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Stability criteria for complex ecosystems

Nature volume 483, pages 205–208 (2012)Cite this article

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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.

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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.

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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.

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Authors and Affiliations

  1. Department of Ecology and Evolution, University of Chicago, 1101 East 57th Street, Chicago, Illinois 60637, USA,

    Stefano Allesina & Si Tang

  2. Computation Institute, University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, USA,

    Stefano Allesina

Authors
  1. Stefano Allesina
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  2. Si Tang
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All authors contributed equally.

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Correspondence to Stefano Allesina.

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The authors declare no competing financial interests.

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

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

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