Evolution of Dispersal in Metapopulations with Local Density Dependence and Demographic Stochasticity

Selective pressures governing the evolution of dispersal rates are difficult to evaluate and currently poorly understood. In particular, predictions of evolutionarily stable dispersal strategies have only been derived under a number of limiting conditions regarding the ecology of of dispersing species. In this paper we predict the outcome of dispersal evolution in metapopulations based on a suit of assumptions that are more likely to be met in the field: (i) population dynamics within patches are density-regulated by realistic growth functions,(ii) demographic stochasticity resulting from finite population sizes within patches is accounted for and (iii) the transition of individuals between patches is explicitly modeled by a disperser pool. In addition we make few further changes which add to the models interest for comparison purposes; (iv) individuals can disperse between habitable patches throughout their lifetime, and (v) metapopulations are described in continuous time instead of relying on season-to-season descriptions. Extending available models in regard to these features, we demonstrate the existence of two general patterns of metapopulation adaptation. We show,first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Instead, without demographic stochasticity, adapted dispersal rates exhibit a maximum for intermediate levels of disturbance and fall off for both higher and lower rates of local extinction. Second, we describe how the demographic stochasticity that inevitably occurs in finite populations affects the evolution of dispersal rates. Contrary to predictions from deterministic models, evolutionarily stable dispersal rates in metapopulations composed of small local populations can remain high even when rates of local extinction are low. The first pattern is shown to be robust, provided that demographic stochasticity is not too severe. under a range of local growth conditions, including logistic growth and its variants. We also demonstrate that high degrees of demographic stochasticity can enrich the behavior of adapted dispersal rates in response to varied levels of disturbance: monotonic increases or decreases can be observed as well as intermediate maxima or minima.