Background/Question/Methods Ecological communities are under the constant threat of perturbations, which are increasing in frequency and magnitude due to human-driven environmental change. In order to avoid a larger loss of biodiversity under these circumstances, it is crucial to understand not only the response of the whole community to perturbations but also of its constituent species. In particular, there is a pressing need to identify which species are more sensitive to perturbations at a given time. Yet, conventional methods to assess response to perturbations focus on community-level indicators (e.g., leading eigenvalue of Jacobian matrix) and rely on equilibrium dynamics under an assumed population dynamics model (e.g., equilibrium Lotka-Volterra dynamics). In this study, we develop a data-driven approach based on nonlinear time series analysis that allows us to rank species under non-equilibrium community dynamics according to their local sensitivity to perturbations. Results/Conclusions We hypothesize that a species sensitivity to perturbations is determined by how aligned this species is with the leading eigenvector of the Jacobian matrix. We test this hypothesis using five models that generate non-equilibrium (i.e., fluctuating) abundance time series. Specifically, we compute how sensitive to perturbations on abundances and how aligned with the leading eigenvector each species is at different points in time. We show that we can accurately rank species sensitivities using the time-varying leading eigenvector, which we infer only with time-series data. Furthermore, we show that ranking species sensitivities solely based on their local abundances or rates of change provides a lower accuracy compared to our ranking method. We then apply our approach to two empirical non-equilibrium communities. Specifically, we perform abundance forecasts using a machine learning algorithm to test the hypothesis that species that are more sensitive to perturbations at a given time are harder to forecast. We find that species that are more aligned with the leading eigenvector show larger forecast errors, corroborating our hypothesis. Overall, our results suggest that species-level measures of sensitivity to perturbations can be improved by incorporating community-level information, potentially enhancing how we monitor and protect communities and their constituent species.
