Modeling spatial synchronization of predator-prey oscillations via the XY model under demographic stochasticity and migration.

The synchronization of oscillations in spatially extended ecological systems is a pervasive phenomenon. Here, we investigate the spatial synchronization of stochastic predator-prey oscillations in a multi-patch landscape. We model the system using the Rosenzweig-MacArthur model with demographic stochasticity. We demonstrate that the collective phase dynamics of the coupled ecological oscillators can be analytically mapped onto a framework inspired by the XY model of statistical mechanics. In this analogy, migration between patches acts as the coupling strength, while intrinsic demographic noise functions as an effective temperature that promotes disorder. This framework allows us to characterize the emergence of spatial synchrony as a noise-induced phase transition. We analytically and numerically identify the critical migration threshold required for global synchronization and show how the interplay between noise and coupling shapes the system's coherence. Our findings provide a robust statistical mechanics foundation for understanding large-scale ecological synchrony and offer new insights into the resilience of metapopulations.