Asymmetric diffusion in a two-patch consumer-resource system

Abstract

This paper considers a two-patch system with consumer diffusion, which characterizes laboratory experiments and includes exploitable resources. Using dynamical systems theory, we exhibit global dynamics of the one-patch subsystem and show existence of stable positive equilibria in the two-patch system. Based on rigorous analysis, we demonstrate that heterogeneously distributed resources with asymmetric diffusion can support higher total population abundance than those with symmetric diffusion, or without diffusion. A novel finding of this work is that the asymmetric diffusion can make heterogeneously distributed resources support higher total population abundance than homogeneously distributed resources, even with species diffusion, which extends previous theory. Meanwhile, we reveal that intermediate asymmetry is favorable for total population abundance, while extremely large or extremely small asymmetry is unfavorable. Our results are consistent with experimental observations and provide new insights. Numerical simulations confirm and extend the results.