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' are similar, except that with N = 10 individuals (2N = 20 alleles), steps occur at intervals of 0.05, compared with 0.005 in the larger populations with N = 100 (2N = 200 alleles). Thus the 'walk' to loss or fixation is faster in smaller populations, though the ratio of
q 'steps' up and down is the same.
Patterns of 'random walk' are similar, except that with N = 10 individuals (2N = 20 alleles), steps occur at intervals of 0.05, compared with 0.005 in the larger populations with N = 100 (2N = 200 alleles). Thus the 'walk' to loss or fixation is faster in smaller populations, though the ratio of
Figure & Text material © 2025 by Steven M. Carr