The stochastic nature of the competitive exclusion principle

Background/Question/Methods

One of the most famous {\em laws} in community ecology is the
so-called competitive exclusion principle. It says that $n$
competitor species cannot co-exist on less than $n$ different
resources. Although it is true that, under certain assumptions,
this principle can be elevated to the rank of a mathematical
theorem [Hoffbauer and Sigmund, 1998], further studies have shown
that this ecological principle does not hold in general.
In fact, there is a number of reasonable ways in which such
assumptions can be relaxed/changed to allow for the coexistence
of an arbitrary number of species competing even for a single
resource [see, for instance, Tilman, 1994].

Results/Conclusions

Here, we show that, when competition is formulated in stochastic terms, a new kind of
competitive exclusion naturally arises with awesome
generality even in the most counterintuitive case of symmetrical competition.
This let us define a truly robust general principle of stochastic
competitive exclusion. Underlying this principle, there is a type of
stochastic bifurcation which does not have a deterministic analog.
Furthermore, we show the validity of the principle across a battery of
theoretical models of competitive communities. We characterize the type
of stochastic exclusion and the type of stationary steady states such
models present. We finally analyze the relevance of these results for
real ecological communities.