Triangulation 4 ( reflections )

Complications in HIR-comparing

Gedmatch, the new comparison tool of John Ohlson offers the opportunity to triangulate ones matches, what simply means, that one can proof, if cousin A also matches cousin B. Unfortunately this seems to be more complicated than expected at first glance. When I perceived the first bud of a multiple cluster of matches in the early beginnings of Relative Finder, I immediately sent out emails to my cousins, pointing to the possibility, that they could also match. No reply! Probably I share this naïve calculation with a lot of other people – if I share a half identical region with cousin A and B, those two should share the same segment too, what is simply wrong!

Let’s pretend, we could represent an IBD segment of an MRCA, a most recent common ancestor with a simple icon and let’s have a closer look on the logical possibilities on triangulated matches.

Cousin A has on the paternal side a segment in common with cousin C, on maternal side a HIR with cousin B, but cousin B and C have nothing in common.

A similar situation. Cousin A has on the paternal side a segment in common with cousin C, on maternal side a HIR with cousin B, but now cousin B and C share a third common ancestor on different stretches of the chromosome. This looks like a perfect triangulated match, but is not.

This is a perfect triangulated match, since the homozygotous status of cousin A does not allow any uncertainty.

It seems, that a given HIR from cousin A can be traced in the complete genome even, if parts of the sequence are removed from paternal to maternal side, like the example of cousin B shows. The multiple shifting of cousin C is of course not very probable, although such events sometimes occur on the borders of a HIR ( fuzzy boundaries ). That’s why members of a younger generation can encounter a longer segment than their parents.

Triangulation 3 (reflections)

My Polish cousin

In spring 2010 the clients of 23andme encountered a new tool - Ancestry Finder. It shows a possible Ashkenazi heritage, as all participants are asked to list especially this item plus the original countries of their grandparents. As the published experiences in some forums show, I was not the only one to be astonished and surprised finding a lot of never expected countries among all those matches with a lowered centiMorgan threshold. A closer look should help to understand this phenomenon. Defining my country of origin had been a problem, since all my German ancestors lived in nowadays Poland. The probability of meeting distant cousins from Poland or other countries in the neighborhood is rather high. This is confirmed by Davidskis and Dienekens diagrams, where I’m placed at the outer most eastern edge, even behind some Polish and Hungarian people (DE1 & DOD219). So a reciprocal genetic influence has to be considered as normal for a country of origin and its neighborhood. But this does not explain matches with countries like Italy or Portugal or Mexico. This question depends on traditional genealogical framesets. Checking the own ascending tree reveals a triangle like pyramid, standing on its top and doubling the number of ancestors in each generation.

The visualization of such a tree leads like a time machine through the generations into time layers of complete different political and social conditions. People had dozens of descendants, one half of them dying early, more than 90% lived on the countryside, mostly starving during the small ice age, the disastrous 30 year war and after. The pressure to leave the own country to create new colonies somewhere in the East or to head unknown continents was a lot higher than today. Most of 23andme users are US citizens with a colonial or more recent immigration background. Matching one of these makes clear, that a second ancestry pyramid is necessary to allow a plausible comparison.

Two different ancestry pyramids only need one common ancestor some 5, 7, 10 generations ago and of course we can encounter in the second pyramid also people from co-emigration or immigration countries, not belonging to one’s own ancestry. This is the reason not to list immigration countries in my Regband project. Of course one has to bear in mind, that this is based on a pure European perspective.
One additional calculation is to mention:
If I have as a German or Polish citizen around 100 relatives in a dataset of about 70000 clients, I can expect more than 2 million cousins in a global North European context. Turning an ancestry pyramid around and setting our most recent common ancestor on top, thus having an irregular triangle reveals, that we can expect the same amount of descendants as above, following all possible lines. In this illustration I only marked two of these lines.