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?