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Recovery rates reflect distance to a tipping point in a living system

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A Corrigendum to this article was published on 18 April 2012

Abstract

Tipping points, at which complex systems can shift abruptly from one state to another, are notoriously difficult to predict1. Theory proposes that early warning signals may be based on the phenomenon that recovery rates from small perturbations should tend to zero when approaching a tipping point2,3; however, evidence that this happens in living systems is lacking. Here we test such ‘critical slowing down’ using a microcosm in which photo-inhibition drives a cyanobacterial population to a classical tipping point when a critical light level is exceeded. We show that over a large range of conditions, recovery from small perturbations becomes slower as the system comes closer to the critical point. In addition, autocorrelation in the subtle fluctuations of the system’s state rose towards the tipping point, supporting the idea that this metric can be used as an indirect indicator of slowing down4,5. Although stochasticity prohibits prediction of the timing of critical transitions, our results suggest that indicators of slowing down may be used to rank complex systems on a broad scale from resilient to fragile.

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Figure 1: The response of two populations of cyanobacteria ( Aphanizomenon flos-aquae ) to dilution events under a regime of gradually increasing light levels.
Figure 2: Indicators of slowing down as a function of light intensity.

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Acknowledgements

We thank M. B. Gonçalves Souza for discussions on the experimental set up. We thank D. Waasdorp and W. Beekman-Lukassen for assistance with the experiments and C. ter Braak for statistical advice. A.J.V., E.J.F., V.D., E.H.v.N. and M.S. are supported by a European Research Council Advanced grant and M.S. is the recipient of a Spinoza award.

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Authors and Affiliations

  1. Department of Aquatic Ecology and Water Quality Management, Wageningen University, PO Box 47, NL-6700 AA, Wageningen, The Netherlands,

    Annelies J. Veraart, Elisabeth J. Faassen, Vasilis Dakos, Egbert H. van Nes, Miquel Lürling & Marten Scheffer

  2. Department of Aquatic Ecology, Netherlands Institute of Ecology, Royal Netherlands Academy of Arts and Sciences, PO Box 50, 6700AB, Wageningen, The Netherlands,

    Miquel Lürling

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  1. Annelies J. Veraart
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  2. Elisabeth J. Faassen
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  3. Vasilis Dakos
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  4. Egbert H. van Nes
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  5. Miquel Lürling
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  6. Marten Scheffer
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Contributions

A.J.V., E.J.F. and M.L. performed the experiments. A.J.V., E.J.F, E.H.v.N. and V.D. analysed the data. M.S., A.J.V., E.H.v.N., E.J.F. and V.D. wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Egbert H. van Nes.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Notes 1-4, Supplementary Figures 1.1, 2.1 and 4.1, Supplementary Table 4.1 and additional references. This file was replaced on 18 April 2012. (PDF 1497 kb)

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Veraart, A., Faassen, E., Dakos, V. et al. Recovery rates reflect distance to a tipping point in a living system. Nature 481, 357–359 (2012). https://doi.org/10.1038/nature10723

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