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Genetic Drift vs. Mutations

Joe Felsenstein joe at evolution.genetics.washington.edu
Tue Apr 18 01:34:14 EST 1995


In article <3mjlut$sj6 at newshost.lanl.gov>,
Martijn A. Huynen <mah at primer.lanl.gov> wrote:
>
>Does anyone know how the expected frequency of a specific nucleotide
>(or allele), and the  distribution of this expected frequency
> depend on the mutation frequency in a case of neutral evolution.
>Kimura describes the change in
>the frequency-distribution in absence of mutations, but this (of course)
>allways goes to fixation. I need a formula that both includes mutations
>and genetic drift.

If the mutation model has the property that the probability of a
particular base arising is u, irrespective of what other base is there
(a property that is met by the Jukes-Cantor mutation model but byt few others)
and if the rate of mutation away from that base is v,  then
the density function of allele frequency  p  in a population of
effective size N is 

              4Nu-1      4Nv-1
f(p)  =   C  p      (1-p)

where C is (I think)   Gamma(4Nu+4Nv)/(Gamma(4Nu)Gamma(4Nv))  or at any
rate whatever is needed to get the integral between 0 and 1 to be 1.

The distribution is a beta-distribution.  This is an old result of
Sewall Wright from 1930.

-----
Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195
 Internet:         joe at genetics.washington.edu     (IP No. 128.95.12.41)



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