  In many natural situations one observes a local system with many competing
species which is coupled by weak immigration to a regional species pool. The
dynamics of such a system is dominated by its stable and uninvadable (SU)
states. When the competition matrix is random, the number of SUs depends on the
average value of its entries and the variance. Here we consider the problem in
the limit of weak competition and large variance. Using a yes/no interaction
model, we show that the number of SUs corresponds to the number of maximum
cliques in a network close to its fully connected limit. The number of SUs
grows exponentially with the number of species in this limit, unless the
network is completely asymmetric. In the asymmetric limit the number of SUs is
${\cal O} (1)$. Numerical simulations suggest that these results are valid for
models with continuous distribution of competition terms.
