from different children) with Family Finder results at FamilyTreeDNA.com (AF and FM); Mary has two GGGgrandchildren from her first marriage (myself PW and my first cousin AD) and one suspected GGgrandchild from her second marriage (TE) with Family Finder results at FamilyTreeDNA.com. (Family Finder results for children and grandchildren of some of these five people are also available, but can not add any additional information.)

The 3x2=6 possible Family Finder comparisons between Catherine's descendants and Mary'sknown and suspected descendants reveal that three of these six pairs are deemed to be FTDNA-overall matches, as shown in this table (courtesy of the Clare Roots project at FTDNA):

If Catherine and Mary were first cousins, then two of the bolded comparisons (repeated on each side of the diagonal in this symmetric table) would involve comparing fifth cousins and the other four would involve comparing fifth cousins once removed. The observed 50% match rate is far more than the predicted 10% or less match rate given by FamilyTreeDNA for such distant relationships. If the match rate for pairs of fifth cousins was 10%, then the probability of three or more matches in six independent fifth cousin comparions would be less than 0.13%. Although the comparisons in this case are not independent, my theory that Catherine and Mary were closely related is clearly a little more than a hunch. The fact that there is only one match out of three between Mary's descendants raises a red flag and suggests that there may be a common ancestor somewhere else on the family tree. There are two more of Mary's descendants at AncestryDNA and GEDmatch.com, but one-to-one comparisons there don't strengthen the case for a relationship between the two dynasties. Further evidence unearthed after I generated the above table confirmed that TE's GGgrandfather Thomas Kelly of Glascloon was not Mary Conors' second husband of that name and townland, but an older namesake, possibly his father.

It would be nice to see if the five individuals in this table have any other matches in common, which is a report that is theoretically available to project administrators, but this operation usually times out. It finally completed on 11 March 2016 and reported "No In Common With Members".

Catherine's mitochondrial DNA has long been known, through one of her GGgrandchildren, to be from Haplogroup - H3-T16311C!. As of 4 May 2018, this GGgranddaughter's only Full Mitochondrial Sequence match with a genetic distance of zero is one of her own daughters. (Her mitochondrial DNA is unlikely to die out any time soon as all of her four children, five of her six grandchildren and her first greatgrandchild are females who have inherited her mtDNA.) As Mary's mitochondrial DNA was available, through one of her GGGgrandchildren, on whom only the Family Finder analysis had been ordered so far, I decided that it was worth paying for mitochondrial analysis on Mary's descendant for the one-in-three or smaller chance that the possible relationship between Catherine and Mary is on the mitochondrial line. Results were promised for some time between 23 March 2016 and 6 April 2016, but I got an e-mail on 11 March 2016 to say that they were already available, and they showed a match date of 2 March 2016.

These results suggested that Mary Conors' numerous mitochondrial descendants belong to mitochondrial haplogroup H27. On 13 February 2018, I was alerted by another FTDNA customer to one of her mtDNA matches who appears to be my second cousin and also a mitochondrial descendant of Mary Conors. But his mitochondrial haplogroup is H27-T16093C. It appears that one mutation since my greatgrandmother has thwarted the FTDNA matching algorithm, which believes that the two second cousins are unrelated. The matching algorithm has worse shortcomings, for it concluded due to similar recent mutations that Blaine Bettinger and his mother were unrelated, although autosomal DNA comparison had confirmed the relationship.

As of 4 May 2018, FTDNA had no perfect (genetic distance of 0) mitochondrial match to my first cousin, but two such matches to my second cousin. By way of comparison, I belong to mitochondrial haplogroup U4b1b2 and FTDNA then had four such mitochondrial matches to me, and I was disappointed at how few matches I had!

FTDNA recalculated its mitochondrial matches in May 2016. Mine remained unchanged. My first cousin acquired three new matches, all backdated to 2 March 2016, two at genetic distance 1 and one at genetic distance 3.

So it's back to the drawing board on the theory that Catherine and Mary were sisters' children. Even if we got a perfect mitochondrial match, we still could not have ruled out the possibility that the relationship between Catherine and Mary was more distant - possibly much more distant - than first cousins.

A sample of six Family Finder comparisons is very small, and we also need more descendants of both women to order Family Finder to provide additional independent evidence, especially at least one descendant each of Mary's daughters Biddy, Kitty and Peggie Galvin.

Tools for analysing mtDNA (or the lack thereof)

There are unexpected and unexplained differences between the tools for analysing mitochondrial DNA matches and those for analysing Y-DNA matches.

For each of my Y-DNA matches at FamilyTreeDNA.com, I can click on a TiP icon and get a Y-DNA TiP Report allowing me to see the likelihood of the most recent common ancestor that I share with the relevant match being a particular number of generations in the past.

For mtDNA matches, there is no equivalent of the TiP icon.

Question 1: How can I work out the corresponding likelihoods in the mitochondrial case?

My 71 Y-DNA37 matches come from many different Y-DNA Haplogroups and are all a genetic distance of 2, 3 or 4 from me.

My 6 mtDNA matches as of 22 November 2015 all come from mtDNA Haplogroup U4b1b, two at a genetic distance of 0 from me and four at a genetic distance of 2 from me.

Anthea's 31 mtDNA matches as of 22 November 2015 all come from mtDNA Haplogroup U5a2b4 and are all a genetic distance of 1, 2 or 3 from her.

Without the ability to turn "genetic distance" into a probability scale, I find it impossible to interpret these results.

Question 2: Why are the Y-DNA interface and the mtDNA interface at FamilyTreeDNA.com so different?

Myself, Anthea and a third person are each half-identical to the other two on the same substantial part of Chromosome 6. Anthea and the third person both belong to mtDNA haplogroups beginning with U5a2. It would be nice to get some idea of the likelihood that the most recent common ancestor from whom we inherited the autosomal match was on the shared matrilineal line of Anthea and the third person. As I have read that mitochondrial mutations are very rare, I suspect that the likelihood in this case is small.

Question 3: How can I put some sort of number or probability on this likelihood?

I started a discussion around these three questions on facebook.com.

