Evolution of an altruistic trait through group selection as studied by the diffusion equation method.

A diffusion model is formulated which incorporates the process of group selection (i.e. interdeme competition) in addition to mutation, migration, individual selection, and random genetic drift. A condition is obtained for group selection to prevail over individual selection in the evolution of an altruistic trait. Let DK = c/(v + v' + m) - 4Nes', where v' and v are mutation rates to and from the altruistic allele (A'), m is the migration rate (assuming Wright's island model), s' is the selective disadvantage of A' with respect to individual selection, Ne is the effective population size of each deme (group) and c is a positive constant such that a deme having A' with frequency x has the advantage c(x - means) relative to the average deme. Then, group selection overrides individual selection if DK greater than 0, while individual selection prevails if DK less than 0.