Incorporating vital rates and harvest into stochastic population models to forecast elk population dynamics
Authors: Paterson J. Terrill , Proffitt Kelly M. , Rotella Jay J. 
Published: January 2022

The dynamics of ungulate populations across variable ecosystems and management strategies demonstrate disparate trajectories such that some populations are overabundant, while other populations are subject to recovery efforts. Understanding how variation in vital rates such as pregnancy and survival integrate to shape the trajectories of populations is, therefore, helpful for informed management, particularly given that our understanding of the dynamics of harvested ungulate populations is often limited. Age‐related variation in vital rates among elk (Cervus canadensis) suggest that suitable population matrix models require age‐specific vital rates that can be logistically and analytically challenging to obtain. Our goals were to use a large, long‐term data set on elk and hierarchical Bayesian models to estimate age‐specific pregnancy and annual survival rates and their process variances, use stochastic population projection matrices to understand the effects of additional mortality from harvest on population dynamics, and identify the influence of different combinations of vital rates on population trajectories. We found that median age‐specific pregnancy rates increased with age from yearlings (0.52, 90% credible interval [CrI] = 0.37, 0.65) to a plateau among prime ages (e.g., 9‐year‐old: 0.91, 90% CrI = 0.87, 0.94), followed by a decline for the oldest ages (e.g., 19‐year‐old: 0.10, 90% CrI = 0.03, 0.28). Annual survival rates plateaued among prime‐aged animals (e.g., 9‐year‐old: 0.94, 90% CrI = 0.92, 0.96), and declined for the oldest‐ages (e.g., 19‐year‐old: 0.21, 90% CrI = 0.04, 0.56). We found higher process variation in pregnancy rates than survival rates; annual pregnancy rates for a 7‐year‐old varied from 0.82 (90% CrI = 0.67, 0.92) to 0.98 (90% CrI = 0.95, 0.99), and annual survival rates varied from 0.94 (90% CrI = 0.85, 0.96) to 0.96 (90% CrI = 0.93, 0.99). Simulated population trajectories indicated that additional mortality due to harvest resulted in a shift in the age structure towards younger animals with lower probabilities of pregnancy. When we held calf survival between 0.48 and 0.50 and specified constant pregnancy rates, changes in age structure alone resulted in variation of the recruitment of female calves from 0.20 to 0.16. We found that populations with a low mean value of calf survival (0.25) and no additional mortality due to harvest had marginal demographic performance ( = 1.02) and could sustain no additional mortality from harvest and still increase. In contrast, productive populations with a high mean value of calf survival (0.75) required high harvests to abate population growth (e.g., harvest rate = 0.20,  = 0.94). Finally, we found a temporally lagged effect of harvest on age structure such that a shift towards younger animals could persist for multiple years following a reduction in harvest, suggesting that harvest may have multi‐year lagged depressive effects on population growth rates above and beyond the direct effects on survival rates. Our work highlights the importance of considering the effect of varying age‐structure on population dynamics, suggests minimum combinations of vital rates required for increasing or decreasing elk population growth rates to general management objectives, and provides the framework required for future management‐specific recommendations using stochastic population projection matrices.