  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 a coarse-graining procedure
accounts for a variety of ecological mechanisms and leads to effective spatial
effects which favour species coexistence. Herein, we provide conditions for
several species to live in an environment with 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.
