Deterministic group selection model for the evolution of altruism

We study the evolution of an infinite population of asexually reproducing individuals, each of which can be either altruist or non-altruist, subdivided into reproductively isolated groups (demes) of finite size under the action of two opposed selective pressures, namely. differential individual reproduction and differential deme extinction. We derive a recursion equation for the deterministic, discrete time evolution of the frequencies of the different types of demes, classified according to the number of altruistic individuals they have. We give emphasis to the detrimental effects of mutation and migration on the stability of the altruistic demes, which are the only stable demes in the absence of these processes. Furthermore? we dram an analogy between the proposed deterministic group selection model and the quasispecies model for molecular evolution.