A Note on the Evolution of Altruism in Structured Demes

A number of authors (Wilson 1975, 1977; Charnov and Krebs 1975, Matessi and Jayakar 1976; Cohen and Eshel 1976) have recently suggested models for the evolution of altruistic behavior in the absence of either kin selection or differential extinction of groups. This possibility arises when the breeding population is divided into units, called trait groups by Wilson, within which behavioral interactions take place. Given sufficient genetic differentiation among trait groups, it can be shown that altruistic genotypes may sometimes increase in frequency in the population as a whole, even if they are at a disadvantage within each trait group, and even if there is random mating among trait groups. In particular, Wilson (1975, 1977) proposed a model where an altruistic individual confers a fitness benefit on other members of its group, but itself suffers a selective disadvantage in consequence. He showed that if variation in gene frequencies between trait groups arises simply because of binomial sampling of individuals from the overall population into trait groups, a gene for altruism of this sort is eliminated. He suggested that differential responses of altruistic and selfish genotypes to environmental heterogeneity might create a sufficiently arge excess in variance over binomial expectation that altruism could be favored. The purpose of this note is to show that this source of excess variance is extremely unlikely to allow a rare gene for altruism to spread, and that restrictions on interbreeding between trait groups are also incapable of promoting the evolution of altruism with this model. Following Wilson, consider a sexually reproducing haploid organism with discrete generations. The population is divided into an infinite number of trait groups of constant size n formed by sampling from the new individuals produced by the breeding population. There are two alleles, A (altruists) and a (selfish). The fitness of A and a within a trait-group containing i altruists are, respectively,