Ranking species based on sensitivity to perturbations under non‐equilibrium community dynamics

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data‐driven approaches (expected sensitivity and eigenvector rankings) based on the time‐varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time‐series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium. Managing ecological communities requires fast detection of species that are sensitive to perturbations, but approaches to perform such detection are mostly based on equilibrium population dynamics. We introduce two data‐driven approaches based on the time‐varying Jacobian matrix to rank species over time according to their sensitivity to perturbations when dynamics are out of equilibrium. We demonstrate the accuracy of our ranking approaches using population dynamics models and illustrate their application to detect sensitive species over time using empirical time series.