A consumer–resource system with source–sink populations and asymmetric dispersal

Abstract

In this paper, we consider a two-patch system with source–sink populations and asymmetric dispersal, which includes exploitable resources and extends a recent model describing experiments. Applying dynamical systems theory, we reveal uniform persistence of the system and exhibit existence of stable positive equilibria. Based on rigorous analysis, we demonstrate that dispersal can lead to survival of species in both patches, and asymmetric dispersal can make the species reach higher density than that with symmetric dispersal or with no dispersal. A new prediction of this paper is that in source–sink populations, the species with asymmetric dispersal can approach a density higher than that in the corresponding homogeneous resource-distributions with or without dispersal, which extends previous theory. It is shown that small asymmetry to the sink patch can increase total population abundance, while extremely large asymmetry would result in extinction of species. Our findings are consistent with experimental results and provide new predictions. Numerical computations confirm and extend the findings.