Reactivity and stability of large ecosystems

*Correspondence: Stefano Allesina, Department of Ecology and Evolution, University of Chicago, 1101 E. 57th, Chicago, IL 60637, USA e-mail: [email protected] The study of local stability has a long tradition in community ecology. Stability describes whether an ecological system will eventually return to its original steady state after being perturbed. More recently, the study of the transient dynamics of ecological systems has been recognized as crucial, given that continuously disturbed systems might never reach a steady state, and thus the instantaneous response to perturbations could largely determine species persistence. A stable equilibrium can be non-reactive—all perturbations decay immediately, or reactive—some perturbations are initially amplified before decaying. Here we derive analytical criteria for the reactivity of large ecological systems in which species interact at random. We find that in large ecological systems both stability and reactivity are governed by the same quantities: number of species, means of the intraand inter-specific interaction strengths, variance of inter-specific interactions, and the correlation of pairwise interactions. We identify two phase transitions, one from non-reactivity to reactivity and one from stability to instability. As reactivity is an intermediate state between non-reactivity and instability, it could be used to develop an early-warning signal for systems approaching instability.