# Are there different amounts of "fuzziness" in the endpoints when doing pairwise 1-1 comparisons among three people at GEDmatch?

I was performing a triangulation at GEDmatch and obtained the following start and end points for the triangulated segment on Chromosome 1 for each comparison:

Person A with Person B: 19,899,991 to 35,145,961

Person A with Person C: 29,909,642 to 36,528,222

Person B with Person C: 29,812,459 to 40,717,609

It is clear from the total shared cM that none of these people is closely related to any other, so these are definitely half-matches on these segments. I infer then that there is a single chromosome segment that each of these people has an identical copy of going from

29,909,642 to 35,145,961

Now it would seem to me that the shared segment between A and C continuing to the right of this to position 36,528,222 and the longer segment shared between B and C continuing on to 40,717,609 really must be a match on that same chromosome -- it would be too unbelievable that the match had just switched over from one of the two chromosomes to the other and matched up perfectly. So it seems reasonable to infer that if it were possible to splice these three segments together to form one large segment from

19,899,991 to 40,717,619,

then the shared common ancestor who gave rise to these segments would have a copy of this long segment on one of his/her chromosomes. Even though the ends of this segment were not triangulated, the fact that they are contiguous with the triangulated segment inherited from the common ancestor makes it very, very likely that they also descended from the same ancestor. Is that a reasonable deduction? (The rest of what I write makes this assumption.)

It is not possible to tell exactly which chunk of this long segment A got by a single comparison with either B or C, but you should be able to figure it out from the two comparisons together. However, in this example, I seem to run into a paradox:

From the A to B comparsion, either A or B must have only a piece of the inherited segment ending at 35,145,961. Looking at the A to C comparison, which has endpoint 36,528,222 significantly farther along the segment, it would seem to be B who has the segment that stops at 35,145,961. But looking at the B to C comparison, it would seem that person B got a piece of the ancestral segment continuing at least as far 40,717,619, the conclusion from the previous sentence.

So I am confused. Can this be resolved by saying that 36,528,222 is not actually significantly farther than 35,145,961? That there was a different amount of fuzziness in the right endpoint when doing the A to B and A to C comparisons? 1.4 million positions to me seems like it would be more than fuzz, but perhaps not? If that really is a significant difference, what else can account for the comparison data above?

• Of course another explanation occurs to me two minutes after I write the long post. I suppose the additional 1.4 million positions in common between A and C could be IBC -- A really has the ancestral segment cut off at 35,145,961, but whatever segment recombined in just to the right of it or else the corresponding segment on the opposite chromosome happens to match the ancestor's segment a little farther along. Is that a more likely explanation here than fuzziness? Sep 1, 2018 at 23:00

So what you've got is this:

You are correct that there is a single segment, represented by the dark blue segment in the diagram, between 30 and 35 Mbp (Mega base pairs) that is the triangulating region and may have been passed down to all three of them from a common ancestor.

And you are correct that it will extend into the light blue segments.

But no, the entire region from 20 Mbp to 40 Mbp may not have come from the common ancestor of all three of these people. If two of the people, say Person A and Person B, have a more recent common ancestor, that ancestor may have had a crossover that lost some of the original common ancestor's segment. It could only happen on one side, since only Person A or Person C can share the more recent common ancestor with Person B. Here's the example:

So in that example, only the region between 28 Mbp and 40 Mbp comes from the Common Ancestor of A, B and C. The region between 20 Mbp and 28 Mbp is from the shared ancestor of A and B who C doesn't share with.

Yes, your paradox is caused by the fuzziness. There are by chance matches over short segments even with double matched and triangulated segments. I have found the fuzziness can be as much as 3 Mbp, which is approximately 3 centimorgans. So I would say beyond a doubt that your 35,145,961 to 36,528,222 difference is very likely a bit of an extra by chance matching between Person A and Person C. That is why I didn't differentiate them in my first diagram at the top. Note also that I rounded them to Mbp because that is the best accuracy you can expect. Then I took the Mbp which gives the smallest triangulated region, because the edges of the region can always be by chance matches.

And you shouldn't think of it as 1.4 million positions. 99.9% of our genome is identical in all humans, so there are only about 1,400 possibly changing positions in that 1.4 Mbp. Of those 1,400 SNPs, only about 300 are sampled. Also, they accept 1 difference in every 100 SNPs. So we're sort of talking about 297 out of 300 SNPs half matching, which is easily possible by chance.

Note also how I was very careful to say that the segment may have been passed down from a common ancestor. A segment passed down to 3 people must triangulate. But segments that triangulate are not necessarily passed down from a common ancestor. Two people may share the common ancestor and the third matches randomly to their common match. But Jim Bartlett, an expert on segment matching, has concluded that triangulations of 7 cM or more are almost certainly real segments passed down. Anything 5 cM and under, be wary, even if they triangulate.

• Oooh, beautiful diagram! The common segment is over 7cM according to the Rutgers mapping program, so that's why I was "confident" in my assertion of the common ancestor (having seen Jim's claim before). But I understand that regardless, there is always a small probability of any random event here. I don't think of it as 1.4 million positions, but I use the language of the GEDmatch output. I've looked through my raw data files, so I've seen the data for the positions jumping up through consecutive markers. Sep 2, 2018 at 11:45
• When you say "297 out of 300 SNPs half matching, which is easily possible by chance", that is true if you add the language "somewhere in the DNA of the two people" on. But if you say, "on a specific predetermined section of 300 SNPs", then no, it is unbelievably unlikely. At a given SNP, if it's totally random which pair of alleles both people get, you'd have a 43/64 chance of being at least a half match. Now repeat the experiment 300 times and ask for at least 297 half-matches, and the probability is about 8 x 10^(-47), i.e., vanishingly small. Sep 2, 2018 at 11:56
• But if you test 700,000 markers and allow the 300 SNP segment to appear anywhere, there are a lot more ways for this to happen -- a lot more little segments that could match -- so the probability goes up considerably that such a match would happen somewhere. I'm still surprised it goes up enough that this occurrence is regularly "observed in the wild", but that's a much harder probability to compute theoretically and it will start to matter that it is almost certainly not like a toss of two four-sided "A, T, C, G" dice when a person gets a pair of alleles at a spot. Sep 2, 2018 at 12:02
• So your argument is that this is most likely an additional IBC segment. That's not the kind of fuzziness I meant. I meant, is there something about how the data is tokenized or otherwise stored/used that can make these endpoints a little different than if you just did straight comparisons out of the raw data files. If this could lead to different endpoints depending on who you compared with, then that could account for the difference in my data. So I still wonder if this explanation is as likely as one that says instead I got a short IBC segment right where I needed it. Sep 2, 2018 at 12:06
• In your diagram, you show only two different left endpoints in the three people's segments: 28 and 30. Also two different right endpoints: 35 and 40. That's what expected to happen. In my data, there were three different right endpoints. That's what I was having trouble wrapping my head around. I didn't see a way for that to happen, even knowing that it is possible that a pair has a more recent common ancestor. Can you see how to make that happen in your diagram? Sep 2, 2018 at 12:17