Evolution of variance in offspring number: the effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145-151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is w(e)=w-sigma(2)/N, where w is the mean fitness, sigma(2) is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145-151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.