Demographic stochasticity and evolution of dispersion II: spatially inhomogeneous environments.

Demographic stochasticity, the random fluctuations arising from the intrinsic discreteness of populations and the uncertainty of individual birth and death events, is an essential feature of population dynamics. Nevertheless theoretical investigations often neglect this naturally occurring noise due to the mathematical complexity of stochastic models. This paper reports the results of analytical and computational investigations of models of competitive population dynamics, specifically the competition between species in heterogeneous environments with different phenotypes of dispersal, fully accounting for demographic stochasticity. A novel asymptotic approximation is introduced and applied to derive remarkably simple analytical forms for key statistical quantities describing the populations' dynamical evolution. These formulas characterize the selection processes that determine which (if either) competitor has an evolutionary advantage. The theory is verified by large-scale numerical simulations. We discover that the fluctuations can (1) break dynamical degeneracies, (2) support polymorphism that does not exist in deterministic models, (3) reverse the direction of the weak selection and cause shifts in selection regimes, and (4) allow for the emergence of evolutionarily stable dispersal rates. Dynamical mechanisms and time scales of the fluctuation-induced phenomena are identified within the theoretical approach.