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Using David Pike's tool:

https://www.math.mun.ca/~dapike/FF23utils/pair-comp.php

I found that my mother and her brother are fully identical on the portion of chromosome(s) 4 from position 122.2 million to position 175.9 million.

Both of them tested at FTDNA. I uploaded both kits to MyHeritage, and today I noticed that a man matches my uncle from position 139.6 million to 150.9 million. However, this man does not appear as a match to my mother.

How can this be possible? Being a fully identical region, my mom and uncle should have the exact same sequence of pairs of nucleotides all through this segment. Even if this man is a false match to one of them, say with the matching alleles bouncing back and forth between the maternal and paternal chromosomes, he should show as a false match to both of them.

All I can think is that David Pike's tool reported that there were two non-matching SNPs in the fully identical region that it assumed were in error and ignored. But it goes against my impression of MyHeritage that they would have an algorithm that is a stickler for these differences. If they are willing on one hand to impute data that isn't even there, presumably to show their customers more matches than their competition would, given the same user database, then would they counteract this effect with the other hand by having a very low tolerance for SNP read errors?

But can there be another explanation? I can't think of one. (My Uncle and Mother match at MyHeritage as they should, so it's not a matter of uploading the wrong kit or something.)

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I suggest uploading everything to Gedmatch, which has an excellent segment mapper. If the man who matches your family is willing.

Your analysis is correct: the fact that it's a fully identical region for your mother and uncle means that anyone who matches one of them in that same location should match the other.

Occasionally, you have issues where a segment isn't reported because of a no-call on an allele, or something like that. It's possible that your mother has a no-call preventing the system from identifying the segment as a match with the man, but not with her brother, because of the preponderance of other matching alleles.

Also, I have to say, My Heritage has a reputation for reporting incorrect matches. Not just what other places might do in counting segments way too small to matter or in overestimating a suggested relationship. No, there are many examples of My Heritage getting things like size of the largest segment wrong. My source is multiple reports from trusted people in the field on the discussion group for the International Society of Genetic Genealogy (ISOGG) and other genetic genealogy groups.

So before drawing any conclusions, I suggest doing your best to get all 3 data sets into Gedmatch and take a close look at that segment.

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  • I agree uploading to GedMatch is desirable. Regarding errors, no-calls should not be much of an issue for any company's matching algorithm. Conflicting errors, where a SNP value is actually called, but wrongly is where the main issue for matching lies since the algorithm should probably accept a few occasional mismatches, but stop matching if there are just a few more encountered too closely. When looking at matching pairs among three people, the miscalls can fall in such a way in the three sets of data that two pairs will show as matches but the third pair will not.
    – RobertShaw
    Commented Jan 22, 2019 at 6:24

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