  It is known that the competitive exclusion principle holds for a large kind
of models involving several species competing for a single resource in an
homogeneous environment. Various works indicate that the coexistence is
possible in an heterogeneous environment. We propose a spatially heterogeneous
system modeling the competition of several species for a single resource. If
spatial movements are fast enough, we show that our system can be well
approximated by a spatially homogeneous system, called aggregated model, which
can be explicitly computed. Moreover, we show that if the competitive exclusion
principle holds for the aggregated model, it holds for the spatially
heterogeneous model too.
