Predator-prey interaction systems with non-uniform dispersal in a spatially heterogeneous environment

Abstract

In nature, species typically migrate to regions of favorable habitat that provide sufficient food and conditions beneficial to survival. When resources in a certain region are insufficient, there tends to be high species motility in search of food. Starvation-driven diffusion (SDD), which is affected by the local habitat conditions in heterogeneous environments, is a dispersal strategy that increases species motility when food or another resource is limiting. In this study, to gain an understanding of how nonuniform random dispersal affects the fitness of species in a heterogeneous region, we examine a Lotka-Volterra-type predator-prey model applied to the situation where the movement of predators follows the rules of SDD. The main result of this study is that when a predator diffuses following the rules of SDD and the prey diffuses uniformly, the predator is more likely to invade a region than when it diffuses uniformly. We conclude that dispersal using an SDD strategy increases species fitness from an evolutionary perspective. The results we present are obtained based on an eigenvalue analysis of the semi-trivial solutions for a linearized operator derived from a model with nonuniform random diffusion. Furthermore, the existence and uniqueness property of coexistence state under appropriate conditions are given. (C) 2020 Elsevier Inc. All rights reserved.