The dampening effect of temporal environmental variation

Existing ecological theory suggests that temporal environmental noise should increase the amount of variation observed in the size of populations across time.  By contrast, two recent empirical studies suggest that populations may exhibit less variation in a more variable environment.  Here I present theoretical results from 3 related models to examine the effect of environmental variation.   All of the models are predator-prey or consumer-resource models based on standard, widely used formulations.  The result is a description of four mechanisms by which temporal environmental variation could reduce temporal variation at the population level.  Environmental variation can reduce the amplitude of cycles in population dynamics due to 1) non-linear averaging, 2) counter-acting other environmental variation, 3) destructive interference, or 4) compensatory dynamics at a tropic level.  In real systems, these mechanisms may act separately or in concert.