For further reading about mitochondrial DNA, these are probably the places to look:

http://www.isogg.org/wiki/MtDNA_testing_comparison_chart
http://www.mitosearch.org/
http://www.mtdnacommunity.org/

Chapter 8:

Aggregating autosomal DNA matches from different websites

DNApainter

• Exclude segments under 8cM
• Exclude larger matches sharing over 600cM in total
• Exclude smaller matches sharing under 8cM in total

• on Chromosome 8, G.C. (related to my paternal grandmother) shares a 7.0cM segment (6.3cM at GEDmatch) with M.F. (related to my paternal grandfather);
• on Chromosome 9, G.C. (related to my greatgrandmother Mary Anne Clancy) shares a 7.2cM segment (7.6cM at GEDmatch) with R.Z. (related to my greatgrandfather Old Johnnie McNamara);
• on Chromosome 15, A.T. (related to my greatgrandfather Old Johnnie McNamara) shares a 7.9cM segment (7.2cM at GEDmatch) with P.M. (related to my greatgrandmother Mary Anne Clancy); and
• on Chromosome 22, B.M. (related to my GGgrandmother Mary Galvin) shares a 7.1cM segment (4.1cM at GEDmatch) with D.P.-B. (related to my GGgrandfather George Clancy). [I have a theory that these two are 4C1R as they descend from two O'Brien next-door neighbours who may have been sisters; but I shouldn't share any O'Brien segments that they share.]

Genome Mate

Genome Mate can be installed and run within your web browser from genomemate.org.

I have created separate Genome Mate profiles for myself, for my paternal first cousin and for my maternal first cousin, by importing match data and chromosome browser data downloaded from FamilyTreeDNA.com for each of us, on 20 July 2014. I accepted the default 7cM/500SNP cutoffs for now.

This enables me to work through my FTDNA-overall-matches and identify those who must be paternal (because they match both me and my paternal first cousin where we match each other) and those who must be maternal (because they match both me and my maternal first cousin where we match each other) .

I eventually worked out the following methodology:

• Select my own profile
• For each chromosome (1 to 22 and X):
  • For each segment, for each relative
    • Point-and-click the relative's name, then point-and-click the View Relative button at the bottom left of the pop-up window
    • If the Relative Details pop-up window shows that (s)he matches both myself and one of my first cousins on overlapping segments, then
      note the name and click on one of the segments to check that my first cousin and myself match on that segment.
    • If so, then
      • Cancel
      • Set ICW Group (in my own profile) to Maternal or Paternal as appropriate
      • point-and-click Update Segments button at bottom middle of pop-up window
      • select my profile
      • check that All DNA Segments, Update ICW Group and Update Confirmed Ancestors boxes are ticked
      • Apply Changes
      • switch to the relevant first cousin's profile on the dropdown at top left
      • point-and-click the relevant Relative name
      • Set ICW group (in my cousin's profile) to Paternal or Maternal as appropriate (as my cousin's are my father's sister's child and mother's brother's child, the selection will always be the reverse of what I selected in my own profile)
      • point-and-click Update Segments button at bottom middle of pop-up window
      • select my cousin's profile
      • check that All DNA Segments, Update ICW Group and Update Confirmed Ancestors boxes are ticked
      • Apply Changes
      • switch back to my own profile on the dropdown at top left
    • Else,
      • If the relative matches myself and a first cousin in non-overlapping locations, then
        • note "Matches myself and [cousin] in different locations." in the Relative Note box, Save, Save
      • Else
        • <Esc><Esc>
    • Proceed to next relative.

This will be a long and tedious process!

Chapter 9:

Integrating genetic and traditional genealogy to find and confirm new relatives

Introduction

Among the trickier parts of genetic genealogy is developing appropriate strategies to adopt:

• after you order and after you receive new DNA results for a known or probable relative;
• after you identify a new possible relative from a list of DNA matches; and
• after a possible relative becomes a probable relative through the discovery of a common ancestral surname and/or a common ancestral location.

Given an individual of interest, these strategies can involve a mixture of:

• searching various DNA databases for further possible relatives to investigate or to contact, in particular:
  • the 1500 one-to-many GEDmatch matches of the individual of interest, if he or she has copied his raw data to GEDmatch.com; and
  • the ADSA output for the individual of interest, if he or she is willing and able to generate it and e-mail it to you;
• searching traditional genealogical sources to verify possible relationships, in particular:
  • the GEDCOM file of the ancestors of the individual on interest, wherever it might be available;
• identifying and recruiting further individuals whose DNA will help your research;
• raising funds to pay for analysis of further DNA samples; and/or
• learning a little more of the scientifc theory behind DNA comparisons.

If not properly thought out and planned, the process can become overwhelming, frustrating or confusing for a variety of reasons:

• this is cutting edge science, and both the commercial and volunteer websites are struggling to keep up with demand, with perceived competition, and with scientific developments;
• DNA inheritance is a game of chance, and you will back losers as well as winners;
• most people have many thousands of relatives within the range of autosomal DNA matching;
• traditional genealogical sources generally do not reach as far back in time as autosomal DNA matching;
• your possible relatives are probably just as overwhelmed or frustrated or confused as you are, and may also have much less time for the subject or much less interest in it than you have;
• etc.

In this chapter, I will set out, in no particular order, as of yet, some of my thoughts on strategies which may prove helpful.

Developing an autosomal research strategy using DNA from more people

This section is inspired by my totally unexpected discovery that my closest initial FTDNA-overall-match is not only an adoptee, but a foundling.

Developing the optimal research strategy, particularly when there has been an adoption or other non-paternity event, requires the research to reconcile conflicting emotional, scientific and economic motivations.

People on both sides of the adoption brick wall may experience unexpected and unpredictable emotional reactions. Some people on both sides of the adoption brick wall will accept that they cannot change the past; others may wish to let bygones be bygones and be unwilling to investigate the past. The biological parent(s) of the adoptee may or may not be the first suspect(s) in the family tree that come to mind as perhaps having had a child out of wedlock.

The scientific approach will suggest taking DNA samples from as many potential relatives as possible, rather than zeroing in immediately on the most likely suspects suggested by the historical evidence.

The economic problem is that DNA analysis is still costly, particularly if there are dozens of members of a large extended family available for sampling. Unless a fairy godmother is willing to pay for the analysis of all the samples that statistical rigour requires, a degree of negotiation between the parties will possibly be required.

Some compromise is inevitable between these three motivations. This may require the combined skills of a social worker, a statistician and a businessman.

Before planning a scientific research strategy, one must decide on the specific objective of the research. In other words, the first step is to decide on the precise hypothesis that one wishes to test. This hypothesis should be something along the lines of "Jack and Jill were siblings" or "Tom was the father of Dick and Harry".

The optimal research strategy will depend critically on both the hypothesis to be tested and the budget, the time and the degree of co-operation from the extended family which are available. Costs will undoubtedly continue to fall, but if we wait for ever we'll all be dead before we get anywhere.

