Background
Natural systems are inherently non-linear and consequently challenging to forecast . This has led to the application of dynamic system theory which aims to provide model-free and generic tools to identify approaching non-linearity . The majority of this work has attempted to detect critical slowing down (CSD), a phenomenon displayed by systems as they approach a bifurcation or ‘tipping point’ . In brief, CSD manifests when, as the distance to the tipping point decreases, the ability of the system to recover from perturbations and return to its average trend also decreases . This stems from the dominant eigenvalue of the system trending towards zero and results in successive snapshots in time being more similar than if the system was far from a tipping point; in practical terms, successive abundance/biomass measurements in time or space begin to correlate more strongly.
Detecting CSD can be as simple as tracking the temporal change in summary statistics. For example, increasing autocorrelation at lag-1 , increasing variance , increasing skewness and kurtosis are all representative of CSD. In univariate data, each of these have been successful in identifying oncoming tipping points in simulated experiments as well as empirical lake regime shifts , boreal forest loss , disease (re)emergence , and psychopathology (McSharry et al. 2003, Schreuder et al. 2020). The popularity and scope of EWSs is consequently expanding to new applications and multivariate data sources to maximise the utility of the approach with the increasingly large amounts of ecological monitoring data now available . There is therefore a general desire to exploit EWSs in both traditional research and policy decision making as evidenced by the rapid increase in the publication and citation of EWS literature per year (Figure 1).