  Environmental stochasticity is known to be a destabilizing factor, increasing
abundance fluctuations and extinction rates of populations. However, the
stability of a community may benefit from the differential response of species
to environmental variations due to the storage effect. This paper provides a
systematic and comprehensive discussion of these two contradicting tendencies,
using the metacommunity version of the recently proposed time-average neutral
model of biodiversity which incorporates environmental stochasticity and
demographic noise and allows for extinction and speciation. We show that the
incorporation of demographic noise into the model is essential to its
applicability, yielding realistic behavior of the system when fitness
variations are relatively weak. The dependence of species richness on the
strength of environmental stochasticity changes sign when the correlation time
of the environmental variations increases. This transition marks the point at
which the storage effect no longer succeeds in stabilizing the community.
