Autosomal DNA triangulation. Part 2: the phenomenon of triangulated segments

In the first article in this two-part series I covered the basics of autosomal DNA inheritance and how triangulation can be successfully used to assign segments to specific ancestors within the last five generations or so in combination with chromosome mapping. I'm now going to take a look at the interesting phenomenon of "triangulated segments" – segments of DNA that are shared in common with multiple people.

We would naturally expect several of our close relatives (grandparents, aunts and uncles, and first cousins) to share some segments in common but once you get out to the fifth or sixth cousin level the chances of sharing any DNA with a specific cousin are very low. If you do match a fifth cousin or a more distant cousin you would only expect to share a single IBD segment.  Despite the low odds, because we have so many distant cousins, we will inevitably find some rare examples of people who match three or more fifth cousins who are descended from the same ancestral couple. This is much more likely to happen if the couple had a large family and their descendants also went on to have lots of children. However, because we all inherit different combinations of segments of DNA from our ancestors you would expect to match other fifth and sixth cousins on different segments rather than all on the same segment. We all inherit different pieces of our ancestors' genetic jigsaw puzzle rather than all sharing the same piece.

While I'm not aware of any scientific papers that have studied the frequency of triangulated segments, AncestryDNA have done some interesting computer simulations which shed some light on the matter. They found that a group of three first cousins shared a matching segment of over 5 cMs in length over 80% of the time. Three second cousins shared the same segment around 60% of the time, but for for third cousins the rate was just 15%. The chances that three fourth cousins would all share the same matching segment were found to be around 1% (see figure below). From this we can infer that it would be similarly extremely unlikely for three or more fifth, sixth or more distant cousins all to match on the same segment through IBD descent from a specific ancestor. This of course assumes that they have inherited enough DNA from their mutual ancestor to show up as a match at all.

Figure reproduced by kind permission of Ancestry DNA from the customer help article
 "Do all members of a DNA Circle share the same matching segment?

The results of the AncestryDNA simulations have been replicated in the real-life findings from their DNA Circles feature. They say:

Data we've gathered from our DNA Circles also shows that it is unlikely to find matching segments among three or more people. Only 4 percent of DNA Circles (that have between 3 and 30 members) have three or more people that share the same matching segment. In the remaining 96 percent of DNA Circles, no more than two people in the Circle share any one particular segment. In other words, even in DNA Circles with 30 descendants, usually only two or three descendants will all inherit the same segment.¹

The results of the AncestryDNA research into triangulated segments has not been published in a peer-reviewed scientific journal. We don't know the assumptions that were made in the models and we have to accept the results in good faith. We also don't have access to the shared segment data for our matches at AncestryDNA so that the findings can be independently verified. However, AncestryDNA do have a good team of scientists working for them. I'm also not aware of any credible research that has disproved their findings.

In contradiction to what we might expect from the AncestryDNA findings, there is a lot of anecdotal evidence that people are seeing lots of matches which all fall on the same segment on the same chromosome. We don't have much data on the extent of the phenomenon in terms of the number of people in each "triangulated group" and the size of the segments that they share. The situation is also complicated because each company has a different matching threshold, which means that we might not see the full extent of the problem.

The hypothesis has been proposed that if multiple people share the same segment and they all match each other then they must all share a recent genealogical ancestor. It is then just a question of comparing family trees and trying to find surnames in common. If you match lots of people on the same segment this process of "triangulation" should in theory be fairly straightforward because it's just a question of looking for recurring surnames and locations in common, and the more family trees you have to compare the easier this should be. However, there are many pitfalls with this approach as we will see.

When I look at my own data I can see that on every chromosome I have at least one segment where I appear to match multiple people. This scenario is best visualised by using Don Worth's Autosomal DNA Segment Analyser, a free utility which is available from the DNAGedcom website. ADSA uses the "in common with" files from Family Tree DNA. This is not "true" triangulation, which requires checking that the people you match also match each other. However, it is in most cases a pretty reasonable approximation. The screenshot below shows the most extreme example from my own data which occurs on chromosome 18. As can be seen, I have a big group of people who all overlap in the same region, though the amount of sharing is quite small and in most cases under 10 cMs. (On the ADSA diagram below my mum's sharing is shown in black and my dad is shown in pink.)