The strategy to be decided at each step basically involves answering the question: "Whose autosomal DNA should be analysed next?" As the solution comes within sight, it may become appropriate to look at other forms of DNA. For example, if you find two female ancestors that you suspect were sisters, then you might want to look at mitochondrial DNA from a matrilineal descendant of each.

Thus one should probably follow all of the following strategies in parallel as funds and time permit.

The hunch strategy

Let your genealogical instinct suggest the precise hypothesis to be tested. If the evidence causes you to reject your hypothesis, go back and come up with a new hypothesis.

In an adoption case, you may have a hunch as to which member or members of the extended family is most likely to have produced a secret love child. So cut to the chase and look for a DNA sample from his or her closest known relative. Even if your suspect is long dead or has lost contact with the family many years ago, a certain amount of diplomacy will be required here. Adoption counselling services are there to help. (As of 7 September 2014, however, the Adoptions Rights Alliance has no reference to DNA or genetics on its home page.)

The rarity strategy

Is the DNA of a particular branch of your family in danger of extinction or dilution?

If you have a relative who is of great age or seriously ill, collect a sample of his or her DNA before it is too late.

Digging someone up to collect DNA after he or she is dead and buried is awkward and expensive and unpleasant and messy and requires exhumation orders and incurs legal costs.

The day is probably not far away when funeral directors will routinely offer to collect and preserve a DNA sample from the body of a deceased person.

Rarity value arises not only from calendar age or life expectancy, but also from position in the family tree.

The DNA of an only surviving child is more irreplacable than the DNA of a child from a large family.

The higher up the family tree an individual is, the more useful his or her DNA will be. For example, the youngest child of the youngest child of an ancestor may have been born long after the oldest child of the oldest child of the oldest child of the ancestor (his first cousin once removed). But he is one generation higher up the tree, so his autosomal DNA is expected to contain twice as much of the common ancestral couple's DNA as that of the oldest person on the next generation down.

If you are just interested in identifying a common ancestor, then the DNA of a child whose parents' DNA has already been collected will be of no incremental value. On the other hand, if you are interested in chromosome mapping and phasing, then sampling a child and both parents is of critical importance. We have already seen in Example A that looking at parents' DNA can help to quickly identify smaller half-identical regions as merely half-identical by chance.

In my case, the rarity strategy points me towards my mother's maternal first cousins. Her last sibling died in 2006 and her last paternal first cousin died in 1981, but three or four of her maternal first cousins were still alive, aged 78 and upwards when I got my own DNA results. My father's paternal first cousins and maternal half first cousins are younger and/or more plentiful.

In any case, start with the earliest living generation - it may cost twice as much, but you will learn more than twice as much by sampling your father or paternal uncle or aunt and your mother or maternal uncle or aunt as you will learn by sampling yourself.

The bisection strategy

If you find a suspected relative, for example an adoptee, and have no idea which side of the family he or she comes from, the most logical approach is to repeatedly bisect your pedigree chart. If neither person is an adoptee, then both can pursue this strategy simultaneously. And it will leave a framework in place for identifying your common ancestor with future mystery matches.

Find a living paternal relative (who is not also a maternal relative), by working through father, paternal grandparent or greatgrandparent, paternal uncle or aunt, paternal first cousin, and so on, until you find someone living and willing to provide a DNA sample. (Your own siblings, nieces, nephews, etc., will not give any independent evidence about the relationship of interest beyond what your own DNA sample has revealed.)

Then find a living maternal relative, by working through mother, maternal grandparent or greatgrandparent, maternal uncle or aunt, maternal first cousin, and so on, until you find someone living and willing to provide a DNA sample.

If the original match matches the paternal relative but not the maternal relative, then you can be fairly sure that he or she is related on the paternal side, and vice versa.

Now move back a generation and repeat the process:

Suppose the original match turns out to come from your maternal side.

Find and sample a living relative on your maternal grandfather's side (maternal grandfather, greatuncle or greataunt on that side, first cousin once removed on that side, second cousin on that side, etc.).

Also find and sample a living relative on your maternal grandmother's side (maternal grandmother, greatuncle or greataunt on that side, first cousin once removed on that side, second cousin on that side, etc.).

If the original match matches the maternal grandfather's relative but not the maternal grandmother's relative, then you can be fairly sure that he or she is related on the maternal grandfather's side, and vice versa.

Continue until you come to a step where the original match matches both sides. Now you've almost certainly found your common ancestral couple.

If cost is not an obstacle, then you can immediately start collecting DNA samples from all those who you might in future want to approach in connection with a particular study, for example:

• two first cousins, one paternal and one maternal
• four second cousins, one descended from each pair of greatgrandparents
• eight third cousins, one descended from each pair of greatgreatgrandparents
• sixteen fourth cousins, one descended from each pair of greatgreatgreatgrandparents
• and so on.

If you have living relatives from a generation before your own on any side, then substitute one of them for the person from the subsequent generation.

As noted above, beyond third cousins there is a significant probability that one or other or both parties will not have inherited any autosomal DNA from the common ancestral couple, so the value of this approach declines.

If the objective is purely to work out to which branch of your ancestry distant DNA matches belong, then you might skip the first and second cousins and just recruit third cousins.

Note that I have not mentioned siblings in this section; the usefulness of their DNA is in increasing the precision of estimated relationships, a topic to which I will now turn.

The precision strategy

Nobody would carry out an opinion poll based on a sample size of one, but that is precisely what the matching algorithms of the DNA companies do.

Another field of applied statistics in which I have extensive experience is the handicapping of racehorses - allotting the weights to be carried by each horse in a race on the basis of observed ability in order to equalise their chances of winning. Handicappers are not required to assess a horse's ability until it has raced three times, typically in races where the number of runners is in double figures. The matching algorithms of the DNA companies are comparable to requiring handicappers to make a definitive judgement of a horse's ability after a single run in a two-horse race.

As in both of these examples, proper statistical analysis generally requires taking a large sample of independent and identically distributed observations and looking at the average of those observations.

The bigger the sample, the smaller the margin of error.

If you have not already done so, ask living relatives from generations older than your own to provide DNA samples. It will be a great help in distinguishing from which side your matches come and how closely they are related to you.

Anyone from an earlier generation is expected to share twice as much autosomal DNA with mutual relatives as you do; those from two generations earlier are expected to share four times as much; and so on. So it is important to obtain samples from parents, aunts and uncles and cousins once removed (and, even more so, from grandparents, greataunts, great uncles and cousins twice removed) before it is too late. These samples will both provide more accurate estimates of relationships and more segments of your common ancestral couple's DNA which may match those inherited by other descendants.

