Asymptotic spreading of predator-prey populations in a shifting environment

Abstract

Inspired by a recent study associating shifting temperature conditions with changes in the efficiency with which predators convert prey to offspring, we propose a predator prey model of reaction-diffusion type to analyze the consequence of such effects on the population dynamics and spread of {the predator} species. In the model, the predator conversion efficiency is represented by a spatially heterogeneous function depending on the variable $\xi=x-c_1t$ for some given $c_1>0$. Using the Hamilton-Jacobi approach, we provide explicit formulas for the spreading speed of the predator species. When the conversion function is monotone increasing, the spreading speed is determined in all cases and non-local pulling is possible. When the function is monotone decreasing, we provide formulas for the spreading speed when the rate of shift of the conversion function is sufficiently fast or slow.

Keywords

• hamilton-jacobi equations, viscosity solution, spreading speed, non-cooperative system, predator-prey, reaction-diffusion equations.