However, I have not been able to identify a common ancestor or even a common surname with any of the people in my own "triangulated groups". It doesn't help that most of the people in these groups are in America with all-American ancestry and no indication of places of origin in the UK. I do have some known relatives who emigrated to America and Canada in the nineteenth and twentieth centuries but I have not come across any other emigrants further back in my family tree. You would have thought that if I was related to lots of people who had emigrated to America in the last 400 years it would have been possible to identify at least some of the connections. This rather suggests to me that if these segments are IBD, they are a signal of very distant shared ancestry that perhaps predates the colonisation of America. I have one triangulated group that looks distinctly Irish in flavour, and I do have some Irish ancestry but Irish research prior to 1800 is difficult at the best of times and especially so when the only surname you've identified is Sullivan!

My own "triangulated segments" are all quite small, but there is anecdotal evidence of people who have matches with large numbers of people on the same segments and where the shared segments are much larger than the ones I'm seeing. Some people have observed "triangulated groups" with segments over 20 cMs in size, which in theory should be more recent in origin and where it should be much easier to identify a common ancestor. But if it really is so difficult for three or more fourth, fifth or distant cousins to match on the same segment why is that we are seeing so many examples of this happening? I can offer a few suggestions that might help explain this phenomenon.  

Lack of phasing
The first difficulty when considering our matches is that our data at Family Tree DNA and 23andMe is not phased. Phasing is the process of sorting out the DNA letters we receive from our parents and assigning them to the maternal and paternal chromosomes. Our autosomal chromosomes come in pairs. We receive one set of 22 autosomes from our mum and another set from our dad. If you look at your raw data you'll see that for each chromosome you have a long list of As, Cs, Ts and Gs divided into two columns. However, the columns with our data for each chromosome aren't conveniently sorted so that all the DNA letters in one column represent all the letters you got from your dad and all the letters in the other column are the letters you got from your mum. The letters are all jumbled up so both columns are a mishmash of all the As, Cs, Ts and Gs that you get from both your parents. The computer algorithms are looking for consecutive runs of As, Cs, Ts and Gs that all match each other but they're looking in both columns to find the matches. If the algorithms find enough matching letters in a run then we can be reasonably certain that the segment is IBD – a true match inherited through successive unbroken generations from grandparent, to child to grandchild and so on. Strictly speaking what we are seeing are not segments of DNA but sets of alleles that form haplotypes.

Phasing matters most with the smaller segments under 15 cMs where there is a law of diminishing returns. As the segments get smaller the chances that the segments will be false positive pseudosegments (mishmashes of As, Cs, Ts and Gs from both the maternal and paternal chromosome) will tend to increase. Independent research from genetic genealogists suggests that 15 cM is the threshold where segments can be assumed to be IBD with reasonable confidence, whereas only 42% of 7 cM segments are likely to be IBD. Even when phasing is done there is still the possibility of false matches with the smaller segments. A study by Durand et al (2014) found that over 67% of phased 2-4 cM segments were false positives (matches found in the child but not in the parents).²

The most accurate phasing is done with parent/child trios. There are various computer programs and third-party tools that will do this (eg, the GedMatch tools and David Pike's tools). However, this sort of analysis is something that only the most advanced genetic genealogists are likely to undertake, and even if you were to phase your own data none of the companies currently provide the facility for you to use a phased genotype. It is also possible to do algorithm-based phasing from reference sequences, and this can be done with a very high degree of accuracy. AncestryDNA use this type of population-based approach, but they have developed their own sophisticated proprietary program. The error rate for the AncestryDNA phasing engine is only about 1% when compared with parent/child trios. However, phasing is computationally challenging and expensive, and AncestryDNA are currently the only company who are able to do this. In theory the matches we get from AncestryDNA should be much more accurate than the matches we get from 23andMe and Family Tree DNA.

