Fixation probabilities when the population size undergoes cyclic fluctuations

Let us assume that there is a monoecious random mating population that chan ges cyclically in size. Then, the probability that a nonrecessive favorable mutant is ultimately fixed, if it is originally present in a single hetero zygote, is approximately proportional to the harmonic mean of the effective population sizes in the cycle and inversely proportional to the population size when the mutant appears, This approximation works well if the selecti ve advantage s of the mutant is small and the length k of a cycle is small in comparison with the population sizes in a cycle. If k is large the harmo nic mean is, in general, replaced by a weighted harmonic mean that puts the largest weights on reciprocals of effective population sizes in the first few generations after the mutant appears, (C) 2000 Academic press.