Early Warning Signals in Ecological Time-Series.

Ecosystems can undergo abrupt, often irreversible transitions between alternative states-phenomena termed critical transitions or regime shifts-with profound consequences for biodiversity, ecosystem services, and human well-being. Early warning signals (EWSs) derived from time-series analysis offer the prospect of anticipating such transitions before they occur, potentially enabling preventive management intervention. This review provides a comprehensive synthesis of EWS methods for ecological systems, encompassing theoretical foundations, statistical indicators, empirical applications, and emerging methodological frontiers. We examine the dynamical basis of EWS in critical slowing down theory, wherein systems approaching bifurcation points exhibit characteristic statistical signatures including rising autocorrelation, increasing variance, and spectral reddening. We present a systematic overview of proposed indicators discuss moving-window frameworks for their computation, and critically evaluate preprocessing requirements and sensitivity to analytical choices. Empirical applications across major ecosystem types-including lakes, coral reefs, grasslands, forests, and marine fisheries-reveal both successes and limitations, with EWS performance depending critically on data quality, transition mechanism, and system-specific dynamics. We address recent advances including machine learning approaches, non-equilibrium thermodynamic indicators, multivariate extensions, and the important distinction between bifurcation-induced, noise-induced, and rate-induced tipping. We conclude with recommendations for specialists, emphasizing the integration of EWS within broader monitoring frameworks, systematic sensitivity analysis, and the interpretation of indicators as probabilistic assessments of changing resilience rather than deterministic predictions of imminent collapse.