Archiver > GENEALOGY-DNA > 2010-02 > 1265567237

From: "Ken Nordtvedt" <>
Subject: Re: [DNA] Intraclade Age Sigma "Unknowable"
Date: Sun, 7 Feb 2010 11:27:17 -0700
References: <009601caa80d$da9ca2a0$5e82af48@Ken1><><000601caa813$70017870$5e82af48@Ken1><><005a01caa81f$93f35210$5e82af48@Ken1>

> ----- Original Message -----
> From: "Al Aburto" <>
>> Aha! :-)

Al, Forgive me imagining what we could learn with super haplotypes. But you
got me started, and during my shower some more things came to mind.

I mentioned that if we could eliminate the stocasticity-driven spread of the
pairwise TMRCA estimates from a clade's haplotype sample distribution we
could see the fraction 2f(1-f) of pairwise TMRCAs being the full clade TMRCA
age. Note that 2f(1-f) peaks for f = 1/2; no more than half the pairwise
TMRCA measurements would show the full clade age.
That's for the MRCA having two sons with non-extinct descending lines.

Suppose he had three sons with non-extinct descending lines. Then the
fraction of pair-wise TMRCA measures which could be the full clade TMRCA
would be:

2 { f(1)f(2) + f(1)f(3) + f(2)f(3) }

with each of those fractions being the three sons' fractional ancestries of
the N haplotypes.

For f(1) = f(2) = f(3) = 1/3 this overall fraction could be 2/3. And so on
for more MRCA sons in the tree.

So if we found the number of largest pairwise TMRCA measurements exceeding
half of the total, we could learn that the MRCA had more than two sons in
the tree.


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