  Local coexistence of species in large ecosystems is traditionally explained
within the broad framework of niche theory. However, its rationale hardly
justifies rich biodiversity observed in nearly homogeneous environments. Here
we consider a consumer-resource model in which effective spatial effects,
induced by a coarse-graining procedure, exhibit stabilization of intra-species
competition. We find that such interactions are crucial to maintain
biodiversity. Herein, we provide conditions for several species to live in an
environment with a very few resources. In fact, the model displays two
different phases depending on whether the number of surviving species is larger
or smaller than the number of resources. We obtain conditions whereby a species
can successfully colonize a pool of coexisting species. Finally, we
analytically compute the distribution of the population sizes of coexisting
species. Numerical simulations as well as empirical distributions of population
sizes support our analytical findings.
