COS 217-4 - Assessing responses to pulse perturbations under non-equilibrium population dynamics

Abstract: Measuring how an ecological community resists to or recovers from shocks on species abundances is an important step in assessing its stability. Yet, the bulk of research on responses to pulse perturbations has assumed population dynamics around an equilibrium point and our knowledge of such responses under transients, cycles, or chaos remains scattered and limited. Here, we compare several stability measures of responses to pulse perturbations under non-equilibrium dynamics and present the challenges of inferring these measures from abundance time series. We first use a suite of population dynamics models to illustrate that, at any given point along a non-equilibrium trajectory, a community that is stable according to one measure can be unstable according to another measure. We then show that, similarly to equilibrium dynamics, a given stability measure under non-equilibrium dynamics can be more appropriate for short- (e.g., singular values of Jacobian matrix) or long-term (e.g., global Lyapunov exponents) responses. Next, we describe how to compute stability measures from abundance time series of sparsely observed communities using empirical dynamic modeling to infer a time-varying Jacobian matrix. We show that the information provided by each measure can change when leaving out certain species or when lumping species together. Finally, we use different empirical non-equilibrium time series to illustrate how to infer and interpret the different stability measures. As expected, inferring multiple measures gives a more complete picture of community stability along a trajectory than inferring a single measure. In addition, ignoring certain species can impact how stability measures change along a trajectory. Overall, our results shed light on our understanding and capacity to infer ecological stability under the widespread setting of non-equilibrium population dynamics.