As the observed ranges of shared DNA for close relatives do not overlap, it is immediately possible to identify and distinguish between parent/child (100%), full-sibling (75%), half-sibling (50%), uncle-or-aunt/nephew-or-niece (25%) and first cousin (12.5%) relationships. Beyond this, the shared percentages are closer together and the standard deviations relatively larger, so it becomes impossible to distinguish between relationships using samples of one. The solution is to obtain DNA samples from known relatives of either or both parties.

This is easy to do if you and/or your suspected relative have siblings and/or half-siblings on the side you are interested in.

Combining information from siblings' DNA to estimate relationships more precisely

A simple way to arrive at more precise relationship estimates is to just collect DNA samples from all the siblings on each side of the brick wall and look at the average of the pairwise Shared cM between the two families. The original single observation may not have been able to distinguish between, say, second cousin (and equivalents), second cousin once removed (and equivalents) and third cousin (and equivalents). The average pairwise Shared cM between the two families will have a much smaller associated standard error, so will potentially give an unambiguous inference. Remember, however, that two first cousins, for example, are expected to share the same percentage of their DNA as a greatuncle and his greatnephew, so traditional genealogical evidence, such as birth dates, will still be required to distinguish between such equivalent relationships.

If you collect DNA from several family groups of first cousins, your observations are no longer independent, so a simple weighted averaging process is necessary.

In the case of the two sibling groups, the averaging procedure is essentially equivalent to estimating the Shared cM between one of the parents of one sibling group and one of the parents of the other sibling group.

If you have samples from several family groups descended from a common ancestor, then you can work back through the generations to estimate the Shared cM between the common ancestor and the person you are trying to fit into the family tree.

For example, suppose Joan and Peter are siblings and have Shared cM of 75.1 and 60.4 respectively with Anthea, whom we have reason to believe is related to them on their now deceased father Richard's side. Joan and Peter each got half of their overall DNA from Richard, so we expect that on average they got half of the DNA that Richard shared with Anthea. From Joan's figure, we can estimate that the Shared cM between Richard and Anthea was 2 x 75.1 = 150.2, and from Peter's figure we can estimate that the Shared cM between Richard and Anthea was 2 x 60.4 = 120.8. The obvious way to combine these estimates is to take the average, so our first crude point estimate of the Shared cM between Richard and Anthea is (150.2 + 120.8)/2 = 135.5.

Now suppose we also have a sample from Richard's first cousin Patricia, whose Shared cM with Anthea is 78.1. Using the same logic as before, Richard's mother Lillian is expected to have 2 x 135.5 = 271.0 Shared cM with Anthea and Patricia's father Thomas is expected to have 2 x 78.1 = 156.2 Shared cM with Anthea. Lillian and Thomas are siblings, so the average of their Shared cM with Anthea will be a more precise estimate than either of these figures on its own: (271.0 + 156.2)/2 = 213.6.

As the standard errors for the original one-to-one comparisons are not reported, it is difficult to work out the standard errors for the averaged comparisons, but they must be smaller.

These examples look only at the aggregate length of the regions on which two siblings are half-identical to a third person. A more sophisticated estimation technique can be used if the locations of the half-identical regions are also known. Ex ante, we would expect both siblings to be half-identical to the third person on 1/3 of the aggregate length; just one sibling to be identical on 2/3 of the aggregate length; and their relevant parent to be half-identical to the third person on a further 1/3 of the aggregate length on which neither child is half-identical to the third person. When we add the aggregate lengths together, double counting the 1/3 on which both siblings are half-identical exactly compensates for not counting the 1/3 on which neither sibling is half-identical. If both siblings are half-identical to the third person on exactly the same region(s), then we should begin to doubt that there was any other region(s) on which the parent was half-identical to the third person; adding the siblings' Shared cM in this case probably overestimates the parent's shared cM. Conversely, if there is no overlap between the regions where the two siblings are half-identical to the third person, then we should begin to suspect that there are other segments shared by the parent and the third person which neither child inherited; adding the siblings' Shared cM in this case probably underestimates the parent's shared cM. A better estimate of the Shared cM between the parent and the third person would be based on two separate estimates of the aggregate length of the regions where the parent but neither child matched the third person.

A little algebraic notation will make the calculations easier to follow. Let x denote the aggregate length of the regions where both siblings match the third person, and let y denote the aggregate length of the regions where exactly one sibling matches the third person. If we just knew x, then we would expect the aggregate length of the regions where the parent but neither child matched the third person to also equal x. Similarly, if we just knew y, then we would expect the aggregate length of the regions where the parent but neither child matched the third person to equal 0.5y. A better estimate of the uninherited length can be obtained averaging these estimates: 0.5x+0.25y. Thus the best estimate of the Shared cM between the parent and the third party is x+y+0.5x+0.25y=1.5x+1.25y.

For example, if both siblings match the third party on the same 100cM regions, then x=100 and y=0, so our best estimate is that the parent matched the third party on 150cM. However, if both siblings matched the third party on non-overlapping 100cM regions, then x=0 and y=200, so our best estimate is that the parent matched the third party on 250cM. As intuition suggested, the first of these estimates is less than the initial crude estimate of 200cM, but the second is greater.

Note that if two known relatives match a third party, the match is more significant (indicative of a closer relationship) if the half-identical regions are non-overlapping. Conversely, if two unconfirmed relatives match a third party, the match is more significant (indicative of an ancestor common to all three people) if the half-identical regions are overlapping; otherwise, the two relationships might be on opposite sides, or the half-identical regions might be only half-identical by chance.

A similar formula is easily derived for the case where n siblings are being compared to a single possible relative. Let l(i) denote the aggregate length of the regions on which exactly i of the n siblings are half-identical to the possible relative. Let f(i,n)=ⁿC_i*2^-n denote the probability of i successes in n binomial trials where the probability of a success in each trial is 50%. We have n separate estimates of the unobservable l(0), namely l(i)*f(0,n)/f(i,n)=l(i)/ⁿC_i for i=1,2,...n. The best estimate of the unobservable l(0) is the simple average of these n separate estimates.

The estimation becomes a little more intricate when DNA from multiple siblings on each side of the brick wall is available for analysis. It becomes more intricate again if we move back another generation and want to estimate the shared cM between the deceased grandparent of two living cousin groups and a possible relative. The segments shared by the grandparent and the possible relative can be broken down into the following categories:

• segments shared with the possible relative by one or more children in both families
• segments shared with the possible relative by one or more children in exactly one of the families
• segments shared with the possible relative by the parents of both families but not by any of the grandchildren
• segments shared with the possible relative by exactly one of the parents of the families but not by any of the grandchildren
• segments shared with the possible relative by the grandparent but not by either of his or her children

The first two categories can be measured. The last three have to be estimated using a similar methodology to that already used when going back just one generation. [A little more thought will be required to come up with a sensible methodology here.]

