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Archiver > GENEALOGY-DNA > 2007-02 > 1171592162


From: (John Chandler)
Subject: Re: [DNA] TMRCA
Date: Thu, 15 Feb 2007 21:16:02 -0500 (EST)
References: <358091.80653.qm@web31512.mail.mud.yahoo.com>
In-Reply-To: <358091.80653.qm@web31512.mail.mud.yahoo.com> (message fromJonathan Day on Thu, 15 Feb 2007 00:31:44 -0800 (PST))


Jonathan wrote:
> Some calculators I have seen ask for the number of
> markers and offer a range of choices on the difference
> (genetic difference of 1, genetic difference of 2
> split over two markers, genetic difference of 2 in a
> single marker, and so on).
>
> Clearly, such calculators are crude.

On the contrary. They recognize that a two-step offset on one marker
has very different implications from two one-step offsets. The former
is very likely to be evidence of a single two-step mutation, while the
latter cannot be such. Such calculators are therefore much more
sophisticated than usual.

> It would seem to me that a good calculator must make
> some attempt at figuring out what the common
> ancestor's markers most likely were.

No, that's almost entirely irrelevant, and, worse, it's unknown and
inaccssible to "figuring out." Moreover, a proper TMRCA calculator
automatically takes into account the range of possible ancestral
haplotypes by dealing with each marker independently. Take a very
simple example -- say you have two haplotypes that differ by one step
at one marker. The ancestral allele is surely one or the other of the
two observed results for that marker. Either way, one subject has the
ancestral allele while the other has a mutation. In the absence of a
clear-cut up/down mutation bias, the TMRCA probability distribution is
the same for both cases.

> All that seems straightforward enough. So, from this,
> I think we can say the following. A calculator, to be
> accurate, must:

Again, you've missed the fundamental limitation of TMRCA calculators
-- they cannot do better than give a range of probabilities, no matter
how many refinements you add. To say that a TMRCA calculator is
"accurate" is to misrepresent the purposes of doing the calculations.
Those purposes are (A) to decide whether the MRCA is close enough to
the present to make him a worthwhile research project and/or (B) to
test whether a proposed identification of the MRCA is plausible.

All of the refinements you propose are of negligible importance
compared to the irreducible spread of the probabilities due to the
low mutation rates (and, to a lesser extent, the uncertainties in
the rates).

John Chandler

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