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From: "Nicholas Penington" <>
Subject: Re: [DNA] Genetic Distance calculation method -- which method is mostcorrect?
Date: Fri, 21 Nov 2003 14:41:47 -0500


I am no mathematician but it seems to me that the hart of this issue that
many of us are finding a little hard to grasp is whether one subscribes to
the infinite alleles or stepwise model of mutations.
The following is from the FTDNA website;

The Anthropology community uses 2 models to explain polymorphism, the
scientific name for mutations. These models are known as the Stepwise
model and the infinite allele model. An explanation of each is contained
below. All of the information below is supplied by Dr. Bruce Walsh,
University of Arizona, who serves on FTDNA's Advisory Board as our
population geneticist consultant. Please find a more in depth explanation
on this subject directly from Dr. Bruce's page especially prepared for
FTDNA customers at: http://nitro.biosci.arizona.edu/ftdna/TMRCA.html

Stepwise model-- The stepwise mutational model tries to better account for
the actual mutational process that occurs at micro satellite markers. What
is scored is marker length.
The stepwise mutation model looks at the frequency spectrum (0,1,2,3 ..)
of the mismatches, namely how many loci show no mismatches, 1 mismatch, 2
mismatches, etc. Its simplest form is the one-step, symmetric model, which
assumes only one step per mutation, with equal probability of increasing
(+1) or decreasing (-1). More complex stepwise mutational models can be
constructed, but this is a little premature until more information on the
mutational process is available. Currently, there is very good evidence
for the one-step model, as only 1/30 to 1/50 of all (the small number of)
observed mutations are two-steps.
If most mutations are one-step, but a few two-step mutants exist, then the
true distribution of the TMRCA (See Q #2) falls between the infinite
alleles and stepwise models. For example, suppose we observed an exact
match at 24 markers, and a two-step mismatch at one marker. This is most
probably a single mutation as opposed to two (or more) one-step mutations.
If the latter were true, we would expect other loci to have mutated as
well, unless they had lower mutations rates.

Infinite Allele Model-- The infinite allele model is just a fancy term
that population geneticists use to refer to those occasions where each
mutations may be of different lengths (i.e., there are an infinite number
of states that an allele can mutate too, hence each mutation is assumed to
be unique).

This is the simplest mutation model, simply scoring loci as match/no
match.

There is a risk of undercounting the total number of mutations, and hence
underestimating the actual TMRCA. If individuals are identical at a large
fraction of the markers, this risk is very small. As individuals differ at
more and more markers, the undercounting can become more severe.


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