Evolutionarily Stable Dispersal Rate in a Metapopulation with Extinctions and Kin Competition

We derive an analytic expression for the evolutionarily stable dispersal rate that formalizes the balance between the effects of four factors: the cost of dispersal, the extinction rate, the coefficient of relatedness and the mode of dispersal (i.e. the probability of common origin of immigrants). This result allows us to study the effects of each factor and, more interestingly, the interactions between them. In particular, we show that the evolutionarily stable dispersal rate is not always a decreasing function of the cost of dispersal and an increasing function of relatedness. These counter-intuitive results are discussed in the light of kin selection theory. We also present the results of numerical simulations in which relatedness is not a fixed parameter but depends on different parameters including dispersal itself. We discuss these results and show how the evolutionarily stable dispersal rate is affected by the environment and the life history traits of the species. More generally, this paper presents a simple formalism allowing the study of the effects of kin selection in unstable environments (i.e. with extinctions and recolonizations). The implications of this formalism for the understanding of the evolution of other life history traits is briefly discussed.