Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature volume 481, pages 357–359 (2012)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  1. Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

    Article  ADS  CAS  Google Scholar 

  2. Wissel, C. A universal law of the characteristic return time near thresholds. Oecologia 65, 101–107 (1984)

    Article  ADS  CAS  Google Scholar 

  3. van Nes, E. H. & Scheffer, M. Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift. Am. Nat. 169, 738–747 (2007)

    Article  Google Scholar 

  4. Ives, A. R. Measuring resilience in stochastic systems. Ecol. Monogr. 65, 217–233 (1995)

    Article  Google Scholar 

  5. Dakos, V. et al. Slowing down as an early warning signal for abrupt climate change. Proc. Natl Acad. Sci. USA 105, 14308–14312 (2008)

    Article  ADS  CAS  Google Scholar 

  6. Scheffer, M. Critical Transitions in Nature and Society (eds Levin, S.A. & Strogatz, S.H.) (Princeton Univ. Press, 2009)

    Google Scholar 

  7. Kleinen, T., Held, H. & Petschel-Held, G. The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dyn. 53, 53–63 (2003)

    Article  ADS  Google Scholar 

  8. Held, H. & Kleinen, T. Detection of climate system bifurcations by degenerate fingerprinting. Geophys. Res. Lett. 31, L23207 (2004)

    Article  ADS  Google Scholar 

  9. Carpenter, S. R. & Brock, W. A. Rising variance: a leading indicator of ecological transition. Ecol. Lett. 9, 311–318 (2006)

    Article  CAS  Google Scholar 

  10. Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering 1st edn (Addison-Wesley, 1994)

    MATH  Google Scholar 

  11. Dakos, V., van Nes, E. H., D’ Odorico, P. & Scheffer, M. How robust are variance and autocorrelation as early-warning signals for critical transitions? Ecology (submitted); preprint at http://dx.doi.org/10.1890/11-0889.1

  12. Carpenter, S. R. et al. Early warnings of regime shifts: A whole-ecosystem experiment. Science 332, 1079–1082 (2011)

    Article  ADS  CAS  Google Scholar 

  13. Drake, J. M. & Griffen, B. D. Early warning signals of extinction in deteriorating environments. Nature (2010)

  14. Huisman, J. The Struggle for Light. PhD thesis, Univ. Groningen. (1997)

  15. Gerla, D. J., Mooij, W. M. & Huisman, J. Photoinhibition and the assembly of light-limited phytoplankton communities. Oikos 120, 359–368 (2011)

    Article  Google Scholar 

  16. Holmgren, M., Scheffer, M. & Huston, M. A. The interplay of facilitation and competition in plant communities. Ecology 78, 1966–1975 (1997)

    Article  Google Scholar 

  17. Scheffer, M., Carpenter, S. R., Foley, J. A., Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Dakos, V., Kéfi, S., Rietkerk, M., van Nes, E. H. & Scheffer, M. Slowing down in spatially patterned ecosystems at the brink of collapse. Am. Nat. 177, E153–E166 (2011)

    Article  Google Scholar 

  19. Huisman, J. et al. Principles of the light-limited chemostat: theory and ecological applications. Antonie Leeuwenhoek. 81, 117–133 (2002)

  20. Andersen, R. A. Berges, J.A., Harrison, P.J. & Watanabe, M.M. in Algal culturing techniques 1st edn 435–436 (Elsevier, 2005)

    Google Scholar 

  21. Huisman, J. & Weissing, F. J. Light-limited growth and competition for light in well-mixed aquatic environments: an elementary model. Ecology 75, 507–520 (1994)

    Article  Google Scholar 

Download references

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.

Author information

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

Authors
  1. Annelies J. Veraart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elisabeth J. Faassen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vasilis Dakos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Egbert H. van Nes
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Miquel Lürling
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Marten Scheffer
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Ethics declarations

Competing interests

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)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature10723

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing Anthropocene

Sign up for the Nature Briefing: Anthropocene newsletter — what matters in anthropocene research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: Anthropocene