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molecular clocks

Joe Felsenstein joe at GENETICS.WASHINGTON.EDU
Sun Sep 8 08:55:19 EST 1991

Tom Holroyd's question was about "totally neutral mutations".  Probably
there aren't any of those.  After all, even a mutation in "junk" DNA
will change the base composition of the organism by a tiny amount and
that will have some tiny effect on fitness.

  But the point is that if the effect on fitness is given by s, and N is
the effective population size, then if  4Ns << 1  the small effect on fitness
is too small to have any noticeable impact on the probability of substitution.
The mutation will substitute as if perfectly neutral, which means that
it will not show bursts of substitution as long as  s  stays small enough
to be below this threshold.  Therefore one need not be too concerned
with perfect neutrality, just with whether the mutant is effectively
neutral.  That is what most of us mean by "neutral".

   The actual formula for probability of fixation of a mutant is (to
extremely good approximation) given by Kimura's formula:

     Prob(fixation)  =  (1 - exp(-4Nsp))/(1-exp(-4Ns))

with p = 1/(2N) if the mutant is initially present in one copy (s is the
increase in fitness in the heterozygote carrying the mutant).  When
4Ns gets small one can verify that this approaches the neutral expectation
of Prob(fixation) = 1/(2N).  In 1968 Kimura pointed out that as there are
expected to be 4Nu new mutants per generation the resulting substition
rate equals the mutation rate, for all mutants whose absolute value of
4Ns is less than 1.

Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195
 Internet:         joe at genetics.washington.edu     (IP No.
 Bitnet/EARN:      felsenst at uwavm
 UUCP:             ... uw-beaver!evolution.genetics!joe

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