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.