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 system’s steady state. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work has been funded by the Engineering and Physical Sciences Research Council through the MathSys CDT [grant number EP/S022244/1]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes Data and code to reproduce results are available at .