The selection for dispersal: a diffusive competition model with a free boundary

Abstract

This paper considers the population dynamics of an invasive species and a resident species, using a diffusive competition model in a radially symmetric heterogeneous environment with a free boundary. We assume that the resident species diffuses and expands in \({\mathbb{R}^n}\) , and the invasive species initially resides in a finite ball, but invades the environment with a spreading front that evolves as the free boundary. Our investigation aims to understand how the model dynamics are affected by the dispersal rate \({d_u}\) , expansion capacity \({\mu}\) and initial number u 0 of the invasive species. We show that a spreading–vanishing dichotomy exists and obtain the sharp criteria for spreading and vanishing by varying the parameters d u , \({\mu}\) and u 0. For the invasive species, we found an unconditional selection for slow dispersal rate, but a conditional selection for fast dispersal rate, that is, the selection for fast dispersal depends on the expansion capacity and initial number of the invasive species.