Stochastic group selection model for the evolution of altruism

We study numerically and analytically a stochastic group selection model in which a population of asexually reproducing individuals, each of which can be either altruist or non-altruist, is subdivided into $M$ reproductively isolated groups (demes) of size $N$. The cost associated with being altruistic is modelled by assigning the fitness $1- \tau$, with $\tau \in [0,1]$, to the altruists and the fitness 1 to the non-altruists. In the case that the altruistic disadvantage $\tau$ is not too large, we show that the finite $M$ fluctuations are small and practically do not alter the deterministic results obtained for $M \to \infty$. However, for large $\tau$ these fluctuations greatly increase the instability of the altruistic demes to mutations. These results may be relevant to the dynamics of parasite-host systems and, in particular, to explain the importance of mutation in the evolution of parasite virulence.