Recently, Benaim and Schreiber (Journal of Mathematical Biology (2019) 79:393) developed new mathematical results to characterize stochastic persistence (i.e. a tendency for all the species' densities to stay bounded away from extinction) and extinction (i.e. a positive probability that one or more of the species' densities asymptotically goes to zero) for stochastic, multispecies models with population structure and temporal autocorrelations. These characterizations rely on invasion growth rates and include the classical mutual invasibility conditions as special case.
Applying these methods to classical ecological modules of exploitative competition and apparent competition, I determine how and when autocorrelated temporal fluctuations alter ecological outcomes.
Results/Conclusions: For competing species and species sharing a common predator, the effect of temporally autocorrelated fluctuations on the community dynamics depends simultaneously on which vital rates are fluctuating and the sign of the temporal autocorrelation. For example, if fecundity of competing species fluctuate, then positive autocorrelations promote coexistence via a storage effect while negative autocorrelations can lead to stochastic priority effects. In contrast, negatively autocorrelated fluctuations in yearly survival of competitors, promotes coexistence by a new fluctuation-dependent coexistence mechanism whereby two conditions for the storage effect are not meet. Similar results occur models with apparent competition e.g. fluctuations in predator attack rates promote coexistence when they are positively autocorrelated, but otherwise can lead to stochastic priority effects. Collectively, these results highlight the potential importance of temporal autocorrelations in structuring ecological communities.