For a new mutant allele A subject to Additive
Selection, the probability of fixation
u, given a selection coefficient s
in a population size N, is
u(s,N) = (1 - e-2s)
/ 1 - e-4Ns)
as plotted in
(A). The equation is true
irrespective of positive or negative selection (
s < 0 or s > 0 ). At
the extremes, u(0,N) = 1/(2N) for a
neutral allele, and if s > 1/(2N)),
fixation will likely occur irrespective of N.
That is, the break point is when s and 2N are
approximately reciprocals of each other.
(B) [red
box in (A)] If u
> 2s, selection is strongly
advantageous and the expectation of fixation of
the new mutant is high irrespective of N.
(C) [green
box in (A)] If selection is weak (
-1 < 2Ns < 1 ), the expectation is closer to
that for a neutral allele. If selection is strongly
deleterious where s < 0 and ( 2Ns
< -1 ), the probability of fixation is almost
nil.
NB: Any new mutant
allele A* necessarily arises in a
heterozygote A*A. If A* is recessive
to A, it has close to a 50:50 chance
of being lost in the next generation despite
any selective advantage, because the two alleles
in the heterozygous carrier are propagated with
equal probability. The expectation
of loss by chance remains high over the first few
generations, unless inbreeding and (or) drift
favor early formation of advantageous A*A*
homozygotes.