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  #1  
Old 5th July 2017, 08:09 PM
Frederator Frederator is offline
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How odd do you think this is?

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/...finder-detect/

Is this weird? How weird? A little? A lot?
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  #2  
Old 6th July 2017, 10:53 AM
John McCoy John McCoy is offline
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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.
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  #3  
Old 6th July 2017, 01:22 PM
Frederator Frederator is offline
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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.
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  #4  
Old 6th July 2017, 02:42 PM
John McCoy John McCoy is offline
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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.
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  #5  
Old 6th July 2017, 02:48 PM
Frederator Frederator is offline
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Quote:
Originally Posted by John McCoy View Post
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.

Quote:
Originally Posted by John McCoy View Post
. .. 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.
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  #6  
Old 6th July 2017, 02:58 PM
ech124 ech124 is offline
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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.
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  #7  
Old 6th July 2017, 03:01 PM
Frederator Frederator is offline
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Quote:
Originally Posted by ech124 View Post
. . . 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.
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  #8  
Old 6th July 2017, 04:25 PM
Broder Tuck Broder Tuck is offline
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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%
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  #9  
Old 6th July 2017, 07:04 PM
Frederator Frederator is offline
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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.
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  #10  
Old 15th July 2017, 12:36 PM
Frank Kelch Frank Kelch is offline
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Quote:
Originally Posted by Frederator View Post

...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.
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