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:

A simple model of bipartite cooperation for ecological and organizational networks

Nature volume 457, pages 463–466 (2009)Cite this article

Abstract

In theoretical ecology, simple stochastic models that satisfy two basic conditions about the distribution of niche values and feeding ranges have proved successful in reproducing the overall structural properties of real food webs, using species richness and connectance as the only input parameters1,2,3,4. Recently, more detailed models have incorporated higher levels of constraint in order to reproduce the actual links observed in real food webs5,6. Here, building on previous stochastic models of consumer–resource interactions between species1,2,3, we propose a highly parsimonious model that can reproduce the overall bipartite structure of cooperative partner–partner interactions, as exemplified by plant–animal mutualistic networks7. Our stochastic model of bipartite cooperation uses simple specialization and interaction rules, and only requires three empirical input parameters. We test the bipartite cooperation model on ten large pollination data sets that have been compiled in the literature, and find that it successfully replicates the degree distribution, nestedness and modularity of the empirical networks. These properties are regarded as key to understanding cooperation in mutualistic networks8,9,10. We also apply our model to an extensive data set of two classes of company engaged in joint production in the garment industry. Using the same metrics, we find that the network of manufacturer–contractor interactions exhibits similar structural patterns to plant–animal pollination networks. This surprising correspondence between ecological and organizational networks suggests that the simple rules of cooperation that generate bipartite networks may be generic, and could prove relevant in many different domains, ranging from biological systems to human society11,12,13,14.

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: Scaled degree distribution.
Figure 2: Nestedness.
Figure 3: Connectivity roles.

Similar content being viewed by others

References

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

    Article  ADS  CAS  Google Scholar 

  2. Cattin, M. F., Bersier, L. F., Banasek-Richter, C., Baltensperger, R. & Gabriel, J. P. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839 (2004)

    Article  ADS  CAS  Google Scholar 

  3. Stouffer, D. B., Camacho, J., Guimerà, R., Ng, C. A. & Nunes Amaral, L. A. Quantitative patterns in the structure of model and empirical food webs. Ecology 86, 1301–1311 (2005)

    Article  Google Scholar 

  4. Dunne, J. A., Williams, R. J., Martinez, N. D., Wood, R. A. & Erwin, D. H. Compilation and network analyses of Cambrian food webs. PLoS Biol. 6, 693–708 (2008)

    Article  CAS  Google Scholar 

  5. Petchey, O. L., Beckerman, A. P., Riede, J. O. & Warren, P. H. Size, foraging, and food web structure. Proc. Natl Acad. Sci. USA 105, 4191–4196 (2008)

    Article  ADS  CAS  Google Scholar 

  6. Allesina, S., Alonso, D. & Pascual, M. A general model for food web structure. Science 320, 658–661 (2008)

    Article  ADS  CAS  Google Scholar 

  7. Bascompte, J. & Jordano, P. in Ecological Networks: Linking Structure to Dynamics in Food Webs (eds Pascual, M. & Dunne, J. A.) 143–159 (Oxford Univ. Press, 2006)

    Google Scholar 

  8. Jordano, P., Bascompte, J. & Olesen, J. M. Invariant properties in coevolutionary networks of plant-animal interactions. Ecol. Lett. 6, 69–81 (2003)

    Article  Google Scholar 

  9. 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 

  10. Olesen, J. M., Bascompte, J., Dupont, Y. L. & Jordano, P. The modularity of pollination networks. Proc. Natl Acad. Sci. USA 104, 19891–19896 (2007)

    Article  ADS  CAS  Google Scholar 

  11. Sampson, R. J., Raudenbush, S. W. & Earls, F. Neighborhoods and violent crime: A multilevel study of collective efficacy. Science 277, 918–924 (1997)

    Article  CAS  Google Scholar 

  12. Ostrom, E., Burger, J., Field, C. B., Norgaard, R. B. & Policansky, D. Revisiting the commons: Local lessons, global challenges. Science 284, 278–282 (1999)

    Article  CAS  Google Scholar 

  13. Hammerstein, P. (ed.) Genetic and Cultural Evolution of Cooperation (MIT Press, 2003)

    Book  Google Scholar 

  14. Ohtsuki, H., Hauert, C., Lieberman, E. & Nowak, M. A. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)

    Article  ADS  CAS  Google Scholar 

  15. Bronstein, J. L. The exploitation of mutualisms. Ecol. Lett. 4, 277–287 (2001)

    Article  Google Scholar 

  16. Waser, N. M., Chittka, L., Price, M. V., Williams, N. M. & Ollerton, J. Generalization in pollination systems, and why it matters. Ecology 77, 1043–1060 (1996)

