GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2010-03 > 1270023942

From: "Sandy Paterson" <>
Subject: Re: [DNA] Questions about alternate means of searching DNA Genealogy
Date: Wed, 31 Mar 2010 09:31:56 +0100

Wow.

Right, I followed your reasoning with CODIS markers, but I'm totally lost
with the Y chromosome.

We're talking in the context of someone who has discovered an adoption in
his ancestry, who has had a 25 marker Y-STR test, and found that 3 of the 25
markers have unusual values. He hopes to be able to identify his blood
ancestry by concentrating his searches on these three unusual marker values,
using the reasoning that if each one of those 3 markers are rare, then the
presence of all 3 values simultaneously will be very rare indeed, and this
should help him in his search.

I agree with him. You seem to disagree with him (if I've understood you
correctly).

Let's simplify the problem and change it to one where he has only 2 markers
with unusual values.

Then, using Bayes Theorem in its simplest form

PR{AB} = Pr{A}.Pr{B/A}
= Pr{B}.Pr{A/B}

We can change Pr to Fr if you like, where Fr denotes frequency rather than
probability.

It seems to me that what you are saying is that Pr{B/A} = 1

I find that counter-intuitive (or perhaps I've misunderstood you).

Looking at it from a different angle, you say that (in Y chromosomes)

"Second, a man with rare alleles on two Y markers will have sons who all
have the
same two rare alleles.

Surely, if we examined the haplotypes of the sons of a large number of men
with two rare alleles, although we'd find that in most cases sons would have
both rare values, we'd also find that some sons would have only 1? And
(albeit very rarely), some brothers would have none?

This seems so obvious to me that I'm now convinced that I've misunderstood
you.

Sandy

-----Original Message-----
From:
[mailto:] On Behalf Of John Chandler
Sent: 30 March 2010 21:08
To:
Subject: Re: [DNA] Questions about alternate means of searching DNA
Genealogy

I wrote

"The Y chromosome is passed on as a whole, and it could well be the same 1%
of the male population that has all three of those rare alleles together."

Sandy replied:
> Really? I suppose it's possible, but I'd say it's highly unlikely. Perhaps
> you can offer an example?

Nothing could be simpler. This is what's called variously "population
structure" or "linkage disequilibrium". Looking at the other side,
let's consider the CODIS markers, all on different chromosomes. The
inheritance of each marker is independent, and so a man with
(heterozygous) rare alleles on two different markers would have
children split into four groups of roughly equal size: (1) with just
rare allele "A", (2) with just rare allele "B", (3) with both rare
alleles, and (4) with neither. (All this assuming his wife doesn't
also have either "A" or "B".) The rare alleles don't stick together.
The distributions of alleles therefore quickly approaches a state of
equilibrium, where no correlation can be found between the frequencies
of different alleles, provided that there is substantial interbreeding
of subpopulations.

For the Y chromosome, none of that happens. First of all, rare
alleles on the Y tend to die out (and daughter out) because there is
only one copy, and half of the children don't get any. Second, a man
with rare alleles on two Y markers will have sons who all have the
same two rare alleles. No mixing, no equilibration. If his line is
reproductively successful over the years, that will make those alleles
slightly less rare and therefore less likely to disappear altogether.
Similarly, an additional mutation to a rare allele on a third marker
in his lineage is likely to either die out or burgeon to the point
where it becomes a major fraction of the still-rare lineage. Genetic
drift is a big factor in small populations because they are small and
therefore have little "inertia".

John Chandler

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