Conditional heteroskedasticity as a leading indicator of ecological regime shifts

Regime shifts are massive, often irreversible, re-arrangements of non-linear ecological processes that occur when systems pass critical transition points. Ecological regime shifts sometimes have severe consequences for human well-being including eutrophication in lakes, desertification, and species extinctions. Theoretical and laboratory evidence suggests that statistical anomalies may be detectable leading indicators of regime shifts in ecological time series, making it possible to foresee and potentially avert incipient regime shifts. Conditional heteroskedasticity is persistent variance which is characteristic of time series with clustered volatility. Here, we analyze conditional heteroskedasticity as a potential leading indicator of regime shifts in ecological time series. We evaluate conditional heteroskedasticity using ecological models with and without four types of critical transition. On approaching transition points, all time series contain significant conditional heteroskedasticity. This signal is detected hundreds of time steps in advance of the regime shift. Time series without regime shifts do not have significant conditional heteroskedasticity. Because probability values are easily associated with tests for conditional heteroskedasticity, detection of false positives in time series without regime shifts is minimized. This property reduces the need for a reference system to compare with the perturbed system.