Decades of research in ecology have led to a solid theory for responses to pulse perturbations for stable fixed points. In an important paper, Arnoldi et al (2018, JTB) have unified several metrics (e.g. resilience, reactivity) under a common framework. 2/7

We followed a similar approach to derive analytical metrics of how perturbations amplify over time under nonequilibrium population dynamics. The metrics quantify the minimum, typical, and maximum amplification of a distribution of perturbations for any time scale (short or long term response). 3/7

We performed several simulations to show that the metrics capture the entire range of perturbation amplification for different types of nonequilibrium dynamics (forced cycle, limit cycle, nonstationary cycle, and chaotic dynamics). The metrics work for both discrete- or continuous-time dynamics. 4/7

A key insight is that perturbation amplification depends on community state in the short term, but not in the long term. For example, for seasonal population cycles, the outcome after a few weeks would depend on when the disturbance occurred but the outcome after an entire year would not. 5/7

By relying only on a sequence of Jacobian matrices, these metrics can be computed from empirical data if we can accurately infer these matrices. Thus, our work creates new opportunities to analyze communities that are far from equilibrium using approaches such as Empirical Dynamic Modeling. 6/7