    Article  Google Scholar 

  17. Noë, R. & Hammerstein, P. Biological markets: supply and demand determine the effect of partner choice in cooperation, mutualism and mating. Behav. Ecol. Sociobiol. 35, 1–11 (1994)

    Article  Google Scholar 

  18. Olesen, J. M. & Jordano, P. Geographic patterns in plant–pollinator mutualistic networks. Ecology 83, 2416–2424 (2002)

    Google Scholar 

  19. Guimarães, P. R., Rico-Gray, V., Furtado dos Reis, S. & Thompson, J. N. Asymmetries in specialization in ant–plant mutualistic networks. Proc. R. Soc. Lond. B 273, 2041–2047 (2006)

    Article  Google Scholar 

  20. Rezende, E. L., Lavabre, J. E., Guimarães, P. R., Jordano, P. & Bascompte, J. Non-random coextinctions in phylogenetically structured mutualistic networks. Nature 448, 925–928 (2007)

    Article  ADS  CAS  Google Scholar 

  21. Santamaría, L. & Rodríguez-Gironés, A. Linkage rules for plant-pollinator networks: Trait complementarity or exploitation barriers? PLoS Biol. 5, 354–362 (2007)

    Article  Google Scholar 

  22. Guimarães, P. R. et al. Building-up mechanisms determining the topology of mutualistic networks. J. Theor. Biol. 249, 181–189 (2007)

    Article  Google Scholar 

  23. Uzzi, B. The sources and consequences of embeddedness for the economic performance of organizations: the network effect. Am. Sociol. Rev. 61, 674–698 (1996)

    Article  Google Scholar 

  24. Carroll, G. R. & Hannan, M. T. The Demography of Corporations and Industries (Princeton Univ. Press, 2004)

    Google Scholar 

  25. Podolny, J. M. Status Signals: A Sociological Study of Market Competition (Princeton Univ. Press, 2005)

    Google Scholar 

  26. Amaral, L. A. N., Scala, A., Barthélémy, M. & Stanley, H. E. Classes of small-world networks. Proc. Natl Acad. Sci. USA 97, 11149–11152 (2000)

    Article  ADS  CAS  Google Scholar 

  27. Moody, J. & White, D. R. Structural cohesion and embeddedness: A hierarchical concept of social groups. Am. Sociol. Rev. 68, 103–127 (2003)

    Article  Google Scholar 

  28. Rodríguez-Gironés, M. A. & Santamaría, L. A new algorithm to calculate the nestedness temperature of presence–absence matrices. J. Biogeography 33, 924–935 (2006)

    Article  Google Scholar 

  29. Girvan, M. & Newman, M. E. J. Community structure in social and biological networks. Proc. Natl Acad. Sci. USA 99, 7821–7826 (2002)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Guimerà, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank J. Dunne, R. Guimerà, J. Kertész, M. Sales-Pardo, D. Stouffer and R. Williams for comments and suggestions. F.R.-T. acknowledges funding from the European Commission under the FP6 NEST Pathfinder Initiative ‘Tackling Complexity in Science’ (MMCOMNET project, contract no. 012999). S.S. held a Doctoral Research Studentship funded by MMCOMNET and CONACYT, and currently is supported by a Postdoctoral Fellowship at the Oxford University Corporate Reputation Centre in conjunction with the CABDyN Complexity Centre.

Author Contributions B.U. provided the NYGI data; F.R.-T. designed the research; S.S., F.R.-T. and B.U. analysed the data; S.S. ran the simulations; S.S. and F.R.-T. wrote the paper.

Author information

Authors and Affiliations

  1. Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

    Serguei Saavedra

  2. CABDyN Complexity Centre,,

    Serguei Saavedra & Felix Reed-Tsochas

  3. Corporate Reputation Centre,,

    Serguei Saavedra

  4. James Martin Institute, Saïd Business School, University of Oxford, Oxford OX1 1HP, UK ,

    Felix Reed-Tsochas

  5. Kellogg School of Management and Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA ,

    Brian Uzzi

  6. Haas School of Business, University of California, Berkeley, California 94720, USA ,

    Brian Uzzi

Authors
  1. Serguei Saavedra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Felix Reed-Tsochas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Brian Uzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Felix Reed-Tsochas.

Supplementary information

Supplementary Information

This file contains Supplementary Text 1 (Comparison of mutualistic models), Supplementary Tables S1-S5, Supplementary Text 2 (Pollination-network datasets), Supplementary Text 3 (The New York garment industry network), Supplementary Figures S1-S3 and Supplementary References. (PDF 935 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saavedra, S., Reed-Tsochas, F. & Uzzi, B. A simple model of bipartite cooperation for ecological and organizational networks. Nature 457, 463–466 (2009). https://doi.org/10.1038/nature07532

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07532

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