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Emergence of structural and dynamical properties of ecological mutualistic networks

Nature volume 500, pages 449–452 (2013)Cite this article

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Abstract

Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants has a key role in the organization of ecological communities1,2,3. Such networks in ecology have generally evolved a nested architecture4,5 independent of species composition and latitude6,7; specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species1. Despite sustained efforts5,8,9,10 to explain observed network structure on the basis of community-level stability or persistence, such correlative studies have reached minimal consensus11,12,13. Here we show that nested interaction networks could emerge as a consequence of an optimization principle aimed at maximizing the species abundance in mutualistic communities. Using analytical and numerical approaches, we show that because of the mutualistic interactions, an increase in abundance of a given species results in a corresponding increase in the total number of individuals in the community, and also an increase in the nestedness of the interaction matrix. Indeed, the species abundances and the nestedness of the interaction matrix are correlated by a factor that depends on the strength of the mutualistic interactions. Nestedness and the observed spontaneous emergence of generalist and specialist species occur for several dynamical implementations of the variational principle under stationary conditions. Optimized networks, although remaining stable, tend to be less resilient than their counterparts with randomly assigned interactions. In particular, we show analytically that the abundance of the rarest species is linked directly to the resilience of the community. Our work provides a unifying framework for studying the emergent structural and dynamical properties of ecological mutualistic networks2,5,10,14.

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Figure 1: The optimization principle.
Figure 2: Relationship between nestedness and species abundance.
Figure 3: Box–whisker plots of the degrees of nestedness for optimized networks.
Figure 4: Optimized networks are less resilient.

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Acknowledgements

A.M. and S.S. acknowledge the Cariparo foundation for financial support. We thank S. Allesina, T. Cooke, J. Grilli and L. Mari for discussions and Studio 7 a.m. for graphics support.

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Authors and Affiliations

  1. Dipartimento di Fisica e Astronomia ‘G. Galilei’ & CNISM, INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy,

    Samir Suweis & Amos Maritan

  2. Center for Complex Network Research and Department of Physics, Biology and Computer Science, Northeastern University, Boston, 02115, Massachusetts, USA

    Filippo Simini

  3. Institute of Physics, Budapest University of Technology and Economics Budafoki ut 8, Budapest H-1111, Hungary,

    Filippo Simini

  4. Department of Physics, University of Maryland, College Park, 20742, Maryland, USA

    Jayanth R. Banavar

Authors
  1. Samir Suweis
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  2. Filippo Simini
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  3. Jayanth R. Banavar
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  4. Amos Maritan
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Contributions

S.S. carried out the numerical calculations and the data analysis. All the authors contributed to other aspects of the paper.

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Correspondence to Samir Suweis or Amos Maritan.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods and Discussions, Supplementary Figures 1-24 and additional references. The Supplementary Methods give the mathematical definition of nestedness and show how we have tuned the connectivity in our simulations. They also give details of the mathematical framework and optimization algorithm. All the analytical results presented in the main text are proved and the numerical simulations are explained in detail. In the Supplementary Discussions, we compare the result obtained by the Species-level Optimization, the Community-level Optimization and the Optimization while assembling the Community. Finally, we discuss the relationship between the total abundance of individuals in the community and the nestedness. See Contents for more details. (PDF 1086 kb)

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Suweis, S., Simini, F., Banavar, J. et al. Emergence of structural and dynamical properties of ecological mutualistic networks. Nature 500, 449–452 (2013). https://doi.org/10.1038/nature12438

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