Quasi-cycles in a spatial predator-prey model

Details Quasi-cycles in a spatial predator-prey model Quasi-cycles in a spatial predator-prey model

2008-06-07

arxiv.org/abs/0806.1287v1

Biology

Quantitative Biology

Populations and Evolution

18 pages, 4 figures

Scientific paper

10.1103/PhysRevE.78.051911

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.

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