Chances of 4th cousin match

[bm_ftdna]

A and B are first cousins. C is their known fourth cousin. A and C have a DNA match (at a level that would be typical for fourth cousins), but B and C do not show as a match.

Can someone tell me the percentage chance of this situation occurring?

My understanding is that there is a 50% chance of 4th cousins showing as a DNA match, so this situation would actually be pretty typical. Am I right? Thanks.

[Frederator]

Assume you are speaking about autosomal DNA.

1/(2^(4+1)^2)*7,174 cM=expected share of 7 cM, too little to trigger a match.

Those are just the base odds. You'd have to figure in the standard deviation in grandparental contribution in order to construct the standard confidence interval. But I believe this is not worth the bother since the base odds are so low.

I think the most useful observation would be that you're lucky to just have the one cousin match, and that you should try really hard to triangulate that specific shared segment if you have any doubt about its attribution.

[John McCoy]

There are at least a couple numbers floating around for the probability of 4th cousins matching by default criteria. The 50 percent number is widely quoted, but I believe I've seen 25 percent (the odds of NOT matching) as well.

However, even if these figures come from a tabulation of results reported by individuals based on their own experience, there is also a possibility of bias, in that (1) most of us don't actually know who all of our 4th cousins are, and so we probably haven't noticed all of them in the autosomal DNA databases, particularly if they don't match, and (2) people who don't find matches, even if they know who their 4th cousins are, may be less likely to report these statistics to an enthusiastic genetic genealogist who is trying to compile these statistics. It's also perhaps worth mentioning that different web sites use different matching criteria, which might affect the observed degree of non-matching.

I can report that I have several cases where even 3rd cousins don't match each other in all combinations, even though they match at the appropriate level with at least one other known 3rd cousin. Non-matching of 3rd, 4th, and more remote cousins is definitely a real thing!

[Frederator]

Well, statistically, probability has traditionally been expressed as a range of percentages, with the base probability (i.e., at 50% confidence level) at the center. I have seen studies that publish the results for variation in grandparental contribution percentages, so I think there is data for a more-or-less authoritative figure available.

The stumbling block in my mind is that the result has disappointingly little practical application. As the field observations you refer to imply, the range of probabilities is so wide, even for very close relationships, that it's not possibly to come to a very strong conclusion based on the one or two observations most of us have available to us, personally. For people with very normal-sized families, the pool of eligible donors is not even that large.

In the case that the original poster cited, even the base probability was less than 100%, so I don't think further analysis would have been very productive.

But I get the feeling that the poster was suspicious that something else was going on. And while there's nothing they can do about the range of probabilities inherent to this degree of kinship, or the number of eligible donors, at least they can investigate the match itself and verify whether their attribution is correct. Perhaps it is not.

[ltd-jean-pull]

It's not possibly to come to a very strong conclusion based on the one or two observations most of us have available to us, personally. For people with very normal-sized families, the pool of eligible donors is not even that large.

That'a where the very large number of grandchildren that two sets of my gtgt-grandparents is useful. One couple had 70 grandchildren (dozens of them have tested) and the other couple had about 45 (only about 20 descendants have tested). Two children of one couple married two children from another couple.

A match appeared last year who was quite close. He was looking for his birth family. It was very clear from his matches that one of his parents was descended from the couple who had 70 grandchildren. But he wasn't matching descendants of only the other couple - only their descendants who were descended from both. My thoughts were that he was descended only from the first couple so all we had to do now was work our way through the 60 or so grandchildren who had children.

We've established who his paternal grandparents were and he is descended from both of the couples. However, he doesn't match two 3C1R at Gedmatch, so he definitely wouldn't match their children who would be his 4th cousins.

A example came up just the other day. A new match appeared at FTDNA for my aunt, but not a match to my aunt's full-sibling. He's a 3C and a descendant of the second couple only.

[bm_ftdna]

These responses are all helpful in answering my question - thanks very much!

[sharzie]

I have a match at Ancestry who is a paper trail documented 4th cousin. We share 16.8 CM according to Ancestry's algorithm. Ancestry "suggested" he would be a 5th to 8th cousin.

Sharon