Periodic travelling waves in cyclic predator-prey systems

Jonathan A. Sherratt Centre for Theoretical Modelling in Medicine, Department of Ma thema tie, Heriot-Watt University, Edinburgh EH14 4AS, U.K. E-mail: jasbma.hw.ac.uk Abstract Predation is an established cause of cycling in prey species. Here, the ability of predation to explain periodic travelling waves in prey populations, which have recently been found in a number of spatiotemporal field studies, is examined. The nature of periodic waves in these systems, and the way in which they can be generated by the invasion of predators into a prey population is discussed. A theoretical calculation that predicts, as a function of two parameter ratios, whether such an invasion will lead to a stable periodic travelling wave that would be observed in practice is presented the alternative outcome is spatiotemporal chaos. The calculation also predicts quantitative details of the periodic waves, such as speed and amplitude. The results give new insights into the types of predator-prey systems in which one would expect to see periodic travelling waves following an invasion by predators.