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.