  Establishing the conditions that guarantee the spreading or the sustenance of
altruistic traits in a population is the main goal of intergroup selection
models. Of particular interest is the balance of the parameters associated to
group size, migration and group survival against the selective advantage of the
non-altruistic individuals. Here we use Kimura's diffusion model of intergroup
selection to determine those conditions in the case the group survival
probability is a nonlinear non-decreasing function of the proportion of
altruists in a group. In the case this function is linear, there are two
possible steady states which correspond to the non-altruistic and the
altruistic phases. At the discontinuous transition line separating these phases
there is a non-ergodic coexistence phase. For a continuous concave survival
function, we find an ergodic coexistence phase that occupies a finite region of
the parameter space in between the altruistic and the non-altruistic phases,
and is separated from these phases by continuous transition lines. For a convex
survival function, the coexistence phase disappears altogether but a bistable
phase appears for which the choice of the initial condition determines whether
the evolutionary dynamics leads to the altruistic or the non-altruistic steady
state.
