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.

Stability criteria for complex ecosystems

Abstract

Forty years ago, May proved1,2 that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations3,4,5. May analysed large networks in which species interact at random1,2,6. However, in natural systems pairs of species have well-defined interactions (for example predator–prey, mutualistic or competitive). Here we extend May’s results to these relationships and find remarkable differences between predator–prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator–prey networks decreases when a realistic food web structure is imposed7,8 or if there is a large preponderance of weak interactions9,10. Similarly, stability is negatively affected by nestedness11,12,13,14 in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator–prey networks can be arbitrarily large and complex, provided that predator–prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Distributions of the eigenvalues and corresponding stability profiles.
Figure 2: Stability criteria for different types of interaction.
Figure 3: Distribution of the eigenvalues for the three types of mutualism.

References

  1. May, R. M. Will a large complex system be stable? Nature 238, 413–414 (1972)

    Article  ADS  CAS  Google Scholar 

  2. May, R. M. Stability and Complexity in Model Ecosystems (Princeton Univ. Press, 2001)

    MATH  Google Scholar 

  3. MacArthur, R. Fluctuations of animal populations and a measure of community stability. Ecology 36, 533–536 (1955)

    Article  Google Scholar 

  4. Elton, C. S. Animal Ecology (Univ. of Chicago Press, 2001)

    Google Scholar 

  5. McCann, K. S. The diversity–stability debate. Nature 405, 228–233 (2000)

    Article  CAS  Google Scholar 

  6. Levins, R. Evolution in Changing Environments: Some Theoretical Explorations (Princeton Univ. Press, 1968)

    Google Scholar 

  7. McNaughton, S. J. Stability and diversity of ecological communities. Nature 274, 251–253 (1978)

    Article  ADS  Google Scholar 

  8. Yodzis, P. The stability of real ecosystems. Nature 289, 674–676 (1981)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  10. Emmerson, M. & Yearsley, J. M. Weak interactions, omnivory and emergent food-web properties. Proc. R. Soc. Lond. B 271, 397–405 (2004)

    Article  Google Scholar 

  11. Bascompte, J., Jordano, P., Melián, C. J. & Olesen, J. M. The nested assembly of plant–animal mutualistic networks. Proc. Natl Acad. Sci. USA 100, 9383–9387 (2003)

    Article  ADS  CAS  Google Scholar 

  12. Okuyama, T. & Holland, J. N. Network structural properties mediate the stability of mutualistic communities. Ecol. Lett. 11, 208–216 (2008)

    Article  Google Scholar 

  13. Bastolla, U. et al. The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009)

    Article  ADS  CAS  Google Scholar 

  14. Thébault, E. & Fontaine, C. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329, 853–856 (2010)

    Article  ADS  Google Scholar 

  15. DeAngelis, D. L. & Waterhouse, J. C. Equilibrium and nonequilibrium concepts in ecological models. Ecol. Monogr. 57, 1–21 (1987)

    Article  Google Scholar 

  16. Allesina, S. & Pascual, M. Network structure, predator–prey modules, and stability in large food webs. Theor. Ecol. 1, 55–64 (2008)

    Article  Google Scholar 

  17. Gross, T., Rudolf, L., Levin, S. A. & Dieckmann, U. Generalized models reveal stabilizing factors in food webs. Science 325, 747–750 (2009)

    Article  ADS  CAS  Google Scholar 

  18. Tao, T., Vu, V. & Krishnapur, M. Random matrices: universality of ESDs and the circular law. Ann. Probab. 38, 2023–2065 (2010)

    Article  MathSciNet  Google Scholar 

  19. Sommers, H. J., Crisanti, A., Sompolinsky, H. & Stein, Y. Spectrum of large random asymmetric matrices. Phys. Rev. Lett. 60, 1895–1898 (1988)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Cohen, J. E., Briand, F., Newman, C. M. & Palka, Z. J. Community Food Webs: Data and Theory (Springer, 1990)

    Book  Google Scholar 

  21. Williams, R. J. & Martinez, N. D. Simple rules yield complex food webs. Nature 404, 180–183 (2000)

    Article  ADS  CAS  Google Scholar 

  22. Bascompte, J., Jordano, P. & Olesen, J. M. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312, 431–433 (2006)

    Article  ADS  CAS  Google Scholar 

  23. Kokkoris, G. D., Jansen, V. A. A., Loreau, M. & Troumbis, A. Y. Variability in interaction strength and implications for biodiversity. J. Anim. Ecol. 71, 362–371 (2002)

    Article  Google Scholar 

  24. Wootton, J. T. & Emmerson, M. Measurement of interaction strength in nature. Annu. Rev. Ecol. Evol. Syst. 36, 419–444 (2005)

    Article  Google Scholar 

Download references

Acknowledgements

We thank J. Bergelson, L.-F. Bersier, A. M. de Roos, A. Eklof, C. A. Klausmeier, S. P. Lalley, R. M. May, K. S. McCann, M. Novak, P. P. A. Staniczenko and J. D. Yeakel for comments and discussion. This research was supported by National Science Foundation grant EF0827493.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally.

Corresponding author

Correspondence to Stefano Allesina.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Table 1, Supplementary Figures 1-7 with legends and additional references. (PDF 1136 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Allesina, S., Tang, S. Stability criteria for complex ecosystems. Nature 483, 205–208 (2012). https://doi.org/10.1038/nature10832

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature10832

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

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