How to quantify the temporal storage effect using simulations instead of math

The storage effect has become a core concept in community ecology, explaining how environmental fluctuations can promote coexistence and maintain biodiversity. However, limitations of existing theory have hindered empirical applications: the need for detailed mathematical analysis whenever the study system requires a new model, and restricted theory for structured populations. We present a new approach that overcomes both these limitations. We show how temporal storage effect can be quantified by Monte Carlo simulations in a wide range of models for competing species. We use the lottery model and a generic integral projection model (IPM) to introduce ideas, and present two empirical applications: (1) algal species in a chemostat with variable temperature, showing that the storage effect can operate without a long-lived life stage and (2) a sagebrush steppe community IPM. Our results highlight the need for careful modelling of nonlinearities so that conclusions are not driven by unrecognised model constraints.