Inducing coexistence in vulnerable three-species ecosystems with cyclic competition

We employ agent-based Monte Carlo simulations on two-dimensional lattices to investigate spatially extended stochastic population dynamics for three cyclically competing species described by the May-Leonard model. Cyclic competition has been identified in diverse natural settings and appears as a characteristic motif in more complex food webs. In this work, we focus on finite model realizations with sufficiently asymmetric rates that would in isolation cause fixation for a single species, accompanied by extinction for the other two. By diffusively coupling a region prone to this finite-size fixation instability with another symmetric, hence stable May-Leonard system, we are able to induce qualitative changes in the behavior of the vulnerable subsystem, namely the stabilization of the three-species coexistence state through invasion fronts originating from the symmetric region. We aim to categorize this emergent behavior by analyzing the spatially inhomogeneous system's parameter space for which stabilization against finite-size fixation and extinction may be achieved, and to semi-quantitatively understand the necessary conditions for successfully implementing this novel control mechanism.