How odd do you think this is?

[Frederator]

I've re-examined my matches since I learned that the average male recombination rate is something like 2/3 of the rate for women, and I found something that I think is a bit unusual. Do you think so?

I have a female 4th cousin who matches my brother with a largest segment of 16 cM yet doesn't match me at all. We both descend from the most recent common ancestors through our respective direct male lines.

Doing a back-of-the-envelope calc reconciled to the published stats from FTDNA, given the gender differential in recombination, I would have thought we'd be a nearly 100% lock for a match.

https://www.familytreedna.com/learn/autosomal-ancestry/universal-dna-matching/probability-relative-share-enough-dna-family-finder-detect/

Is this weird? How weird? A little? A lot?

[John McCoy]

Doesn't sound weird or unusual to me! It would be useful to have data from some realistic simulations that apply the differential male and female recombination rates, so that we could get an idea of the expected distribution of outcomes. If that has been done, I have never seen the results. Simulations have only been done, as far as I know, using a uniform (gender neutral) recombination model. I hope someone will step up to this problem!

My guess is that the odds of seeing the situation you describe are still fairly high.

[Frederator]

Well, we know an awful lot. We don't have to leave it to some vague sense that we should match, in some unquantifiable way.

The published matching statistics must use the intersex average recombination rate, since the vast majority of a person's ancestors are neither through the direct male nor direct female lines.

And since the male rate is ~2/3 the female rate, the implication is that the male rate is ~80% of the intersex average rate.

Therefore the probability of retaining intact a significant segment of DNA is, at each generation, ~125% higher at the male recombination rate as compared to the intersex average.

In my fact situation both donors descend from the MRCAs in a direct male line. All the other variables should be the same in the formula underlying the published figures. So the probability that two 4th cousins in the direct male line will match should be 100%.

50% published rate *( 125%^4)=122.07%, limited to 100%.

The fact that my little back-of-the-envelope calc returns a figure greater than 100% makes total sense, because the benchmark for registering a match is a largest shared block of at least 7 cM or thereabouts. Intuitively, larger shared segment sizes correlate with closer relationships and higher probability of registering as a match in general.

[John McCoy]

What you don't have is the probability distribution of result of random recombination and assortment of chromosomes with the added variable of gender-specific recombination rates. Without that, you can't assess how likely any particular outcome is. I agree, the effect should be large enough to detect, given a sufficiently large sample size.

[Frederator]

What you don't have is the probability distribution of result of random recombination and assortment of chromosomes . . .

Don't need 'em. As I said, other than the fact that BOTH donors in my fact case are direct male line descendants, all variables are the same.

. .. with the added variable of gender-specific recombination rates. . .

This is just wrong. We most certainly do know the relationships between the male, female and intersex average rates.

[ech124]

I think the example you quoted is quite common.
Really it boils down to the DNA segment existed in your father and one brother got it and one didn't. Sometimes a segment gets inherited slightly smaller, but sometimes it is just gone.

I took a look at just two siblings (brothers) and easily found 57 examples of not-in-common matches where the the missing segment was 16 cM or higher. The very highest was a 42 cM segment.

[Frederator]

. . . I took a look at just two siblings (brothers) and easily found 57 examples of not-in-common matches where the the missing segment was 16 cM or higher. The very highest was a 42 cM segment.

I don't know how compelling that observation is. It's not put into the context of their specific relationships, lines of descent and probability of matching as per an established authority.

[Broder Tuck]

For any single segment, these are the options:

A: Passed down intact
B: Passed down partially, either above or below the threshold.
C: Not passed down.

A+B+C=100%.

After that, I'd welcome input on my thinking below:

* Only the chance of B is directly affected by the recombination rate, as more crossover spots means more segments may become split.

* The (average) chance of B for a single segment is its cM value. Is this correct?

* The chances of A and C are more or less equal, and make up what's left after B.

If this is true, for a small(ish) segment like 16cM, the risk of C happening (one not getting the segment at all from a parent) is still in the vicinity of 40%

[Frederator]

You're raising some interesting points that I want to address. But I don't want there to be any confusion because they are only tangentally related to my original question.

You're getting into specifics of the overall probability distribution calculation, which is a trickier beast. I think that was John McCoy's point.

I do have some thoughts on the overall probability distribution calculation, but I want to be clear that they don't really have any bearing on the specific question that I started this thread with.

My specific case was identical to the case underlying the company's published data for 4th cousins in everything except the applicable recombination rates. So arriving at an informed interpretation of that specific data point wasn't dependent on having a thorough command of the whole probability distribution curve.

That said, I think you are correct to say that the overall distribution calculation is dependent on knowing the likely proportion of inherited DNA that is intact, so-to-speak, at any given number of generations remove from the MRCA. That is, in blocks >= 7 cM. And I think you are correct to assume that is the significance of the published recombination rates.

