Temporal environmental variations affect diversity in communities of competing populations. In particular, the covariance between competition and environment is known to facilitate invasions of rare species via the storage effect. Here we present a quantitative study of the effects of temporal variations in two-species and in diverse communities. Four scenarios are compared: environmental variations may be either periodic (seasonal) or stochastic, and the dynamics may support the storage effect (global competition) or not (local competition). In two-species communities, coexistence is quantified via the mean time to absorption, and we show that stochastic variations yield shorter persistence time because they allow for rare sequences of bad years. In diverse communities, where the steady-state reflects a colonization-extinction equilibrium, the actual number of temporal niches is shown to play a crucial role. When this number is large, the same trends hold: storage effect and periodic variations increase both species richness and the evenness of the community. Surprisingly, when the number of temporal niches is small global competition acts to decrease species richness and evenness, as it focuses the competition to specific periods, thus increasing the effective fitness differences.
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