Increasing environmental fluctuations can dampen variability of endogenously cycling populations

Abstract

Future climate projections predict a more variable world. Understanding how populations respond to increasing variability is a major focus for modelers and natural resource managers attempting to predict extinction risk. Current theory of extinction risk is based on models that assume populations reach a stable, deterministic equilibrium in the absence of environmental variation. The lesson from these models is clear: Increasing environmental variability increases population size variability and extinction risk. Although useful, these models fail to describe a broad class of empirically observed dynamics, namely cycles. We develop new theory for the effects of environmental variability on the dynamics of cycling populations. We find that when populations are driven by endogenous cycles, increasing environmental variability can reduce population size variability, contrary to all prior expectations that populations fluctuate more in more variable environments. This result relies on strong density-dependent feedback and represents a novel mechanism by which stochastic variation interacts with density-dependence. Moreover, these results highlight that theories of extinction and stability must be expanded to include more complex forms of the interactions between density-dependence and stochasticity.