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I'm focusing on triangulation groups and so looking at matching segments that overlap each other. I'm frequently finding the situation where, at a single website, match A's segment is shown as triangulating with match B's segment, and match B's segment is shown as triangulating with match C's segment, but match A is not shown as triangulating with person C.

Sometimes, the explanation is that the overlap between the segments inherited by A and C is too small, below the threshold established by the company to flag people as matches.

But I'm frequently finding intransitivity even when this is not the case. For instance, I just found on MyHeritage the situation:

Person A and Person B have exactly the same start and end position for their segments that match my kit, and these segments are shown as triangulating. Person C has a segment contained within the segment of A and B, and her segment is shown as triangulating with A's but not with B's. In the situation I'm looking at now the longer segments are 14cM and the shorter one contained within them is 12cM.

I can only guess that person A and B actually had a few differences that were ignored, person B and person C also had a few differences that were ignored, but person A and person C had the union of these differences and put together there were too many for them to be called a match. Is that what I should assume is happening here? Can I put these people all in the same triangulation group, or should I be hesitant?

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Since you have two chromosomes of each pair, every match you have must be either:

  1. An IBD (Identical by Descent) match on your paternal side,
  2. An IBD match on your maternal side, or
  3. A false match.

All the overlapping IBD matches on your paternal side will have to match each other and thus form a triangulation group, and all the overlapping IBD matches on your maternal side will have to match each other, and thus form a second distinct triangulation group over the same segment. Any IBD segment has to be in one of those two triangulation groups.

To answer your question, first realize that any IBD segment must triangulate with another IBD match overlapping on the same segment. If two matches appear to be in the same triangulation group but don't match each other then there's a few possible reasons.

  1. One is a false match and happens to match some of the others in the triangulation group by chance.
  2. The testing company's matching algorithm created false matches for one or both of them. MyHeritage DNA does imputation and stitching when matching and can create some longer false positives than the other companies.
  3. The two that don't seem to match each other on that segment actually do, but fall under the criteria of the testing company to be a match to each other because their total centimorgans matching with each other is not enough. So the company does not show them as matching on the segment.

Don't get too hung up on exact starting and ending positions. Most companies group SNPs into blocks of maybe 100 for comparison, so starting and ending positions are often the same. And random bits of matching between any two people in the group can make them appear to start before or end after the others, when in reality they might not.

The bottom line is you shouldn't just blindly put anyone in the same triangulation group unless they are shown to all match each other. If one doesn't match any one of the others in the group, at least mark them in some way so that you'll remember who they don't seem to match to in the group. Use that to make sure you don't jump to conclusions about them without identifying why they don't match.

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  • Thanks. The issue is, often I have 6 or more people who all match every one of the others on the same segment, except for one pair who are shown as non-matches. I hesitate to throw one (or both) out of the group over this, when there are four others they match. And this happens when the overlap where they match is well over the minimum threshold.
    – Barry
    Commented Sep 23, 2018 at 20:58
  • Will your points 1 and 2 still be relevant if the group I am forming has four or more people and I'm using longish segments? I'm only looking at segments >10cM, often over 15cM, so one false match would be a rare occurence, but still happens. But with four or more in the group, I'd think you'd need two false matches on that segment to see this behavior, which seems exceedingly unlikely. That is, if all but one person in the group are really matching, then the false match should match all of these people in the same false way, so would appear as a match to all of them.
    – Barry
    Commented Sep 23, 2018 at 21:09
  • Longish segments shouldn't have too many false matches if people are triangulating. More often, those problems would come from whatever matching criteria the DNA company uses. The more imputation and stitching a company does, the more false matches it might have. I've heard of false matches somewhat larger than 15 cM at MyHeritage.
    – lkessler
    Commented Sep 23, 2018 at 22:12

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