An Assessment of Eberhardt’s Ratio-Dependent Wolf-Ungulate Model

A growing number of ecological studies suggest ratio-dependence may be common in many predator-prey systems. I assessed Eberhardt’s ratio-dependent wolf-ungulate model using 22 years of wolf (Canis lupus) and elk (Cervus elaphus) survey data, and 28 years of elk hunter harvest data from the northern range of Yellowstone National Park, USA. This model required estimation of eight parameters, of which four were determined from other studies and four were evaluated by statistical model fitting. Modelled trends in wolf and elk abundance were correlated with survey estimates, and modelled trends in wolf predation rates were correlated with empirical estimates. The equilibrium ratio of wolves to elk was 0.0063 and the equilibrium ratio of elk to habitat carrying capacity was 0.680. While this simple model provided a realistic portrait of wolf-elk dynamics in a complex predator-prey system, the performance of the model could be improved by including the sex and age structure of the elk population, a wolf functional response, and temporal variation in wolf and elk demographic rates. This model provides additional support for ratio-dependence in large mammal predator-prey systems.