If you and/or your suspected relative have no siblings or members of an earlier generation available for sampling, or have already sampled all available siblings and want to move out to first cousins, then start with one cousin from each family. If an uncle by chance inherited less autosomal DNA than expected from the relevant side of the family, then his children can all be expected to have also inherited less autosomal DNA than otherwise expected from that side of the family. In other words, the information supplied by the DNA from two of his children is not independent in the same way as that supplied by two first cousins would be.

For this reason, if you are sure that your suspected relative is from your maternal side rather than from your paternal side, then you will actually learn more by sampling your maternal first cousins (one from each family) than by sampling your own siblings.

If funds extend to sampling multiple first cousins from different family groups, similar principles apply. Suppose Beatrice, Thomas (Jr.), Martin, Catherine and Anne, all now deceased, were siblings, children of Thomas (Sr.) and Mary, but you have DNA samples from three of Beatrice's children, five of Thomas's children, one of Martin's children, one of Catherine's children, and two of Anne's children. Let's suppose we want to investigate how Thomas (Sr.) or Mary was related to Anthea. First we estimate Beatrice's relationship to Anthea by averaging the Shared cM for Beatrice's three children, then doubling the result (since each child is expected to have inherited half of Beatrice's Shared cM). Similarly, average the Shared cM for Thomas (Jr.)'s and Anne's children and double the results, and double the Shared cM for Martin's child and Catherine's child. Now we have five independent estimates of the expected Shared cM between Anthea and the children of Thomas (Sr.) and Mary. Again just average these five estimates and double the result to estimate the Shared cM between Anthea and whichever of Thomas (Sr.) and Mary is related to her. If this Shared cM figure is not high enough to prove that Anthea is a direct descendant of Thomas (Sr.) and Mary, then further evidence (following the bisection strategy above) will be required to determine whether the relationship is on Thomas (Sr.) 's side or Mary's side.

In the same way as we can now combine Shared cM data for many descendants of a long-dead ancestor to estimate that long-dead ancestor's relationship to a living person, we could potentially combine the observed genome or SNPs of many descendants of the long-dead ancestor to estimate the genome of that ancestor. Blaine Bettinger takes this idea much further in his blog post Genetic Genealogy in 2050 (or Maybe 2015?).

The other-types-of-DNA strategy

If there is a choice between equally related individuals, always choose someone who might share X-DNA with someone whose DNA has already been sampled over someone who cannot. Within those who might share X-DNA, choose a male, who has only one X chromosome.

For example, I have two paternal first cousins, my uncle's daughter and my aunt's son. The uncle and aunt are both long deceased, so not available for sampling. My uncle's daughter has two X chromosomes: one on her mother's side which is of no interest to me; the other on her father's side, which comes from my paternal grandmother's parents (McNamara and Clancy). My aunt's son has one X chromosome, which comes from my paternal (his maternal) grandparents (Waldron and McNamara). If I was interested in investigating a relationship on the Clancy side, then I should get a sample from my uncle's daughter. If I was interested in investigating a relationship on the Waldron side, then I should get a sample from my aunt's son. Otherwise, my aunt's son's DNA will be more useful, as his mitochondrial DNA traces back to the mother of the four Galvin sisters and their Kelly half-sister, who founded an enormous dynasty of direct female line descendants.

On the other side, I have nine living maternal first cousins, all uncle's children, five male and four female. The males get their X-DNA from their mothers, who are not related to me. The females are my X cousins, so their samples are of more interest to me. One of them is an only child, so is the obvious candidate to sample first.

Ultimately, using X-DNA allows one to see whether the possible ancestor might be narrowed down to the sets of people from whom each individual inherits X-DNA. If the two autosomal matches are X-DNA matches and either of them is male, then a relationship on the paternal side (and on any line involving two males in consecutive generations) can immediately be ruled out.

Using X-DNA to further one's analysis involves no extra cost; using Y-DNA or mtDNA will require an extra payment. Once that extra payment has been made, it is relatively straightforward to use Y-DNA or mitochondrial DNA to investigate whether the relationship being investigated might be on the direct male line or on the direct female line.

What to do before and after results for your paternal and maternal relatives arrive

I eventually decided to follow the bisection strategy outlined above.

On 23 February 2014, I convinced two first cousins, my father's sister's son Antoin and my mother's brother's daughter Mary, to allow me to order Family Finder for them. As they live outside the USA, there was really no choice about which DNA company to use: ancestry.com still refused at that time to take orders from anywhere outside the USA and 23AndMe imposes exorbitant shipping charges which are far better spent on having an extra person's DNA analysed by FamilyTreeDNA.

If you already have a FamilyTreeDNA account and want to order a kit for another person:

• go to https://www.familytreedna.com/
• enter your Kit No. or Username and Password and LOG IN
• go back to https://www.familytreedna.com/
• select the link to go to https://www.familytreedna.com/family-finder-compare.aspx
• select the Add to cart link which will generate a pop-up menu comprising your existing kit number and "Kit #2"; select the latter
• You will have at least one coupon for uploading your GEDCOM, so select the "Do you have a coupon?" link at the bottom right and copy and paste Your Coupon Code from the e-mail generated when you uploaded your GEDCOM.
• select Apply.
• If you have uploaded your GEDCOM more than once, either because you have learned new information, or because you were unable to discover which character set FTDNA expects your GEDCOM to use, then you will have multiple coupons, but it appears to be possible to use only one coupon per order.
• In the top middle, "Select this tester's gender" by ticking the relevant radio button.
• Proceed to checkout.
• Your billing address will already be filled in; select Edit at the bottom right to fill in the shipping address for your relative (and Save), and complete the Payment Method section at the bottom left (and Accept Terms & Complete Purchase).
• This gives you a new kit number; log out and log in again to the new kit to prepare your relative's profile.

Neither of my first cousins was interested enough to want their own e-mail address or telephone number used! So I immediately received their kit numbers and passwords. What next?

While waiting for DNA results to arrive from FamilyTreeDNA, the following steps need to be taken. You will want to make an immediate impression on your DNA matches, so it is too late to do this after the results arrive. You can keep an eye on your Order History page to see when you should expect to receive your results. Sometimes the results begin to appear on the website a day or two before e-mail notification arrives.

