Sticky extinction states and the egalitarian transition

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.