Robust stabilization of an extinction prone predator-prey environment

The effects of environmental variability on biodiverse ecosystems are of growing interest due to their potential applications in protecting endangered species or eradicating harmful organisms. The predator-prey Lotka-Volterra model is readily modified to include environmental effects by introducing a finite carrying capacity that represents limited resources for both species. Any finite stochastic system will eventually reach its final absorbing state (typically total extinction), but on a timescale that scales exponentially with its system size, effectively rendering itself stable. Through agent-based Monte Carlo simulations, this work employs a two-dimensional, stochastic lattice model subjected to a spatially varying carrying capacity resulting in two different, diffusively-coupled environments. One environment experiences stable coexistence of predators and preys, whereas its neighbor is a vulnerable, extinction-prone region due to the spatial heterogeneity of resources. By placing the two environments in diffusive contact, traveling wave fronts emerging from the coexisting system into the region experiencing total extinction, the predator and prey populations are revived. The robustness of this stabilization mechanism in the context of this model and similar predator-prey type models is discussed as well as (semi-) quantitative criteria that describes this phenomena.