Exit time as a measure of ecological resilience

Resilience is an important concept in the study of critical transitions and tipping points in complex systems and is defined by the size of the disturbance that a system can endure before tipping into an alternative stable state. Nevertheless, resilience has proved resistant to measurement. Arani et al. show how the mathematical concept of mean exit time, the time it takes for a system to cross a threshold, can help to solve this problem and characterize the resilience of complex systems. They derived a model approach to estimate exit time from time series data and applied it to examples from a grazed plant population model, lake cyanobacterial data, and Pleistocene-Holocene climate data. This approach may improve our understanding of the dynamical properties of complex systems under threat. Science , aay4895, this issue p. eaay4895 Ecosystem resilience can be estimated via a time series modeling approach, improving the anticipation of critical transitions. Ecological resilience is the magnitude of the largest perturbation from which a system can still recover to its original state. However, a transition into another state may often be invoked by a series of minor synergistic perturbations rather than a single big one. We show how resilience can be estimated in terms of average life expectancy, accounting for this natural regime of variability. We use time series to fit a model that captures the stochastic as well as the deterministic components. The model is then used to estimate the mean exit time from the basin of attraction. This approach offers a fresh angle to anticipating the chance of a critical transition at a time when high-resolution time series are becoming increasingly available.