Variation in stability of elk and red deer populations with abiotic and biotic factors at the species-distribution scale.

Stability in population dynamics is an emergent property of the interaction between direct and delayed density dependence, the strengths of which vary with environmental covariates. Analysis of variation across populations in the strength of direct and delayed density dependence can reveal variation in stability properties of populations at the species level. We examined the stability properties of 22 elk/red deer populations in a two-stage analysis. First, we estimated direct and delayed density dependence applying an AR(2) model in a Bayesian hierarchical framework. Second, we plotted the coefficients of direct and delayed density dependence in the Royama parameter plane. We then used a hierarchical approach to test the significance of environmental covariates of direct and delayed density dependence. Three populations exhibited highly stable and convergent dynamics with strong direct, and weak delayed, density dependence. The remaining 19 populations exhibited more complex dynamics characterized by multi-annual fluctuations. Most (15 of 19) of these exhibited a combination of weak to moderate direct and delayed density dependence. Best-fit models included environmental covariates in 17 populations (77% of the total). Of these, interannual variation in growing-season primary productivity and interannual variation in winter temperature were the most common, performing as the best-fit covariate in six and five populations, respectively. Interannual variation in growing-season primary productivity was associated with the weakest combination of direct and delayed density dependence, while interannual variation in winter temperature was associated with the strongest combination of direct and delayed density dependence. These results accord with a classic theoretical prediction that environmental variability should weaken population stability. They furthermore suggest that two forms of environmental variability, one related to forage resources and the other related to abiotic conditions, both reduce stability, but in opposing fashion: one through weakened direct density dependence and the other through strengthened delayed density dependence. Importantly, however, no single abiotic or biotic environmental factor emerged as generally predictive of the strengths of direct or delayed density dependence, nor of the stability properties emerging from their interaction. Our results emphasize the challenges inherent to ascribing primacy to drivers of such parameters at the species level and distribution scale.