How to model the local interaction in the predator–prey system at slow diffusion in a heterogeneous environment?

We examine the nonlinear reaction–diffusion–advection equations to modeling of the predator–prey system under heterogeneous carrying capacity of the prey, and Holling type II functional response. When advection and diffusion fluxes are absent or small, we detect the discrepancy between the resource (carrying capacity) and species distributions. The large diffusion eliminates this effect. We propose a modification of the functional response coefficients to provide the correlation between species distribution and resource in both cases. The numerical simulation of several models both under small and moderate advection–diffusion fluxes is carried out. •The adequate modeling of species dispersal remains a challenging task in mathematical biology.•Reaction–diffusion–advection equations model predator–prey system with heterogeneity.•To describe species interaction, we introduce the coefficients depending on spatial variable.•Computer experiment with small and large advection–diffusion fluxes is presented.