Evolution of an Altruistic Trait through Group Selection as Studied by the Diffusion Equation Method

Abstract

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 evolutionv of an altruistic trait. Let D_K = c /( v + v ′ + m ) − 4 N _e s ′, 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, N_e 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 − x ¯) relative to the average deme. Then, group selection overrides individual selection if D_K >0, while individual selection prevails if D_K <0.