Fluctuating Growth Rates Link Turnover and Unevenness in Species-Rich Communities

The maintenance of diversity, the 'commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental stochasticity, intra- and interspecific competition, and dispersal. We show that, even if species have the same time-average fitness, fluctuations tend to drive the community towards ever-growing unevenness and species extinctions, but self-limitation and/or dispersal allow species-rich states to be sustained. Species abundance-distributions vary systematically in a Buffering-Stabilisation parameter plane that describes the relative strength of the underlying ecological processes, and cover different empirically relevant power-law and unimodal shapes. A model describing the effective dynamics of a focal species relates static abundance distributions with turnover dynamics, also when species have different mean fitness. The model suggests how community statistics and time series of individual species can inform on the relative importance of the ecological processes that structure diversity.