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:

Chaos in a long-term experiment with a plankton community

Nature volume 451, pages 822–825 (2008)Cite this article

Abstract

Mathematical models predict that species interactions such as competition and predation can generate chaos1,2,3,4,5,6,7,8. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations9,10,11,12. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web was isolated from the Baltic Sea, and consisted of bacteria, several phytoplankton species, herbivorous and predatory zooplankton species, and detritivores. The food web was cultured in a laboratory mesocosm, and sampled twice a week for more than 2,300 days. Despite constant external conditions, the species abundances showed striking fluctuations over several orders of magnitude. These fluctuations displayed a variety of different periodicities, which could be attributed to different species interactions in the food web. The population dynamics were characterized by positive Lyapunov exponents of similar magnitude for each species. Predictability was limited to a time horizon of 15–30 days, only slightly longer than the local weather forecast. Hence, our results demonstrate that species interactions in food webs can generate chaos. This implies that stability is not required for the persistence of complex food webs, and that the long-term prediction of species abundances can be fundamentally impossible.

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: Description of the plankton community in the mesocosm experiment.
Figure 2: Predictability of the species decreases with increasing prediction time.
Figure 3: Exponential divergence of the trajectories.

Similar content being viewed by others

References

  1. May, R. M. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645–647 (1974)

    Article  CAS  ADS  Google Scholar 

  2. May, R. M. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)

    Article  CAS  ADS  Google Scholar 

  3. Gilpin, M. E. Spiral chaos in a predator–prey model. Am. Nat. 113, 306–308 (1979)

    Article  MathSciNet  Google Scholar 

  4. Hastings, A. & Powell, T. Chaos in a three-species food chain. Ecology 72, 896–903 (1991)

    Article  Google Scholar 

  5. Vandermeer, J. Loose coupling of predator–prey cycles: entrainment, chaos, and intermittency in the classic MacArthur consumer–resource equations. Am. Nat. 141, 687–716 (1993)

    Article  Google Scholar 

  6. Huisman, J. & Weissing, F. J. Biodiversity of plankton by species oscillations and chaos. Nature 402, 407–410 (1999)

    Article  ADS  Google Scholar 

  7. Van Nes, E. H. & Scheffer, M. Large species shifts triggered by small forces. Am. Nat. 164, 255–266 (2004)

    Article  Google Scholar 

  8. Huisman, J., Pham Thi, N. N., Karl, D. M. & Sommeijer, B. Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature 439, 322–325 (2006)

    Article  CAS  ADS  Google Scholar 

  9. Ellner, S. P. & Turchin, P. Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nat. 145, 343–375 (1995)

    Article  Google Scholar 

  10. Costantino, R. F., Desharnais, R. A., Cushing, J. M. & Dennis, B. Chaotic dynamics in an insect population. Science 275, 389–391 (1997)

    Article  CAS  Google Scholar 

  11. Becks, L., Hilker, F. M., Malchow, H., Jürgens, K. & Arndt, H. Experimental demonstration of chaos in a microbial food web. Nature 435, 1226–1229 (2005)

    Article  CAS  ADS  Google Scholar 

  12. Graham, D. W. et al. Experimental demonstration of chaotic instability in biological nitrification. ISME J. 1, 385–393 (2007)

    Article  CAS  Google Scholar 

  13. Zimmer, C. Life after chaos. Science 284, 83–86 (1999)

    Article  CAS  ADS  Google Scholar 

  14. McCann, K., Hastings, A. & Huxel, G. R. Weak trophic interactions and the balance of nature. Nature 395, 794–798 (1998)

    Article  CAS  ADS  Google Scholar 

  15. Neutel, A. M., Heesterbeek, J. A. P. & de Ruiter, P. C. Stability in real food webs: weak links in long loops. Science 296, 1120–1123 (2002)

    Article  CAS  ADS  Google Scholar 

  16. Heerkloss, R. & Klinkenberg, G. A long-term series of a planktonic foodweb: a case of chaotic dynamics. Verh. Int. Verein. Theor. Angew. Limnol. 26, 1952–1956 (1998)

    Google Scholar 

  17. Scheffer, M. & Rinaldi, S. Minimal models of top-down control of phytoplankton. Freshwat. Biol. 45, 265–283 (2000)

    Article  Google Scholar 

  18. Fussmann, G. F., Ellner, S. P., Shertzer, K. W. & Hairston, N. G. Crossing the Hopf bifurcation in a live predator–prey system. Science 290, 1358–1360 (2000)

