Macroscopic dynamic effects of migrations in patchy predator-prey systems

Different mechanisms at the behavioural or physiological levels determine many properties of predator-prey systems at the population level. In this paper, we present a method of obtaining complex predator-prey dynamic models from models at a detailed, behavioural level of description. We consider a multi-patch predator-prey model, the dynamics of which contains two time-scales: a fast one, associated with migrations between patches, and a slow one, on which interactions, reproduction and mortality occur. We use methods of perturbation theory in order to aggregate the multi-patch system into a reduced system of two differential equations for the total prey and predator populations. Several models for the aggregated systems are obtained from specific migration scenarios. At the global level, complex expressions for the functional and numerical responses emerge from simple models at the local and behavioural levels. We show that, even if the predator growth rate is directly related to prey deaths at the local level, this may no longer be true at the global level. As a consequence, the coupling between the predator and prey equations may be broken when a predator-prey model is derived from behavioural considerations. (C) 1997 Academic Press Limited.