Background/Question/Methods: We study coexistence in a model of competing annual plants in the presence of a seed predator and an auto-correlated fluctuating environment. As in past investigations, coexistence by the storage effect occurs but here the storage effect divides into two mechanisms, the storage effect due to predation and the storage effect due to competition. These separate mechanisms can be defined and assessed quantitatively through temporal covariances, respectively covariance between environmental fluctuations and competition, and covariance between environmental fluctuations and predation.

Results/Conclusions: In the past, models for annual plants did not find a storage effect due to predation except in multi-species settings with frequency-dependent predation. However, temporal auto-correlation leads to the storage effect due to predation because predator density builds up on environmentally favored prey (covariance between environment and predation), depressing their densities, and providing opportunities for other species to increase in settings with any number of species. Surprisingly, the storage effect due to competition decreases in magnitude with auto-correlation in the absence of predation because auto-correlation reduces covariance between environment and competition. In the presence of predation and competition, whether auto-correlation has an overall positive effect on coexistence depends on the strength of predation and the type of competition. Increased predation intensity increases the positive effect of auto-correlation on the storage effect due predation, while the storage effect due to competition is less negatively affected by predation and auto-correlation when competition is closer to the contest than the scramble form.