Quasi-cycles in a spatial predator-prey model

TL;DR

This paper demonstrates that stochastic fluctuations in spatial predator-prey models lead to oscillations in populations, which are amplified by resonance, extending previous non-spatial analyses to spatial systems.

Contribution

It analytically characterizes quasi-cycles in spatial predator-prey models, showing their origin in stochastic resonance and generalizing non-spatial results.

Findings

Predator and prey populations oscillate in space and time due to stochastic effects.

Analytical power spectra match stochastic simulation results.

Spatial quasi-cycles are a natural extension of non-spatial models.

Abstract

We show that spatial models of simple predator-prey interactions predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic fluctuations about the time-independent solutions of the deterministic equations which are amplified due to the existence of a resonance. We calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations. This work extends the analysis of these quasi-cycles from that previously developed for well-mixed systems to spatial systems, and shows that the ideas and methods used for non-spatial models naturally generalize to the spatial case.