It has been suggested that segments which "triangulate" must be IBD but I see no rationale for this assumption and, to the best of my knowledge, this hypothesis has not been tested. We already know that some small segments don't triangulate with close relatives. I have some examples in my blog post on Tracking DNA segments through time and space. If this can happen with small segments perhaps it can also happen with large segments too.

Genotypes versus whole genome sequencing
The second point we have to consider is that the currently available autosomal DNA tests are not sequencing all six billion DNA letters in our genomes. The testing is done on an Illumina chip which looks at around 700,000 different letters scattered across the genome.³ This process is known as genotyping. The Illumina chip that all the companies use was designed for health purposes and not for genealogy. The SNPs that are included are those that are useful for genome-wide association studies (GWAS) where the goal is to look for SNPs shared at the population level not SNPs that are shared at the family level. The density of SNPs on the chip varies and some regions are better covered than others. Segments containing rare alleles are much easier to identify than segments with alleles which have a high frequency in the population. The segments that are used for matching purposes in autosomal DNA tests do not therefore provide a complete sequence of all the letters in the "segment" but merely a run of consecutive SNPs with many missing intervening letters. This introduces the possibility of errors, particularly for shorter segments. In addition, two separate segments could be stitched together to give the appearance of one single segment because the intervening SNPs that might break up the sequence aren't on the chip.

Shared descent through multiple ancestral pathways
We saw in my previous blog post how pedigree collapse and endogamy can affect relationship predictions within recent generations but pedigree collapse and endogamy affect all our family trees sooner or later. We are all endogamous. It is just a matter of degree. The number of ancestors doubles with every generation. You only have to go back 20 generations before you find that you theoretically have 1,048,576 genealogical ancestors. You eventually reach a point where your theoretical number of ancestors exceeds the entire number of people who have ever lived on the planet. We have a world population of over seven billion people but we all trace our ancestors back to a historical population of just one billion in 1850.

What this means in practice is that everybody is related to everybody else and we are all related much more recently than we intuitively realise. For many people this endogamy will not be documented in their family trees. The only example I can find in my own family tree of two ancestors who were already related when they married dates back to the late seventeenth century in North Molton, Devon. My ggggggg-grandparents Daniel Locke and Mary Bright were first cousins when they married in 1667. However, even though I cannot trace all the distant relationships it is an escapable fact that all my ancestors who were marrying in rural villages in Devon, Somerset, Gloucestershire, Essex and Hertfordshire back in the 1700s must have been closely related to each other and were probably third, fourth, fifth and more distant cousins many times over. I also have lots of London ancestors and they would be more distantly related because of the sheer size of the London population and the fact that people migrated to London from all over Britain and elsewhere. Eventually all our ancestral lines will come together in a tangled and complex network of relationships connected on many different pathways. To get an idea of what our collapsed pedigrees might look like have a look at this wonderful 80-generation pedigree chart for a border collie dog showing 90% pedigree collapse.

Two peer-reviewed papers studying present-day populations have confirmed the mathematical predictions of  our ubiquitous recent shared ancestry. Henn et al (2012) found tens of thousands of 2nd to 9th degree cousin pairs within a dataset of 5,000 Europeans. They also found that some highly endogamous populations such as Native Americans and the Kalash of Pakistan were effectively the genomic equivalents of second cousins.⁴ Ralph and Coop (2013) studied genomic data for a population of 2,257 Europeans. The found that "a pair of modern Europeans living in neighboring populations share around 2-12 genetic common ancestors from the last 1,500 years, and upwards of 100 genetic ancestors from the previous 1,000 years".⁵

These findings have also been replicated by AncestryDNA who found that their customers who are in DNA Circles were getting roughly the expected number of matches four and five generations ago with third and fourth cousins but progressively more matches than would be expected  with fifth and sixth cousins six and seven generations ago.

Figure reproduced by kind permission of AncestryDNA from the customer help article
 "Why do DNA Circles only go back six generations?"

