THE EVOLUTION OF SLOW DISPERSAL RATES - A REACTION-DIFFUSION MODEL

We consider n phenotypes of a species in a continuous but heterogeneou s environment, it is assumed that the phenotypes differ only in their diffusion rates. With haploid genetics and a small rate of mutation, i t is shown that the only nontrivial equilibrium is a population domina ted by the slowest diffusing phenotype. We also prove that if there ar e only two possible phenotypes, then this equilibrium is a global attr actor and conjecture that this is true in general. Numerical simulatio ns supporting this conjecture and suggesting that this is a robust phe nomenon are also discussed.