Effects of diffusion and advection on predator-prey dynamics in closed environments

Abstract

We investigate the dynamics and the asymptotic profiles of positive steady states of a specialist predator-prey model and a generalist predator-prey model in closed advective environments. The threshold dynamics are determined by the mortality rate of the specialist predators and the predation rate of the generalist predators, respectively. We demonstrate that, no matter how large advection and diffusion rates are, the specialist predators can successfully invade as long as the mortality rate is sufficiently small, while the generalist predators can take-over the prey if the predation rate is relatively large. Finally, we explore the impacts of diffusion and advection on the asymptotic profiles of positive steady states. Our results imply that large advection rates and small diffusion rates will lead to the concentration of the species at the downstream or the upstream. Moreover, if the diffusion rates are large, then the densities of the species will be less spatial heterogeneous.