A PREY-PREDATOR MODEL IN A MULTI-PATCH ENVIRONMENT WITH DIFFERENT TIME SCALES

Abstract

Ecological systems are large scale systems involving a large number of variables. By aggregation, it is possible to obtain at each level of organization an approximate and simple system of differential equations which can be studied more easily than the whole system involving a very large number of variables. Important differences in the orders of magnitude of the time scales in ecological systems allow us to apply methods of perturbation theory in order to replace large scale systems by reduced systems described by a few number of global variables. Perturbation theory determines the conditions required for aggregation. As examples, we present prey-predator models taking into account the activity sequences of animals at the individual level. In this way, the predation pressure depends on the individual strategies selected by the animals. We compare numerical simulations for the whole system and for the reduced system. We show that as soon as the orders of magnitude for the slow and fast dynamics are sufficiently different, then the orbits obtained for the reduced system are very close to the orbits obtained for the whole system.