The effect of advection on a predator–prey model in open advective environments

Abstract

This paper deals with a reaction–diffusion–advection system that characterizes the interactions between predators and prey in open advective environments, subject to an unidirectional flow, such as streams or rivers. To explore the influence of advection rates on the dynamics of this system, we study its dynamical classification by taking advection rates of two species as the variable parameters. It turns out that there exist some critical curves in the parameter plane of advection rates, which classify the dynamics of this system into several scenarios: (i) coexistence, (ii) persistence of prey only, (iii) persistence of predators only, (iv) extinction of both species. Furthermore, some qualitative properties of these critical curves are given by rigorous mathematical analysis and numerical computations. Our analytical and numerical results show that predators can invade successfully when they take relatively small advection rates. Especially, specialist predators always coexist with the prey when they invade successfully because they must keep pace with the prey for food. Nevertheless, generalist predators can take over the habitats when the prey’s advection rate is suitably large, which implies that the prey’s advection can facilitate the invasion of generalist predators. In addition, we numerically observe that the boundary loss rate has a significant influence on the dynamical classification. All of these results provide us with some deep insights into the dynamics of this system.