  Abundance fluctuations caused by environmental stochasticity are proportional
to population size. Therefore, populations that reach low density tend to
remain in this state and can increase only due to rare sequences of favorable
years. This stickiness can affect the composition of a community, as many
species become trapped in an almost permanent state of rarity. Here, we present
a solution for the species abundance distribution in scenarios where
environmental stochasticity is the dominant mechanism. We show that in the
absence of processes that impose a lower bound on abundances (such as
immigration), the community is dominated, at equilibrium, by a single species.
In the presence of immigration, the community undergoes a transition from an
egalitarian state, under weak stochasticity, to a very skewed abundance
distribution when stochasticity is strong.
