EFFECT OF DIFFUSION ON A CONSUMER-RESOURCE SYSTEM WITH SOURCE-SINK PATCHES

A consumer-resource system is considered, where the consumer moves between multiple source-sink patches with both resource and toxicant. By applying Lyapunov method and theoretic-graph theory, we show global stability of positive equilibria in the system. Then it is shown that diffusion could make the consumer persist in sinks, even make it reach total population abundance larger than if non-diffusing. Asymmetry in diffusion, toxicant distribution, and geographic pattern of patches are important to the persistence and increase. It is also shown that under certain conditions, diffusion could make the total abundance less than if non-diffusing, even make the consumer go into extinction in all patches. An interesting finding of this paper is that when toxicants are distributed homogeneously, asymmetric diffusion always makes the total abundance less than if non-diffusing, which extends experimental conclusions. Our results are consistent with experimental observations and demonstrate new predictions. This work is important for conservation of biodiversity and strategies in toxicant distribution.