Environmental heterogeneity and biological pattern in a chaotic predator-prey system

This work investigates predator-prey interactions and diffusion in a heterogeneous environment. It has been previously shown that weak diffusion along an environmental gradient can drive an otherwise periodic predator-prey model into quasiperiodicity and chaos. The model is a reaction-diffusion equation with a Type II functional response of the predator and a logistic growth of the prey. The intrinsic growth rate of the prey varies linearly in space. We compare the spatial patterns of the populations to the underlying gradient. The spatial patterns of the predator and prey can differ strongly from the underlying environmental gradient. As diffusion becomes weaker, and the system moves from limit cycles through quasiperiodicity to chaos, this difference is magnified and the population patterns display smaller spatial scales.