Stochasticity-induced stabilization weakens in diverse communities.
Environmental stochasticity and the temporal variations of demographic rates associated with it are ubiquitous in nature. The ability of these fluctuations to stabilize a coexistence state of competing populations (sometimes known as the storage effect) is a counterintuitive feature that has aroused much interest. Here we consider the performance of environmental stochasticity as a stabilizer in diverse communities. We show that the effect of stochasticity is buffered because of the differential response of populations to environmental variations, and its stabilizing effect disappears as the number of populations increases. Of particular importance is the ratio between the autocorrelation time of the environment and the generation time. Species richness grows with stochasticity only when this ratio is smaller than the inverse of the fundamental biodiversity parameter. When stochasticity impedes coexistence and lowers the species richness, the ratio between the strength of environmental variations and the speciation (or migration) rate governs its effect.