Abstract: Environmental variability, temporal changes in an organism's environment, has long been known to play a critical role on the stability of animal populations. Theoretical ecology has developed the tools to model and project the impacts of environmental variation on population growth when populations exhibit density dependence. A key result from this past work is that as environments become more variable populations do as well. However, many populations are influenced by more complicated ecological feedbacks that drive phenomena such as population cycles. To determine how cycling populations respond to increases in the variability of their environment we develop a cyclical population model where we can can change the strength of the unstable equilibrium. This allowed us to determine how changing the strength of the population cycles influenced the stochastic properties of the population. Our results show that predictions from classic theory break down as environments become more variable, specifically, populations that cycle can exhibit increased stability in more variable environments. This effect arises because population regulation is weak in the region between the high and low values of the cycle. If the population enters this region, it is often retained for short transient periods leading to reduced variance. This result highlights how the responses of complex dynamical systems to environmental change can be highly dependent on the mechanisms driving population regulation, but that new tools can be used to predict the qualitative responses of these systems to global change. Forecasting the response of populations to increases in environmental fluctuations may be more difficult than previously thought, but new tools can be used to address these complications.
