Early warning signals

Miner's canary When a system approches a tipping point it may exhibit certain signs of instability that could potentially be used as early warning signals.  Two main theoretical phenomena that describe this effect are critical slowing down and flickering.   Critical slowing down is based on the generic mechanism that in the vicinity of a bifurcation or tipping point, the rate at which a system recovers from small perturbation becomes very slow.  In contrast, flickering refers to a system that switches back and forth between alternative states in response to relatively large impacts.  Analyses of model time-series show that increasing variance and changes in autocorrelation and skewness may represent early warning signals.  The challenge in the real world is to find sufficiently high resolution time-series before an observed tipping point so that these theories can be tested.  It is also important in real world situations to rule out other explanations for the apparent signals, such as the variations in the variable of interest driven by the fluctuations in some other variable. 





Figure:  Early warning signals for a critical transition in a time series generated by a mathematical model of a harvested population driven slowly across a bifurcation.  As the biomass declines (a) towards the transition F1, the standard deviation (c) and autocorrelation (d) metrics of the residuals (b) from the detrended biomass curve both show increasing trends.  Increasing, or rising variance, and increasing autocorrelation are signs of critical slowing down prior to a transition (Scheffer et al 2009).