Applied Mathematics Colloquium

Abstract: The selection of dispersion is a classical problem in ecology and evolutionary biology. Deterministic dynamical models of two competing species differing only in their passive dispersal rates suggest that the lower mobility species has a competitive advantage in inhomogeneous environments, and that dispersion is a neutral characteristic in homogeneous environments. We consider models including local population fluctuations due to both individual movement and random birth and death events to investigate the effect of demographic stochasticity on the competition between species with different dispersal rates. For homogeneous environments where deterministic models predict degenerate dynamics in the sense that there are many (marginally) stable equilibria with the species' coexistence ratio depending only on initial data, demographic stochasticity breaks the degeneracy. A novel large carrying capacity asymptotic analysis, confirmed by direct numerical simulations, shows that a preference for faster dispersers emerges on a precisely defined time scale. While there is no evolutionarily stable rate for competitors to choose in these spatially homogeneous models, the stochastic selection mechanism is the essential counterbalance in spatially inhomogeneous models including demographic fluctuations which do display an evolutionarily stable dispersal rate.