Anatomy of a population cycle: the role of density dependence and demographic variability on numerical instability and periodicity.

Determining the causes of cyclic fluctuations in population size is a central tenet in population ecology and provides insights into population regulatory mechanisms. We have a firm understanding of how direct and delayed density dependence affects population stability and cyclic dynamics, but there remains considerable uncertainty in the specific processes contributing to demographic variability and consequent change in cyclic propensity. Spatiotemporal variability in cyclic propensity, including recent attenuation or loss of cyclicity among several temperate populations and the implications of habitat fragmentation and climate change on this pattern, highlights the heightened need to understand processes underlying cyclic variation. Because these stressors can differentially impact survival and productivity and thereby impose variable time delays in density dependence, there is a specific need to elucidate how demographic vital rates interact with the type and action of density dependence to contribute to population stability and cyclic variation. Here, we address this knowledge gap by comparing the stability of time series derived from general and species-specific (Canada lynx: Lynx canadensis; small rodents: Microtus, Lemmus and Clethrionomys spp.) matrix population models, which vary in their demographic rates and the direct action of density dependence. Our results reveal that density dependence acting exclusively on survival as opposed to productivity is destabilizing, suggesting that a shift in the action of population regulation toward reproductive output may decrease cyclic propensity and cycle amplitude. This result was the same whether delayed density dependence was pulsatile and acted on a single time period (e.g. t-1, t-2 or t-3) vs. more constant by affecting a successive range of years (e.g. t-1,…, t-3). Consistent with our general models, reductions in reproductive potential in both the lynx and small rodent systems led to notably large drops in cyclic propensity and amplitude, suggesting that changes in this vital rate may contribute to the spatial or temporal variability observed in the cyclic dynamics of both systems. Collectively, our results reveal that the type of density dependence and its effect on different demographic parameters can profoundly influence numeric stability and cyclic propensity and therefore may shift populations across the cyclic-to-noncyclic boundary.