How early can an upcoming critical transition be detected?

Numerous studies have suggested the use of early warning signals (EWSs) of critical transitions to overcome challenges of identifying tipping points in complex natural systems. However, the real-time application of EWSs has often been overlooked; many studies show the presence of EWSs but do not detect when the trend becomes significant. Knowing if the signal can be detected early enough is of critical importance for the applicability of EWSs. Detection methods which present this analysis are sparse and are often developed anew for each individual study. Here, we provide a summary and validation of a range of currently available detection methods developed from EWSs. We include an additional constraint, which requires multiple time-series points to satisfy the algorithms conditions before a detection of an approaching critical transition can be flagged. We apply this procedure to a simulated study of an infectious disease system undergoing disease elimination. For each detection algorithm we select the hyper-parameter which minimises classification errors using receiver operating characteristic (ROC) analysis. We consider the effect of time-series length on these results, finding that all algorithms become less accurate as the amount of data decreases. We compare EWS detection methods with alternate algorithms found from the change-point analysis literature and assess the suitability of using change-point analysis to detect abrupt changes in a systems steady state.