Temporally varying resources amplify the importance of resource input in ecological populations
Temporally and spatially varying resource levels are present in most ecological systems. Very simple models incorporating the key features of temporally varying resources and specific descriptions of survivorship for consumer species show the overriding importance of the time dependence of available resources and the role that allochthonous inputs play as essentially insurance in allowing species to persist. Persistence of species with lifetimes short relative to the timescale of resource variability is determined by the geometric mean of resource levels, while the persistence of species where resources vary on a much shorter time scale (or with exponential survivorship) are determined by the arithmetic mean of resource levels. Models that incorporate features of time-varying resources and explicit life histories dramatically change our understanding of how fluctuations in resource availability through time and space will affect population persistence and community dynamics.