Island models for takeover by a social trait facing a frequency-dependent selection barrier in a Mendelian population

A population genetic model is presented for selection of a Mendelian trait controlling for cooperative behavior between unrelated conspecifics. Under simple and robust assumptions, such a trait will be selected on a frequency-dependent basis, with a critical threshold frequency (beta(2) (crit)) of the social trait which must be exceeded before favorable selection of this trait can occur. Existence of this threshold gives rise to a basic evolutionary problem as to how evolution from an asocial state (beta congruent with 0) to a social state (beta congruent with 1) can take place. A formal model of this evolution is proposed which rests on obstacles to random mixing (population viscosity). The key fact is the possibility that an initial local concentration of the social trait may be able to spread out under the joint effects of selection and migration and eventually take over a much larger species population. It is argued that this model is the first formal model to capture the ideas of Wright concerning group selection of an altruist trait in an island-structured population.