I have, in fact, developed a crude calculator that makes such calculations extending beyond the relationship levels that FTDNA has published. For recent generations from the MRCA it does return results consistent with FTDNA's published figures, which is good.

But because it's an exponential function, any error I make would be expected to be relatively trivial at the small number of published data points for the company's own, authoritative calculation. The serious errors errors in my mock-up of the overall distribution curve would probably come at more remote levels of relationship, which as far as I know the company has NOT published. Therefore I'm not terribly confident about them.

Which, again, I don't need to be for the purposes of my specific question. The specific fact case I laid out in the original post is identical in everything except the applicable recombination rates to a data point whose probability has been published by the company. And at a relatively "safe" point in the curve, too.

Again, to be clear, the math I laid out in my answer to John McCoy was NOT an attempt to reproduce the overall probability distribution curve. It was simply making an observation about a single, very specific point on that curve. I didn't need to know the intricate inter-relationships among the terms of the overall curve function for that point because my fact situation was identical in everything except the applicable recombination rate.

[Frank Kelch]

...I have a female 4th cousin who matches my brother with a largest segment of 16 cM yet doesn't match me at all. We both descend from the most recent common ancestors through our respective direct male lines...
Is this weird? How weird? A little? A lot?

It's not unusual or uncommon at all.

[Frederator]

Can you point to a specific instance matching every detail in that scenario from your personal experience? Or is that just a generalized 'gut feeling'?

[travers]

Can you point to a specific instance matching every detail in that scenario from your personal experience? Or is that just a generalized 'gut feeling'?

What does your calculations state the odds of 4th cousins once remove or 5th cousins matching? As the numbers you are throwing out seem hard to believe where 4th cousins would be over 100% chance to match. I have a group of 5 5th cousins who match on Y-DNA and only 2 match in Family Finder another two men who are 4th cousins once removed who match with Y-DNA yet don't match in Family Finder. I don't know offhand of any 4th cousins in my project who have taken both tests.

I don't think you are going to prove NPE with what you are trying to do based off math as 4th cousins are too far removed to make a determination based off a non match between 2 people. If you can't find a Y-DNA participant can't you find other descendants to test with Family Finder?

[Frederator]

Thanks.

I'm assuming that the degrees of cousinship that you mention are through their direct paternal lines. I'm stipulating that specifically because I have a lot of cousin-marriages in my own family tree where the most recent relationship between agnatic relations is NOT in their direct male lines.

In the specific case of 5th cousins, all through the direct male line, my model predicts at a ~96% confidence level that the true odds that any two of them will register as matches to one another on Family Finder are ~81%. That implies that the chance that only two of five randomly selected cousins from this pool match is ~5%.

In the specific case of 4th cousins once removed, both through the direct male line, my model predicts at a ~94% confidence level that the true odds that any two of them will register as matches on Family Finder is 100%. That leaves a ~6% chance that the true odds that any two randomly selected cousins meeting these conditions match in Family Finder is less than 100%.

So pretty similar cases. A small but non-negligible chance of them not matching.

I never said that I would conclusively prove an NPE for cousins this distantly related through autosomal DNA alone. Only that these scenarios could indicate a heightened probability.

I was soliciting actual case histories for this very reason. Just last night I asked for specific feedback on my calculation of the confidence levels.

These cases are very interesting, but probably not completely decisive in and of themselves, either. It's a sample size of 7 individuals, and they're certainly not randomly drawn. If these men are like the typical Y DNA project participant, several of them are likely immediate relations to one another. And in any case, their selection is biased because I specifically asked for cases which ran counter to my model.

Most likely I need to revisit my confidence calculation. But the significance of the differential in male and female recombination rates, applied exponentially, suggests that there's something here worth defining more clearly.

[Frederator]

Another thought is that my minimum sharing threshold of 7cM is too small. I think that strictly speaking, the absolute minimum is 9cM, although people with largest segments of 7.5cM may match provided their total shared cM is >=20 cM.

My formula is indifferent as to distinctions of the size of individual segments inherited from the MRCAs.

I didn't really regard either of these as a particular hindrance because I was able to replicate FTDNA's published generic matching predictions. Of course, that's not saying that FTDNA's figures are necessarily correct, either. Similar products return significantly different predictions according to ISOGG.

https://isogg.org/wiki/Cousin_statistics

They're not immediately comparable because they do test different arrays of SNPs and have different matching thresholds, but it's something to consider.

[Frederator]

Yet another thought crossed my mind from the very beginning of this project. Namely, that what FTDNA published was NOT the odds that any two randomly selected cousins would match, but rather the odds that enough of the MRCAs' DNA would survive intact among ALL their descendants that at least two of them would match. That's very different.

It's a depressing thought because it would imply that the odds of any two randomly selected cousins register as matches is so small beyond 3rd cousins as to be not worth considering.

But I have a hard time believing that. I wouldn't like to think the companies would have published the statistics that they did if that were so. It would be grossly misleading.