Stochastic predation events and population persistence in bighorn sheep

Abstract

Many studies have reported temporal changes in the relative importance of density-dependence and environmental stochasticity in affecting population growth rates, but they typically assume that the predominant factor limiting growth remains constant over long periods of time. Stochastic switches in limiting factors that persist for multiple time-steps have received little attention, but most wild populations may periodically experience such switches. Here, we consider the dynamics of three populations of individually marked bighorn sheep (Ovis canadensis) monitored for 24-28 years. Each population experienced one or two distinct cougar (Puma concolor) predation events leading to population declines. The onset and duration of predation events were stochastic and consistent with predation by specialist individuals. A realistic Markov chain model confirms that predation by specialist cougars can cause extinction of isolated populations. We suggest that such processes may be common. In such cases, predator-prey equilibria may only occur at large geographical and temporal scales, and are unlikely with increasing habitat fragmentation.

Figure 1

Number of adult ewes (circles) and total numbers of bighorn sheep at (a) Ram Mountain (1975–2004), (b) Sheep River (1981–2004) and (c) National Bison Range (1979–2004). Filled bars indicate years of cougar predation episodes.

Figure 2

(a) Plot of the natural log of population size in one year against the natural log of population size in the previous year for data from the Ram Mountain population (open symbols) and from one simulation of 100 years (solid symbols). The simulated data included a probability of predation commencing of 0.1 and an expected duration of 3.5 years. (b) Plot of population growth, r, against logged population size using the same data as in (a). The model captured the essential features of the population dynamics. (c) Probability of extinction as a function of the probability of a predation episode commencing in any one year and of its expected duration.