AncestryDNA conclude:

Our research shows that descendants of an ancestor who lived more than six generations ago have more DNA in common with other descendants of that ancestor than they’d be expected to. This discrepancy increases the more generations you go back in time and suggests that descendants are actually related through multiple ancestors.⁶

If researchers are seeing such relatively high levels of IBD sharing in the present-day population we can assume that 300 years ago, when we trace back to a very much smaller population, everyone must have been much more closely related than we are today. We don't have a time machine so that we can travel back to the 1700s and get autosomal DNA tests done on all 1024 of our gggggggg grandparents. However, if we could, we might expect that a very high percentage of our ancestors would show up as matches to each other with many of the relationships being as close as fourth, third or second cousins. The effect would be compounded by the fact that the ancestral population of Europe went through an extreme genetic bottleneck in the fourteenth century when the Black Death wiped out over half of the population of Europe. The cumulative effect of this population structure is that the genomes of our ancestors 300 years ago would perhaps have the same characteristics as that of a highly endogamous population today. They would share more segments in common than would be expected for the degree of relationship and, if many of those ancestors were second or third cousins, then a number of them might be expected to match on the same segment. If there were lots segments shared by many people in the historical population then it's easy to understand how these segments could also be found in their descendants today, but these segments would be passed on through a variety of different pathways, making it very difficult, if not impossible, to determine the individual lines of descent.

As an example, if you have ancestors in the 1700s, A, B, C, D and E, who all share the same 8 cM segment there are five possible pathways in which that segment could have been passed on to you. You might match a cousin who has Ancestors A, F, G, H and I in her tree who are similarly all related and share that same 8 cM segment. She too has five possible pathways in which that segment could have been passed down to her. It may be that you can both identify Ancestor A in your genealogical trees, and you assume that you are genetically related because you both share descent through ancestor A. You each have a 1 in 5 chance of inheriting that segment from Ancestor A, but there is only a 1 in 25 chance that you have both inherited the same segment from Ancestor A. The most probable scenario is that you have both inherited the segment from different ancestors and neither of you has inherited the segment from Ancestor A. You will share a common genetic ancestor but that ancestor will be the progenitor of ancestors A, B, C, D, E, F, G H and I and not Ancestor A, and might well be beyond the reach of genealogical records.

It therefore seems likely that if lots of people match on the same segment this indicates that the segment is prevalent in the population from which they descend as a result of historical endogamy rather than an indication that they all share that same segment from a recent genealogical ancestor within the last 300 years or so. Indeed many of the tools produced by population geneticists use haplotype frequency as a way of detecting IBD. For example, Browning and Browning (2011) say “Haplotype frequency is critical because a shared common haplotype is unlikely to reflect recent IBD, whereas a shared haplotype that is very rare is likely to be identical by descent”.⁷

Pile-up regions
In addition to the problem of historical endogamy, which makes it very difficult to infer distant relationships with the currently available tests, it is also known that there are some regions of our genome which are prone to what the population geneticists call "excess IBD sharing" or what are more colloquially known as pile-up regions. These are segments which are widely shared at the population level. For a summary of some of the research into this subject see the section on excess IBD sharing in the ISOGG Wiki page on identity by descent. AncestryDNA use a proprietary algorithm known as Timber to filter out segments which occur at high frequency in the database. In some cases AncestryDNA found segments that were shared by thousands of people which suggested that these people weren't recently related to each other but shared DNA because they were descended from the same gene pool. There was not a direct correlation between the size and frequency of a shared segment and some of the segments that were filtered out using this method were quite large. See the blog post from Julie Granka on Filtering DNA matches at AncestryDNA with Timber which includes a table showing the size of the segments that were removed by this process. There is always going to be a trade off between false positive and false negative matches and no algorithm is perfect. Some genetic genealogists who have tested parents and children at AncestryDNA have reported that up to 35% of their child's matches, including some fourth cousin matches, do not appear in the match list of either parent. This discrepancy has not yet been explained but appears to be related to the use of the Timber algorithm.

Conclusion
Autosomal DNA testing for genetic genealogy is still very much in its infancy, and we clearly have a lot to learn about the interpretation of results, particularly for endogamous communities and for the more distant relationships beyond the fourth or fifth cousin level where family trees start to get very patchy and where relationship predictions become more difficult. The lack of phasing at 23andMe and Family Tree DNA means that our matches, particularly those with the smaller segments, are unreliable and there are both false positives and false negatives. Many of the ambiguities in our results would disappear if we were to move to whole genome sequencing, and preferably with phased genotypes too. That is unlikely to happen in the next few years but will no doubt be routine at some point in the not too distant future.

