Archiver > GENEALOGY-DNA > 2007-06 > 1182394856

From: "Ken Nordtvedt" <>
Subject: Re: [DNA] TMRCA Corrections
Date: Wed, 20 Jun 2007 21:00:56 -0600
References: <004101c7b33f$d2296bf0$6400a8c0@Ken1><>

----- Original Message -----
From: "John Chandler" <>
To: <>
Sent: Wednesday, June 20, 2007 8:12 PM
Subject: Re: [DNA] TMRCA Corrections

> Ken wrote:
>> Here are some tables for the increase in TMRCA estimates along with
>> their confidence intervals for the extreme case that one's pair of
>> haplotypes have no steps of difference and are of the clade's modal
>> haplotype.
> The maximum-likelihood estimate of TMRCA for equal haplotypes is 0
> generations. I take it your tables apply equally to any percentile
> level in the TMRCA probability distribution for this extreme case.

Yes; The modified probability curve for TMRCA is close to another
exponential with smaller decay rate, so all percentile levels scale about
the same factor.

I did this extreme case first because it is simplest.

>> Remember the reasons for these rescalings of TMRCA. Because the
>> haplotype distribution for the clade descendants is spreading each
>> generation, haplotypes at the center of the clade distribution will
>> find a higher percentage of the population with haplotypes at the
>> modal haplotype at the center of the distribution the further back
>> in time it looks for the MRCA.. For haplotypes out at the fringes
>> of the clade's haplotype distribution, the opposite will happen: it
>> will find a higher percentage of haplotypes in the population which
>> could be the MRCA the more recently in time it looks back.
> But the point is that every haplotype *except* the center will be
> increasing in frequency as time goes on, until the population has
> effectively lost its well-defined center. This means that the
> tables for cases even just a few steps away from modal will have
> to be carefully calculated with proper weighting. I hope you are
> proceeding with these calculations, or at least a sample.

There is actually an N dimensional spheroid or ellipsoid like volume in
haplotype space (N is number of markers) surrounding the original founder's
haplotype and which grows in size as time goes by --- within this volume the
percentage for each haplotype is falling and outside the volume the
percentage for each haplotype is growing, and on the surface of this volume
we have haplotype percentages which are momentarily not changing. So what
you say in your paragraph above is only true in the extreme youth of the

I am organizing an assault on sample cases of unequal haplotypes. But
first I'll do a case of equal haplotypes but several steps of mutation from
the founder's haplotype. There are two things going on with respect to the
pairs of haplotypes: how far they are from each other, and how far they are
from the central founder's haplotype.
> John Chandler
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