Invasion fronts prevent extinction in a diffusively coupled inhomogeneous predator-prey ecosystem

Mathematical modeling of the effects of environmental variability on biodiverse ecosystems is of growing interest due to its potential applications in protecting endangered species or eradication of harmful organisms. The paradigmatic Lotka-Volterra model for predator-prey competition and coexistence is readily modified to include environmental effects by implementing a finite carrying capacity to represent limited resources for both competing species. This work studies a stochastic Lotka-Volterra model on a two-dimensional lattice (with periodic boundary conditions) subject to a spatially varying carrying capacity. Specifically, a region experiencing stable predator-prey coexistence is placed in diffusive contact with a similar subsystem that owing to high predation rates is prone to stochastic total extinction events. We investigate this coupled inhomogeneous system through agent-based Monte Carlo simulations. Due to traveling wave fronts emerging from the coexisting system into the region experiencing total extinction, the predator and prey population are sustained because of abundant prey. Our aim is to obtain (semi-) quantitative criteria to determine under what conditions a (finite) endangered ecosystem, which in isolation is likely to suffer stochastic extinction events, may be effectively stabilized through immigration waves emanating from a neighboring stable region.