Noise-induced versus intrinsic oscillation in ecological systems.

Studies of oscillatory populations have a long history in ecology. A first-principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing oscillations. We employ statistical physics concepts, including measures of spatial synchrony, that incorporate patterns at all scales and are novel to ecology, to show that spatial patterns can, under broad and well-defined circumstances, elucidate drivers of population dynamics. We find that when neighbours are coupled (e.g. by dispersal), noisy intrinsic oscillations become distinguishable from noise-induced oscillations at a transition point related to synchronisation that is distinct from the deterministic bifurcation point. We derive this transition point and show that it diverges from the deterministic bifurcation point as stochasticity increases. The concept of universality suggests that the results are robust and widely applicable.