Reactivity and transient dynamics of predator-prey and food web models

Stability and resilience characterize the asymptotic responses of perturbations to the equilibria of ecological models. Short-term responses, however, can differ markedly from asymptotic responses. Perturbations to a stable equilibrium may, for example, produce trajectories that initially move away from, rather than towards, the equilibrium. The maximum short-term rate of departure from the equilibrium is called the reactivity, and stable equilibria with positive reactivity are called reactive. These transient responses can be large and long-lasting, and have been reported in a variety of ecological models. In this paper we explore the reactivity of predator-prey and food web models. We show that coexistence equilibria are reactive in all predator-prey and food web models in which at least one species has a per capita growth rate that is independent of its own density. These constitute the vast majority of published models. When density-dependent mortality of the top predator is included in the form of a non-linear closure term, reactivity always decreases, and may be eliminated altogether. Our results imply that short-term amplification of perturbations is a real possibility for predator-prey interactions and food webs. (C) 2004 Elsevier B.V. All rights reserved.