Oct 1, 1983

Diffusion model of intergroup selection, with special reference to evolution of an altruistic character

Proceedings of the National Academy of Sciences of the United States of America


Assume a diploid species consisting of an infinite number of competing demes, each having N(e) reproducing members and in which mating is at random. Then consider a locus at which a pair of alleles A and A' are segregating, where A' is the "altruistic allele," which has selective disadvantage s' relative to A with respect to individual selection, but which is beneficial for a deme in competition with other demes; namely, a deme having A' with frequency x has the advantage c(x - x) relative to the average deme, where c is a positive constant and x is the average of x over the species. Let varphi = varphi(x;t) be the distribution function of x among demes in the species at time t. Then, we have partial differentialvarphi/ partial differentialt = L(varphi) + c(x - x)varphi, where L is the Kolmogorov forward differential operator commonly used in population genetics [i.e., L = (1/2) ( partial differential(2)/ partial differentialx(2))V(deltax) - ( partial differential/ partial differentialx)M(deltax)], and M(deltax) and V(deltax) stand for the mean and variance of the change in x per generation within demes. As to migration, assume Wright's island model and denote by m the migration rate per deme per generation. By investigating th...Continue Reading

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