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Establishing the conditions that guarantee the spreading or the sustenance ofaltruistic traits in a population is the main goal of intergroup selectionmodels. Of particular interest is the balance of the parameters associated togroup size, migration and group survival against the selective advantage of thenon-altruistic individuals. Here we use Kimura's diffusion model of intergroupselection to determine those conditions in the case the group survivalprobability is a nonlinear non-decreasing function of the proportion ofaltruists in a group. In the case this function is linear, there are twopossible steady states which correspond to the non-altruistic and thealtruistic phases. At the discontinuous transition line separating these phasesthere is a non-ergodic coexistence phase. For a continuous concave survivalfunction, we find an ergodic coexistence phase that occupies a finite region ofthe parameter space in between the altruistic and the non-altruistic phases,and is separated from these phases by continuous transition lines. For a convexsurvival function, the coexistence phase disappears altogether but a bistablephase appears for which the choice of the initial condition determines whetherthe evolutionary dynamics leads to the altruistic or the non-altruistic steadystate.

Nonlinear group survival in Kimura's model for the evolution of altruism