1. Once you have a kit number and password, fill in the FTDNA personal profile for the DNA subject.  If there is no password in the first e-mail that you receive from FamilyTreeDNA, then you can reset the password from the Forgot Your Password? page.
   1. The most important things to complete is the Genealogy section. Remember that the request for Most Distant Ancestors (Direct Paternal and Direct Maternal) is a request for the earliest known patrilineal ancestor (the father's father's father's line, from which the subject's Y-DNA has come, or would have come if she was not female) and the earliest known matrilineal ancestor (the mother's mother's mother's line, from which the DNA subject's mitochondrial DNA has come), and that you have to squeeze names, dates, places and comments into for each into a 50-character string.
   2. There is no need to complete the Surnames section manually, as this will be populated automatically when you upload a GEDCOM file.
   3. Compile a GEDCOM file showing the DNA subject's ancestors on all sides and use the Upload GEDCOM link under your kit number at the top right hand corner of the myFamilyTree page to upload it. If you are not dealing with your own DNA, remember that the DNA subject's FTDNA-overall-matches can be expected to include not just your mutual relatives but also people related to the DNA subject on the other side of his or her family. As a courtesy to such people, you should include as much information as you can for that side of the family. In my case, this was not a burden, as I have worked with the cousins who provided DNA samples on both sides of their family trees in the past. (In one case, the relevant files had to be recovered from a very old computer!)
      I use Ancestral Quest to create GEDCOMs. There are lots of options provided. I got absoutely no help from the FTDNA website, FTDNA forums, FTDNA facebook page or FTDNA e-mail support in my efforts to work out what options to choose. By a lengthy and tedious process of trial and error, I initially discovered that setting 'Export for import into:' to 'Other' and 'Char Set' to 'ANSI' allowed accented vowels in names to be displayed correctly. Then FTDNA changed the entire family tree interface, and it took another year or more to learn by trial and error that setting 'Char Set' to UTF-8 now worked.
      GEDmatch.com specified clearly: "if your genealogy software has an option to select 'character encoding', use 'UTF-8'. Otherwise, some non-english characters may not display properly."
      I also discovered that anyone logged into the FTDNA website can see my own GEDCOM, whether or not deemed to match my DNA.
   4. I recommend that the "About Me" field be used to direct people to a web page, such as this one, in which you lay out your standard reply to anyone tempted to contact you.
   5. Find and upload a nice headshot photograph of the DNA subject (with his or her approval).
2. Register at GEDmatch.com and DNAgedcom.com if you have not already done so. You can manage multiple kits from a single account on each of these sites.
3. Join the relevant FamilyTreeDNA projects, both surname projects (e.g Chambers/Chalmers) and geographical projects (e.g. Clare Roots project, for anyone with roots in County Clare, Ireland). If there is no project for your surname, you can always start one.
4. Make a list (with GEDmatch Kit Numbers and e-mail addresses) of the groups of known relatives in each of the following categories who have already submitted DNA samples and with whom you will want to compare the results when they arrive:
   1. your known relatives (starting with yourself);
   2. your probable relatives (known to you outside of genetic genealogy); and
   3. your possible relatives (discovered through genetic genealogy).
5. While waiting for results for paternal and maternal relatives, check whether your paternal and maternal relatives might be related to each other:
   
   1. One of GEDmatch.com's data analysis tools is "Are your parents related?"
      For me, this clearly reported no "segment of SNPs with greater than 500 matches".
      However, GEDmatch only tells you that you did not inherit any segment that was shared by your father and mother from both of them.  If both parents shared a segment, there is only a 25% chance that you inherited the shared segment from both of them.  So there is a huge difference between finding no evidence in your DNA that your parents were related and your parents actually being unrelated.
   2. A more sophisticated tool is David Pike's Search for Runs of Homozygosity. For me, this found a longest run of homozygosity in SNPs of length 480, from position 30087558 to position 30424959 (0.34Mb, 0.01cM) on Chromosome 6, and a longest run of homozygosity in base pairs of length 215, from position 46962428 to position 48550157 (1.59Mb, 1.38cM) on Chromosome 19. The lengths in centiMorgans are not reported by David Pike's own tool, but can be calculated using the GEDmatch Genetic Distance Calculation, also called the centiMorgan Calculator. It would be too tedious to search manually for the longest run of homozygosity in centiMorgans.
      David Pike also has a complementary Search for Heterozygous Sequences. For me, this found a longest run of heterozygosity of only 18 SNPs, from position 33161660 to position 33166752 (0.01Mb) on Chromosome 6, too small for the centiMorgan Calculator to measure.
      The difference in the lengths of the longest runs of homozygosity and heterozygosity is staggering. Clearly homozygosity is not independent from one SNP to the next. If it were, given that I am homozygous at 70.403% of SNPs, then a run of 18 heterozygous SNPs would have a probability of the order of 10^-10 but a run of 480 homozygous SNPs would have a probability of the order of 10^-72.
      Although the GEDmatch threshold is 500SNPs, the figure of 480 got me wondering whether my parents might be related. After all, both were from Ireland, where the population has been small enough that I estimated that the probability that any two randomly selected Irish people are 12th cousins or more closely related is 95%.

After the results arrive for each person:

1. Upload the raw data files for the new kits to GEDmatch.com; you need to do this only once, but remember that the hyperlinks below probably wont work.
   1. Login to your existing GEDmatch.com account
   2. In the middle column of the home page, open in a new tab the links to FTDNA Family Finder and FTDNA X-DNA and follow the instructions given.
2. Download the match files from FamilyTreeDNA.com to DNAgedcom.com; you need to repeat this periodically as new matches appear at FamilyTreeDNA.com.
3. Generate an ADSA report at DNAgedcom.com.
4. Start comparing with your prepared list. For each person:
   1. Do a one-to-one comparison with the relevant kit numbers at GEDmatch.com and copy the segment details to your segments spreadsheet.
   2. Search the ADSA report for the e-mail address and note in particular the segments where two half-related people on one side of a genealogical brick wall are both half-identical to two half-related people on the other side of the genealogical brick wall.

An example

GEDmatch estimates that my parents were not related to each other, so I had no reason to expect that my first cousins Antoin and Mary would be related to each other. However, GEDmatch reports that they share numerous half-identical regions, the longest in cM being 4.3cM on Chromosome 12 and the longest in SNPs being 958 on Chromosome 3. In fact, each of us is half-identical to the other two on a region of 4.28cM and 584SNPs comprising most of the afore-mentioned region on Chromosome 12. Standard triangulation arguments would deduce that all three of us have a common ancestral couple, and thus that my parents were indeed related.

