Modeling biological invasion into a periodic environment

Abstract

Seo and Kim [1] and Shigesada et al. [2, 3] proposed a reaction-diffusion equation set in a periodic environment to model the invasion dynamics of biological organisms in heterogeneous environments. While Shigesada et al. [2, 3] argue that a species should reduce its diffusivity in less favorable patches to increase the chance of successful invasion, Seo and Kim [1] present contrasting findings, offering a more intuitive outcome. The main difference between the two authors lies in applying Fick and Wereide’s diffusion law, where a single constant power adjustment changes one equation from the other. Seo and Kim [1] show that Fick’s diffusion law inadequately captures dispersal phenomena in such an environment. The subsequent analysis encompasses the stability of invasion conditions and the determination of the minimum wave speed for a periodic traveling wave. The theoretical findings are subsequently subjected to numerical validation.