Stochasticity, predator-prey dynamics, and trigger harvest of nonnative predators

Environmental stochasticity is one of the premier features of population models used to forecast population persistence; however, most population viability analyses ignore interactions with other species. By contrast, theory in community ecology draws from a tradition of determinism: focusing on the processes (competition, predation) that promote the coexistence of groups of species (i.e., coexistence), while generally ignoring environmental variation in these processes (process noise or environmental stochasticity). Here I considered the role of deterministic and stochastic sources of variation in a predator-prey interaction on the probability of prey population extinction. Using discrete-time stochastic versions of a classic predator-prey model I show that even low levels of predator process noise increase the probability of prey extinction. Surprisingly, predator process noise has stronger negative effects on prey persistence than stochasticity in the population growth rate of the prey species itself. This conclusion is robust across a wide range of deterministic model behaviors, suggesting that the effects of stochastic variation in predator abundance on prey persistence may be pervasive. I then applied these insights to the management of endangered prey populations threatened by a nonnative predator and examined the relative efficacy of three predator control techniques at reviving declining prey populations. These techniques included immediate eradication and reduction of predator populations through either "proportional" harvest or "trigger" harvest. Under a proportional harvest regime, a constant proportion of predators were removed each year, with little attention paid to the natural variation experienced by predator populations. By contrast, I implemented trigger harvest by reducing predator abundance to a fixed threshold abundance level only in years in which the predator exceeds this harvest threshold. Trigger harvest reduces both the relative abundance and variance of predators, whereas proportional harvest only reduces the abundance of these species. My analysis suggests that the reduction of predator variance through trigger harvest can revive declining prey populations and, in some cases, revive them more effectively than a proportional reduction of predator abundance: the default control strategy when eradication cannot be achieved.