In view of the known levels of historical endogamy in the human population and the almost impossible mathematical odds of multiple fifth and sixth cousins matching on the same IBD segment through descent from the same ancestral couple, I would suggest that any segment that triangulates with multiple distant cousins is unlikely to be indicative of a recent genealogical relationship. The common ancestor will probably have lived much further back in time and may well be beyond the reach of genealogical records. Our focus should perhaps instead be on all the rare haplotypes in our match list – the segments that we share with just one of our distant matches. I hope that it might be possible to find a way of testing some of these competing hypotheses.

In the meantime, it's very important that we don't jump to conclusions based on patterns seen in the data. In science and in genealogy it is important to look not for evidence that will prove your hypothesis but for evidence that will disprove your hypothesis.

Related blog posts

• Small segments and pile-ups - a visualisation

Further reading

• "Puzzled Researcher". Chromosome pile-ups in genetic genealogy: examples from 23andMe and FTDNA. Genealogy and Genomics blog, 31 January 2015
• Ann Turner. What a difference a phase makes. A guest post on Blaine Bettinger's The Genetic Genealogist blog, 30 March 2015.
• Ann Turner. The trouble with triangulation: preliminary notes. 4 April 2015.
• "Puzzled Researcher". Genealogy and autosomal DNA matches: common errors in proving an ancestor and the allure of easy gateway ancestors Genealogy and Genomics blog, 19 April 2015.
• Ann Turner. Anatomy of an IBD segment. A guest post on Jim Bartlett's Segmentology blog, 1 October 2015

Notes and references

1.  AncestryDNA. Do all members of a DNA Circle share the same matching segment? An article in the AncestryDNA help menu "Learn more about DNA Circles" which is accessible to AncestryDNA customers only. 

2. Durand EY, Eriksson N, McLean CY (2014). Reducing pervasive false positive identical-by-descent segments detected by large-scale pedigree analysis. Molecular Biology and Evolution 31(8): 2212-2222.

3. Both AncestryDNA and FTDNA test around 690,000 SNPs. The 23andMe v4chip has around 577,000 SNPs.

4.  Henn BM, Hon L, Macpherson JM, Eriksson N, Saxonov S, et al (2012). Cryptic distant relatives are common in both isolated and cosmopolitan genetic samples. PLoS ONE 7(4): e34267. See also the blog post from 23andMe How many relatives do you have? summarising the findings of this paper.

5. Ralph P, Coop G (2013). The geography of recent genetic ancestry across Europe. PLoS Biol 11(5).

6. AncestryDNA. Why do DNA circles only go back six generations? From the AncestryDNA help menu "Learn more about DNA Circles" which is accessible to AncestryDNA customers only.

7. Browning BL and Browning SR (2011). A fast, powerful method for detecting identity by descent. American Journal of Human Genetics 88(2):173-82. See also: Browning SR, Browning BL (2012). Identity by descent between distant relatives: detection and applications. Annual Review of Genetics 2012; 46: 617-33. In the latter article the authors state: "The key idea behind IBD segment detection is haplotype frequency. If the frequency of a shared haplotype is very small, the haplotype is unlikely to be observed twice in independently sampled individuals, so one can infer the presence of an IBD segment. This criterion can be applied in several ways. The first is length of sharing, which is a proxy for frequency. If two densely genotyped haplotypes are identical at all or most (allowing for some genotyping error) assayed alleles over a very large segment of a chromosome, then the haplotypes are likely to be identical by descent across the whole segment. The second is direct use of haplotype frequency: Shared haplotypes with estimated frequency below some threshold are determined to be identical by descent. The third makes use of a population genetics model to infer probability of IBD. Given the frequency of the shared haplotype and a probability model for the IBD process along the chromosome, one can estimate the probability that the individuals are identical by descent at any position on the segment."

© 2016 Debbie Kennett