Another example

As mentioned above, my first known relative to give a DNA sample was my fifth cousin Cindy. We don't share an awful lot of autosomal DNA. GEDmatch.com, with its then default settings, reported these four half-identical regions:

The first thought that crossed my mind was to search for other people who may have inherited any such identical segments from the same Keas or O'Halloran ancestors.

I decided to start with the longest half-identical region on the centiMorgan scale (the one on chromosome 8) and the longest half-identical region on the SNP scale (the one on chromosome 14), in the hope of finding someone half-identical to both of us in both regions. I opened GEDmatch.com in four browser tabs and started the Find people who match with you on a specified segment process in each tab - two for Cindy and two for me; two for the region on chromosome 8, two for the region on chromosome 14. (GEDmatch.com has since removed this process as it placed too heavy a load on its servers.) The maximum number of hits that can be returned by each process is 301, and three of the four ran into this limit.

This procedure eventually identified:

• one person who is half-identical to me (but not Cindy) in both regions but who doesn't provide an e-mail address;
• one person with two separate 23AndMe kits who is half-identical to both of us on chromosome 14;
• one person with two separate 23AndMe kits who is half-identical to both of us on chromosome 8;
• one person with separate 23AndMe and Ancestry kits who is half-identical to both of us on chromosome 8;
• one person with kits from all three companies who is half-identical to both of us on chromosome 8;
• one e-mail address with FamilyTreeDNA and Ancestry kits with different pseudonyms (LAD45 and JoanHat) which are both half-identical to both of us on chromosome 8; and
• 23 other kits which are half-identical to both of us on chromosome 8.

Which, if any, of these should I approach about comparing paper trails?

The two kits with the same e-mail address seemed the most promising, as the chance of being half-identical by chance would be greatly reduced if they were only half-related. However, the total of segments > 3 cM shared by these two kits is 2,799.2 cM which suggests that they are siblings. The GEDmatch expanded graphic confirms that they are full-identical in the region of interest, so the second kit adds nothing to the information provided by the first kit.

The vast difference between the numbers who match with us on regions of 875 and 1,177 SNPs suggests that many half-identical regions of 875 SNPs or fewer must be merely half-identical by chance.

What I do when a possible relative's data has been processed by GEDmatch.com

I have slowly evolved this regular manual procedure. I really must automate it, but full automation will be prevented by GEDmatch.com's login policy.

• add the new person to my GEDmatch.xlsx spreadsheet and note the GEDmatch kit number in my Ancestral Quest notes
• one-to-one compare new person at 1cM/500SNP thresholds with myself and all my known relatives who are already at GEDCOM (Copying and pastings URLs for this generated within the spreadsheet worked briefly, but GEDmatch policy then changed and it is now necessary to fill in four fields in the form manually for every comparison.)
• copy and paste matching segments and total of segments to my Segments.xlsx spreadsheet (and fill additional columns using an Excel macro)
• sort spreadsheet by chr, start, end
• for each known relative, filter Kit1 and Kit2 columns to show myself, new person and known relatives
• eyeball the start and end columns to identify regions where all three are each half-identical to the other two
• copy and paste the relevant three rows to a new spreadsheet named PaddyNewpersonEtAl.xlsx
• if the GEDmatch centiMorgan calculator is up, calculate the lengths of the three-way overlaps in cM using the GEDmatch cM calculator
• calculate the lengths of the three-way overlaps in FTDNA SNPs by manually searching for the start and end locations using TextPad in my own Build 36 Autosomal Raw Data (which I have saved at C:\pwaldron\GENEALOG\Genetics\Data\310654-autosomal-o36-results.csv, all 23,025KB of it; for some kits, this is the default file name, but for others the default file name is ffo followed by a very long and meaningless string of dashes and hexadecimal digits)
• [This SNP-counting is a bit mysterious; I noticed that a region where my first cousin and I are half-identical is described by GEDmatch as Chromosome 6, Start 25,059,788, End 29,813,667, 2.0cM, 2400 SNPs; but when I looked at our raw data I found that there are not 2,400 but 2,440 SNPs between the start and end locations where both of us have clean data, plus another 41 SNPs where one or other of us has a no-read.]
• More importantly, count the number of SNPs in the overlap at which I and the other person are both homozygous, and so not guaranteed to be half-identical to everyone (there is no easy way to do this at the moment; in principle, I could do it in Excel, but Excel is tediously slow on my top-of-the-range 2012 laptop when handling files of the size of autosomal DNA raw data files.)
• forward spreadsheet to new person

Strategy to be followed by two people who have found a common ancestral couple and half-identical regions of DNA

Two people who have found a common ancestral couple and half-identical regions of DNA will naturally want to progress their research further, both in traditional genealogy and in genetic genealogy. This section will address how they can make progress in genetic genealogy. The following steps are suggested:

1. Find others in both the FTDNA and GEDmatch databases who are deemed to be overall matches to both. This is a prerequisite to Step 2, which will narrow down the list considerably.

   GEDmatch

   Run 'People who match one or both of 2 kits' for each pair of descendants of the common ancestral couple.

   Run 'One-to-one' compare for the new matches found with each of the known relatives.

   FTDNA

   If the two known relatives are FTDNA-overall-matches, then an ICW list is readily available; otherwise, the ICW list must be generated manually.

   In the process of running the ADSA at DNAGedcom.com, each person will have created a file named xxxxxx_Family_Finder_Matches.csv (where xxxxxx is the relevant kit number). An equivalent file can be generated by selecting the Excel button at the bottom right corner of the Matches page. If each person copies the first column (Full Name) from this file, some crude copying and pasting to a Microsoft Excel spreadsheet and use of the VLOOKUP() function will reveal kit numbers which are on both lists.

2. Find others in both the FTDNA and GEDmatch databases who are half-identical to both on the same regions. The people found in the first step are possibly related to both of you through different common ancestors. Those who are half-identical to you on the same regions are extremely likely to be related to you through the same most recent common ancestral couple.
   

   GEDmatch

   [The full GEDmatch.com service was down at the time of writing.]

   FTDNA

   In the process of running the ADSA at DNAGedcom.com, each person will have created a file named xxxxxx_ChromsomeBrowser.csv (where xxxxxx is the relevant kit number). Filter these files to pick out first the people who FTDNA-overall-match both of you, and then the chromosomes on which you match each other. Look for overlapping regions. For each region, you need to filter for regions which either start before your shared region starts and end after your shared region starts, or regions which start before your shared region ends and end after your shared region ends. It should be possible to write a Microsoft Excel macro to do this.

