Non-equilibrium early-warning signals for critical transitions in ecological systems

Li Xu, Denis Patterson, Simon Asher Levin, Jin Wang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

Original languageEnglish (US)
Article numbere2218663120
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number5
StatePublished - Jan 31 2023

All Science Journal Classification (ASJC) codes

  • General


  • critical transitions
  • early warning signals
  • global stability of ecological systems
  • landscape-flux theory
  • tipping point prediction


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