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  • Review Article
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Early-warning signals for critical transitions

Nature volume 461, pages 53–59 (2009)Cite this article

Abstract

Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

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Figure 1: Some characteristic changes in non-equilibrium dynamics as a system approaches a catastrophic bifurcation (such as F 1 or F 2, Box 1).
Figure 2: Early warning signals for a critical transition in a time series generated by a model of a harvested population 77 driven slowly across a bifurcation.
Figure 3: Ecosystems may undergo a predictable sequence of self-organized spatial patterns as they approach a critical transition.
Figure 4: Critical slowing down indicated by an increase in lag-1 autocorrelation in climate dynamics.
Figure 5: Subtle changes in brain activity before an epileptic seizure may be used as an early warning signal.

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Acknowledgements

Our work was supported by the Institute Para Limes and by the South American Institute for Resilience and Sustainability Studies. The work of S.R.C. is also supported by the US National Science Foundation. The research of M.R. and V.D. is supported by the Netherlands Organisation of Scientific Research, Earth and Life Sciences, in the case of M.R. through a Vidi grant. The work of J.B. is supported by the European Heads of Research Councils, the European Science Foundation and the European Commission Sixth Framework Programme through a European Young Investigator Award. G.S. was supported by Deutsche Bank Jameson Complexity Studies Fund, and by an NSF/NOAA CAMEO Grant NA08OAR4320894.

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Authors and Affiliations

  1. Department of Environmental Sciences, Wageningen University, PO Box 47, 6700 AA Wageningen, The Netherlands,

    Marten Scheffer, Vasilis Dakos & Egbert H. van Nes

  2. Integrative Ecology Group, Estación Biológica de Doñana, Consejo Superior de Investigaciones Científicas, Calle Américo Vespucio s/n, E-41092 Sevilla, Spain,

    Jordi Bascompte

  3. Department of Economics, 1180 Observatory Drive,

    William A. Brock

  4. Center for Limnology, 680 North Park Street, University of Wisconsin, Madison, Wisconsin 53706, USA,

    Stephen R. Carpenter

  5. Max Planck Institute for Meteorology, Bundesstraße 55, 20146 Hamburg, Germany,

    Victor Brovkin

  6. Potsdam Institute for Climate Impact Research, PO Box 601203, D-14412 Potsdam, Germany,

    Hermann Held

  7. Department Environmental Sciences, Utrecht University, Faculty of Geosciences, Copernicus Institute, PO Box 80115, 3508 TC Utrecht, The Netherlands,

    Max Rietkerk

  8. Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093, USA,

    George Sugihara

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Correspondence to Marten Scheffer.

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Scheffer, M., Bascompte, J., Brock, W. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009). https://doi.org/10.1038/nature08227

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