  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.

Populations and Evolution;Statistical Mechanics