Robust stabilization of an extinction prone predator-prey environment through invading activity fronts

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. Any finite stochastic system will eventually reach its final absorbing state (typically total extinction), but on a characteristic time that usually grows exponentially with its system size, thus often rendering itself effectively stable for experimentally reasonable timescales. However, tuning system parameters can reduce the characteristic extinction time and induce stochastic extinction events. Through agent-based Monte Carlo simulations, this work investigates the Lotka-Volterra predator-prey model on a two-dimensional lattice subjected to a spatially varying carrying capacity resulting in two distinct diffusively-coupled environments. One subsystem experiences stable predator-prey coexistence, whereas its neighbor is a vulnerable, extinction-prone region. Upon placing the two environments in diffusive contact, wave fronts emerging from the coexisting system into the vulnerable region excite and revive the predator and prey populations. The robustness of this stabilization of finite-size, excitable systems is discussed in the context of this model and related systems.