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).