Abstract
Mechanistic models for herbivore populations responding to rainfall-driven pasture are used to explore the effect of temporal variability in a primary resource on the abundance and distribution of a species. If the numerical response of the herbivore to pasture is a convex function, then gains made over time intervals with above average rainfall do not compensate for losses incurred when rainfall is below average. Populations therefore fare worse when rainfall is variable compared with when rainfall is reliable. It is demonstrated that this result is independent of the distribution of rainfall. Sensitivity of a species to variability, and hence the limit to its distribution in variable environments, is directly proportional to the difference between population growth rate under ideal conditions and the estimated rate of decline as the species' resource tends to zero. When density dependence is included in the numerical response, the average abundance of a species declines with increasing variability in its primary resource. However, a model for the dynamics of pasture and rabbits (Oryctolagus cuniculus) and red foxes (Vulpes vulpes) in southern Australia, is used to illustrate that trophic interactions can reverse the effect of variability: in the absence of foxes, the mean abundance of rabbits declines with variability as expected, but in the full model the mean abundance of rabbits increases.