Increasing environmental fluctuations can dampen variability of endogenously cycling populations

Abstract

Understanding how populations respond to increasingly variable conditions is a major objective for natural resource managers attempting to forecast extinction risk. The lesson from current modeling is clear: Increasing environmental variability increases population abundance variability. We show that this paradigm fails to describe a broad class of empirically observed dynamics, namely endogenously-driven population cycles. In contrast to the dominant paradigm, these populations can exhibit reduced long-run population variance under increasing environmental variability. We hypothesize that this paradox arises from interactions between environmental stochasticity and nonlinear density dependence. Such interactions violate the oft-assumed additivity of stochastic and deterministic drivers of population fluctuations present in many models that forecast population size. We show evidence for the interaction in two canonical cyclical populations: flour beetles and Canadian Lynx. To help identify the interaction, we develop new theory to quantify the strength of these interactions by partitioning the effects of nonlinear dynamics and stochastic variation on dynamical systems. In both empirical examples, the partitioning shows that the interaction between deterministic and stochastic dynamics reduces the overall variance in population size. Our results highlight that previous predictions about extinction under environmental variability may prove inadequate to understand the effects of climate change in many populations.