Testing the irruptive paradigm of large-herbivore dynamics

A dominant paradigm in understanding and managing large herbivores is that, after introduction to new range or release from harvesting, the herbivore population increases to peak abundance, crashes to a lower abundance, and then increases to a carrying capacity lower than peak abundance. However, support for the paradigm has been largely anecdotal. We first developed two mathematical models to better describe irruptive dynamics. The models differed in the form of the postcrash growth toward carrying capacity: the "Caughley model" included a time lag that generated dampening oscillations, and the "Leopold model" did not. We then evaluated which of four models (theta-logistic, delayed-logistic, Leopold, and Caughley) best described the dynamics of seven ungulate populations either introduced to new range (n = 5 populations) or released from harvesting (n = 2). The dynamics of six of the populations were best described by irruptive models (two by the Leopold, one by the Caughley, and three by the delayed-logistic), and one of the populations did not display irruptive dynamics (theta-logistic model). The limited data thus support the widespread existence of irruptive dynamics, and we encourage the consideration of irruptive models in studies of large-herbivore dynamics.