Section: New Results
Global behavior of competing species with strong diffusion: diffusion leads to exclusion
In  , we study the following problem. For a large class of models involving several species competing for a single resource in a homogeneous environment, it is known that the competitive exclusion principle holds: only one species survives eventually. Various works indicate though that coexistence of many species is possible when the competition occurs in a heterogeneous environment. We propose here a spatially heterogeneous system modeling several species competing for a single resource, and migrating in the spatial domain. For this model, it is known, at least in particular cases, that if migrations are slow enough, then coexistence occurs. In this paper we show at variance that if the spatial migrations are fast enough, then our system can be approximated by a spatially homogeneous system, called aggregated model, which can be explicitly computed, and we show that if the competitive exclusion principle holds for the aggregated model, then it holds as well for the original, spatially heterogeneous model. In other words, we show the persistence of the competitive exclusion principle in the spatially heterogeneous situation when migrations are fast. As a consequence, for fast migrations only one species may survive, namely the best competitor in average. We last study which is the best competitor in average on some examples, and draw some ecological consequences.