    Article  CAS  ADS  Google Scholar 

  19. Sugihara, G. & May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990)

    Article  CAS  ADS  Google Scholar 

  20. Nychka, D., Ellner, S., Gallant, A. R. & McCaffrey, D. Finding chaos in noisy systems. J. R. Stat. Soc. B 54, 399–426 (1992)

    MathSciNet  Google Scholar 

  21. Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Perseus, Cambridge, Massachusetts, 1994)

    MATH  Google Scholar 

  22. Takens, F. in Dynamical Systems and Turbulence, Warwick 1980 (Lecture Notes in Mathematics vol. 898) (ed. Rand, D. A. & Young, L.S.) 366–381 (Springer, Berlin, 1981)

  23. Kantz, H. & Schreiber, T. Nonlinear Time Series Analysis (Cambridge Univ. Press, Cambridge, UK, 1997)

    MATH  Google Scholar 

  24. Rosenstein, M. T., Collins, J. J. & De Luca, C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  25. Lorenz, E. N. Atmospheric predictability experiments with a large numerical model. Tellus 34, 505–513 (1982)

    Article  ADS  Google Scholar 

  26. Gaedeke, A. & Sommer, U. The influence of the frequency of periodic disturbances on the maintenance of phytoplankton diversity. Oecologia 71, 25–28 (1986)

    Article  CAS  ADS  Google Scholar 

  27. Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995)

    MathSciNet  MATH  Google Scholar 

  28. Redfield, A. C. The biological control of chemical factors in the environment. Am. Sci. 46, 205–221 (1958)

    CAS  Google Scholar 

  29. Kendall, B. E. Cycles, chaos, and noise in predator–prey dynamics. Chaos Solitons Fract. 12, 321–332 (2001)

    Article  ADS  Google Scholar 

  30. Theiler, J. Spurious dimension from correlation algorithms applied to limited time-series data. Phys. Rev. A 34, 2427–2432 (1986)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

We thank W. Ebenhöh for suggestions on the experimental design, H. Albrecht, G. Hinrich, J. Rodhe, S. Stolle and B. Walter for help during the experiment, T. Huebener, I. Telesh, R. Schumann, M. Feike and G. Arlt for advice in taxonomic identification, and B. M. Bolker and V. Dakos for comments on the manuscript. The research of E.B., K.D.J. and J.H. was supported by the Earth and Life Sciences Foundation (ALW), which is subsidized by the Netherlands Organisation for Scientific Research (NWO). S.P.E.’s research was supported by a grant from the Andrew W. Mellon Foundation.

Author Contributions R.H. ran the experiment, counted the species and measured the nutrient concentrations. E.B., J.H., K.D.J., P.B. and S.P.E. performed the time series analysis. E.B., J.H., M.S. and S.P.E. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Author information

Author notes

  1. Klaus D. Jöhnk

    Present address: Present address: Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Alte Fischerhütte 2, 16775 Neuglobsow, Germany.,

  2. Elisa Benincà and Jef Huisman: These authors contributed equally to this work.

Authors and Affiliations

  1. Aquatic Microbiology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam, the Netherlands ,

    Elisa Benincà, Jef Huisman, Klaus D. Jöhnk & Pedro Branco

  2. Aquatic Ecology and Water Quality Management, University of Wageningen, Wageningen, the Netherlands

    Elisa Benincà, Egbert H. Van Nes & Marten Scheffer

  3. Institute of Biosciences, University of Rostock, Rostock, Germany

    Reinhard Heerkloss

  4. Ecology and Evolutionary Biology, Cornell University, Ithaca, New York 14853, USA ,

    Stephen P. Ellner

Authors
  1. Elisa Benincà
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jef Huisman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reinhard Heerkloss
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Klaus D. Jöhnk
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pedro Branco
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Egbert H. Van Nes
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Marten Scheffer
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Stephen P. Ellner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jef Huisman.

Supplementary information

Supplementary Information

The Supplementary Information presents detailed information on the following aspects of the long-term experiment and subsequent time series analysis:1) Materials and methods of the mesocosm experiment; 2) Earlier analysis of the same time series; 3) Transformation of the time series (including Figures S1-S2); 4) Spectral analysis (Figures S3-S4); 5) Predictability (Table S1, Figure S5); Methods for estimating Lyapunov exponents (Figures S6-S7); 7) Temperature fluctuations (Table S2, Figure S8). (PDF 1204 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benincà, E., Huisman, J., Heerkloss, R. et al. Chaos in a long-term experiment with a plankton community. Nature 451, 822–825 (2008). https://doi.org/10.1038/nature06512

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06512

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

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

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