Expected
behavior of neutral alleles in multiple populations
(N = 10 or
100, q0 = 0.5; W0 = W1 = W2 = 1)
In each of 100 populations,
initial f(B) = q0 = 0.5.
(1) With N = 10 @, the distribution of
population-specific q rapidly flattens
across the interval q = 0.0 ~ 1.0. Starting at Generation
6, approximately equal numbers (48 & 52) go to
loss or fixation of B within 70 generations. (2) With N
= 100 @, loss or fixation begins to occur after about
50 generations, and is only complete after nearly 1,000
generations when 49 & 51 populations have gone to loss
or fixation. Note that the last polymorphic population (in
yellow) drifts to q > 0.7 at about 800
generations before drifting to q = 0,0 at about 950
generations.
Patterns of 'random walk' in the
two population sizes are similar, except that step sizes are
larger in smaller population. With N = 10 individuals
and 2N = 20 alleles, allele frequencies necessarily
occur at intervals of 0.05, compared with 0.005
in the larger populations. Thus the 'walk' to loss or
fixation is faster in smaller populations, though the ratio
of q 'steps' up and down is the
same.
Figure & Text material © 2024
by Steven M. Carr