Triangulation, the X-Chromosome, and the Three-Legged Stool

+8 votes

I have been working on a triangulation with a couple of 23andme matches to my grandmother.  They all share a common 28 cM overlap on the X-chromosome.

After some digging, I managed to trace the ancestry of each to Joseph Roy and Marie Catherine Bolduc in a way that was consistent with the X-chromosome inheritance patterns for each of them.  My grandmother was 4th cousin once removed with one of the matches, and 4th cousin thrice removed with another.

However, it turns out that the two matches are related to each other a little more closely than the "three-legged stool" analogy in the triangulation help page allows.  Instead of sharing the same MRCAs or one generation below, they share MRCAs two generations below Joseph Roy and Catherine Bolduc.

Given the nature of the X-chromosome, there are essentially fewer potential common ancestors between my grandmother and these individuals.  Does this give me any flexibility regarding this three-legged stool triangulation rule?  Is my triangulation valid?  If so, can we extract a general rule about working with the X-chromosome like this?

In a broader question, why is the three-legged stool defined the way it is?  I would be more inclined to define the requirements consistently with the third-cousin or closer requirements for direct, one-to-one confirmation.  Namely, that triangulation is valid if the two more closely related matches have a MRCA no more distantly related than third cousin to the same-generation ancestor of the more distantly related match (I believe this ends up allowing a "minor" MRCA up to 4 generations below the "major" MRCA).  I'm interested in any opinions on this.  I've also cross-posted another take on this as a comment on the confirmation instruction feedback thread.

in The Tree House by Brian Lamothe G2G6 Mach 2 (24.9k points)
edited by Brian Lamothe

Cross-posted comment: I had also suggested changing the "three-legged stool" because it seems a bad analogy. There wasn't any feedback from someone who wants to defend the thre-legged stool, but nothing happened either. I still feel the analogy is bad -- the point of the requirement is having "independently sampled" segments from the three individuals. That would translate into keeping the stool legs from joining close to the ground, not keeping them from joining up close to the seat.

Do we have any further discussion on this? I have a segment match between two 3rd and one 5th cousins which results in the legs meeting two generations below the seat.
Nope. Not even of someone arguing against changing the rule. We're just shouting into the wind, as far as I can tell.
I have a somewhat similar situation.

Through DNA tests I discovered a 4th cousin (J) who matches to me, my sister, and our second cousin D on a 16.5-cM section of the X chromosome (the match to my sister and me is longer), and has additional matches on one other autosomal chromosome (but not the same segments) with me, second cousin D, and another second cousin M (who is first cousin to D). I am rather confident about the genealogy, and the only identified shared ancestors for J, D, M, and me who could be responsible for these DNA matches are the couple that all four of us identify as 3G grandparents. (We are descended from two daughters of the family, so we cannot tell whether our X chromosome match comes from 3G grandma or 3G grandpa.)

I have chosen in the past to regard this situation as confirmation with DNA. With all these cousins sharing DNA, it sure would be nice to be able to do that.

Footnote: Now there is an additional cousin. This is D1, a 4th cousin 1x removed (i.e., child of a 4th cousin to me), who is descended from another daughter of the 3G grandparent couple (but the rest of his genealogy is not as solidly known) who has matches with all of the rest of us, including an 18.9-cM 3-way match with J and me. Unfortunately, D1 has not replied to my email, so I have not been able to confirm what he knows about his other ancestry, to make sure we are not doubly related.

2 Answers

+1 vote
I feel that we need to follow the science on this but I don't know what the science is. I hope someone will come forward and explain the rules by genetic probabilities.
by Mark Adams G2G1 (2k points)
+1 vote
Cousin Brian,

Cousin Mark's recent response brought my attention to this old post so forgive me for not having seen this when it was posted during the holidays . . .

I see your point and need to say that there are many logical points that can be made and validly so.  One of the issues, though, is that one can start to complicate the rules to the point that they are impossible to understand.  This is not to say that we ought not move forward on some of those valid points rather that we need to exercise due care and consideration.

As you are dealing with x chromosome matches, I should point out that those matches do not always require triangulation (see:  Specifically, when the match is between two males.  Now, as an exercise in logic, let us take a man (Fred) and a woman (Betty), a distant cousin, who match and, as they are not both males, triangulation is required.  Betty then has her son (BamBam) tested, and he matches Fred on the same X chromosome but for a smaller but still sufficient length, so no triangulation is required.  Why?  He certainly did not inherit that X from his father (Barney).  He inherited it as a combination of Betty's two X chromosomes where the matching segment with Fred survived.  So, why is the Fred/BamBam match treated more favorably than the Fred/Betty match?  

N.B. the example in the help page is between a male and female without using triangulation and should NOT be a valid match according to the rule stated.  As they are close cousins, it is possible that they match on that basis, but that would require a different confirmation statement.
by Thom Anderson G2G6 Mach 4 (44.6k points)

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