Form letter for first contact with a possible relative (not at ancestry.com)

Dear Charles

I found your e-mail address at FamilyTreeDNA.com (where I am Patrick Joseph Martin Waldron)/GEDmatch.com (where my kit number is F310654) and I believe that we may be related.

Our autosomal DNA is half-identical on the following region(s):

Furthermore, we are part of a group of three people, also including ..., who are each half-identical to the others on the ... of these regions.

I have uploaded a copy of my family tree database (as it was on 24 Feb 2014, minus the details of living people) to

http://pwaldron.info/tng/

You can Register for a User Account at

http://pwaldron.info/tng/newacctform.php

Furthermore, ... and I are known relatives (9th cousins twice removed). Our most recent common ancestral couple are Richard Blackall and his wife (whose maiden name was also Blackall). Richard came to Ireland from England during the reign of Charles I of England (1625/1649) and settled in county Limerick.

... and I have another possible but unconfirmed relationship through Robert Blakeney (d.1658/60) and his wife Susannah Ormsby (d.1659) of Castle Blakeney, county Galway; if that is confirmed, then it would also make us ninth cousins twice removed.

Once I have approved your registration on my TNG website, you will be able to see exactly how ...'s GGGGGuncle and I are related at

http://pwaldron.info/tng/relationship.php?secondpersonID=I1&primarypersonID=I11731

and how ...'s GGGGGuncle and my possible GGGGuncle are related at

http://pwaldron.info/tng/relationship.php?secondpersonID=I33441&primarypersonID=I11731

from where you can navigate around the tree and look for a possible link to your own known ancestry.

In ...'s version of the family tree, he is at

http://trees.ancestry.com/tree/6240035/person/-1324643958

the son of our common ancestral couple is at

http://trees.ancestry.com/tree/6240035/person/7017465396

and the grandson of our other possible common ancestral couple is at

http://trees.ancestry.com/tree/6240035/person/24046251078

I have looked at your GEDCOM file at FamilyTreeDNA.com/GEDmatch.com. I have (not) found any common ancestor.

/Where can I see your family tree so that I can search for our possible common ancestral couple?

I have four known relatives whose DNA is, or shortly will be, available for comparison:

• my paternal first cousin ... (GEDmatch kit number ...);
• my maternal first cousin ... (GEDmatch kit number ...);
• my paternal fifth cousin ... (GEDmatch kit number ...); and of course
• my ninth cousin twice removed ... (GEDmatch kit number ...).

What known relatives do you have whose DNA is available for comparison? If you don't have any yet, I recommend that you encourage at least one paternal relative (if still living, a paternal grandparent, greatuncle or greataunt, father or paternal cousin) and at least one maternal relative (if still living, a maternal grandparent, greatuncle or greataunt, mother or maternal cousin) to submit a DNA sample for analysis.

If you have not already copied your DNA data to GEDmatch.com, I recommend that you do so. I also recommend the Autosomal DNA Segment Analyzer at

http://www.dnagedcom.com/adsa/

and my own account of my experiences with autosomal DNA at

http://pwaldron.info/newdna.html

Yours sincerely

Paddy Waldron

Form letter for first contact with a known relative at ancestry.com

Dear John

You show up as a DNA match to your fourth cousin Paddy Waldron, whose AncestryDNA kit I manage, as I am his cousin on the other side of his family.

He also has his DNA at FamilyTreeDNA.com and GEDmatch.com and would love to hear from you directly by e-mail at ...

He has a vast amount of information on your common McNamara ancestors which he will be delighted to share.

Form letter for second contact with a known relative at ancestry.com

Dear John

I am very anxious to look more closely at our shared DNA segments and see what we can learn from them about our ancestors and other common relatives, but first let's share what we know of our common ancestors.

You might enjoy the account of how I became aware of my relationship to the Kunzmann family through the Talty Millions case, at

http://pwaldron.info/oks/

http://pwaldron.info/tng/

You can Register for a User Account at

http://pwaldron.info/tng/newacctform.php

Once I have approved your registration on my TNG website, you will be able to see exactly how we are related at

http://pwaldron.info/tng/relationship.php?secondpersonID=I1&primarypersonID=I61141

from where you can navigate around the tree.

I have looked at your own family tree at

http://trees.ancestry.com/tree/79437082/family?cfpid=34401375965

We have two other known mutual relatives whose DNA is available for comparison at GEDmatch.com and FamilyTreeDNA.com but not at Ancestry.com

• my paternal first cousin ... (GEDmatch kit number F335377); and
• our fourth cousin twice removed ... (GEDmatch kit number F221835).

What other known relatives do you have whose DNA is available for comparison? If you don't have any yet, I recommend that you encourage at least one paternal relative (if still living, a paternal grandparent, greatuncle or greataunt, father or paternal cousin) and at least one maternal relative (if still living, a maternal grandparent, greatuncle or greataunt, mother or maternal cousin) to submit a DNA sample for analysis.

If you have not already copied your DNA data to GEDmatch.com, I strongly recommend that you do so. I also recommend my own account of my experiences with autosomal DNA at

http://pwaldron.info/newdna.html

I will do my best to answer any other questions that you may have about our common ancestors or about DNA.

Yours sincerely

Paddy Waldron

Form letter for reply to first contact from a possible relative

Dear Nancy

Thank you for your e-mail about our possible DNA match.

You neglected to mention in your e-mail which of the many DNA kits associated with this e-mail address on several different websites you are writing about.

First, we need to know each other's GEDmatch.com kit numbers.

I used the GEDmatch User Lookup tool to search for your kit number(s), but it does not recognise your e-mail address. What is your GEDmatch.com kit number?

You can use the same tool if you need a reminder of the long list of kit numbers associated with this e-mail address. Which of them do you match?

Second, we need to see each other's online pedigree charts.

My own is at

http://pwaldron.info/tng/pedigreetext.php?personID=I1&generations=5

In order to see it, you will have to first register at

http://pwaldron.info/tng/newacctform.php

and then wait for an e-mail confirming that I have approved your registration.

Where is your online pedigree chart?

Finally, you may find the answers to other questions that you might want to ask me about DNA testing on my website, starting at

http://pwaldron.info/DNA/nextstep.html

Best wishes

Paddy Waldron

For my further thoughts on this subject, see Measuring the length, the rarity and the relevance of pieces of shared autosomal DNA.

My own online family tree is at http://pwaldron.info/tng/index.php but to see it you will have to Register for a New TNG User Account.

Comments about this page can be left on the facebook posts where I originally announced Chapter 1 and Chapter 2.