Fixation Probabilities When the Population Size Undergoes Cyclic Fluctuations1

Let us assume that there is a monoecious random mating population that changes cyclically in size. Then, the probability that a nonrecessive favorable mutant is ultimately fixed, if it is originally present in a single heterozygote, 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 selective 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 harmonic 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.