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From: "Anatole Klyosov" <>
Subject: [DNA] "counting mutations" versus "GD from the modal"
Date: Mon, 15 Feb 2010 06:39:43 -0500
References: <mailman.4910.1266220546.2099.genealogy-dna@rootsweb.com>


>From: "Lancaster-Boon" <>
>If you use the term "first order" (as you do) it implies there is a second
>order (which in your case you blamed me for assuming from your words).

Sure. In physical chemistry (chemical kinetics and related disciplines, and
this includes ways how mutations occur in haplotypes) a first-order reaction
is A-->P. A second-order reaction is A+B -->Q.

In other words, in first-order reactions (or first-order processes) the
mutation in a haplotype is going - in terms of its description by the
respective mutation rate constants - "by itself". In second-order reactions
a mutation would have been a result of a collision of two haplotypes (or two
different entities, one of them is the haplotype). It would have been quite
different in mechanism, origin, descriptions.

In first-order reactions accumulation of mutations in a haplotype set should
match the decrease of base haplotypes in the same dataset. Therefore, for
first-order reactions the linear and logarithmic methods should produce the
same results in terms of TMRCA, and we actually see it. This is why those
matches are important for descriptions of haplotype datasets.

There are no "second-order" processes in mutations in haplotypes, or at
least nobody has seen them. You took the term without knowing its meaning.
What was worth, without defining it.

Branches and other deviations from first-order kinetics are described not by
"second-order" processes, but as a combination of the first-order processes.

Of course, you are free to call them however you want, but you should have
given a clear definition what the "second-order" was in your description.

Regards,

Anatole Klyosov



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