How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Quantifying stability properties of ecosystems is an important problem in ecology. A common approach is based on the recovery from pulse perturbations, and posits that the faster an ecosystem return to its pre-perturbation state, the more stable it is. Theoretical studies often collapse the recovery dynamics into a single quantity: the long-term rate of return, called asymptotic resilience. However, empirical studies typically measure the recovery dynamics at much shorter time scales. In this paper we explain why asymptotic resilience is rarely representative of the short-term recovery. First, we show that, in contrast to asymptotic resilience, short-term return rates depend on features of the perturbation, in particular on the way its intensity is distributed over species. We argue that empirically relevant predictions can be obtained by considering the median response over a set of perturbations, for which we provide explicit formulas. Next, we show that the recovery dynamics are controlled through time by different species: abundant species tend to govern the short-term recovery, while rare species often dominate the long-term recovery. This shift from abundant to rare species typically causes short-term return rates to be unrelated to asymptotic resilience. We illustrate that asymptotic resilience can be determined by rare species that have almost no effect on the observable part of the recovery dynamics. Finally, we discuss how these findings can help to better connect empirical observations and theoretical predictions.