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.

  • Article
  • Published:

Self-regulation and the stability of large ecological networks

Nature Ecology & Evolution volume 1, pages 1870–1875 (2017)Cite this article

Subjects

Abstract

The stability of complex ecological networks depends both on the interactions between species and the direct effects of the species on themselves. These self-effects are known as 'self-regulation' when an increase in a species’ abundance decreases its per-capita growth rate. Sources of self-regulation include intraspecific interference, cannibalism, time-scale separation between consumers and their resources, spatial heterogeneity and nonlinear functional responses coupling predators with their prey. The influence of self-regulation on network stability is understudied and in addition, the empirical estimation of self-effects poses a formidable challenge. Here, we show that empirical food web structures cannot be stabilized unless the majority of species exhibit substantially strong self-regulation. We also derive an analytical formula predicting the effect of self-regulation on network stability with high accuracy and show that even for random networks, as well as networks with a cascade structure, stability requires negative self-effects for a large proportion of species. These results suggest that the aforementioned potential mechanisms of self-regulation are probably more important in contributing to the stability of observed ecological networks than was previously thought.

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

Fig. 1: Species self-regulation as an indicator of community stability.
Fig. 2: Two relevant quantities determine the minimum fraction of self-regulating species.

Similar content being viewed by others

References

  1. Puccia, C. J. & Levins, R. Qualitative Modeling of Complex Systems (Harvard Univ. Press, Cambridge, MA, 1985).

    Book  Google Scholar 

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

    Article  Google Scholar 

  3. MacArthur, R. H. Species packing and competitive equilibria for many species. Theor. Popul. Biol. 1, 1–11 (1970).

    Article  CAS  PubMed  Google Scholar 

  4. May, R. M. Stability and Complexity in Model Ecosystems (Princeton Univ. Press, Princeton, NJ, 1973).

    Google Scholar 

  5. Wollrab, A., Diehl, S. & De Roos, A. M. Simple rules describe bottom-up and top-down control in food webs with alternative energy pathways. Ecol. Lett. 15, 935–946 (2012).

    Article  PubMed  Google Scholar 

  6. Sterner, R. W., Bajpai, A. & Adams, T. The enigma of food chain length: absence of theoretical evidence for dynamical constraints. Ecology 78, 2258–2262 (1997).

    Article  Google Scholar 

  7. Moore, J. C. & de Ruiter, P. C. Energetic Food Webs (Oxford Univ. Press, Oxford, 2012).

    Book  Google Scholar 

  8. Pimm, S. L. & Lawton, J. H. Number of trophic levels in ecological communities. Nature 268, 329–331 (1977).

    Article  Google Scholar 

  9. Tilman, D. Resource Competition and Community Structure (Princeton Univ. Press, Princeton, NY, 1982).

    Google Scholar 

  10. Pimm, S. L. Food Webs (Univ. of Chicago Press, Chicago, IL, 2002).

    Google Scholar 

  11. Chesson, P. in Ecological Systems: Selected Entries from the Encyclopedia of Sustainability Science and Technology (ed. Leemans, R.) Ch. 13 (Springer, New York, 2013).

  12. Turchin, P. Complex Population Dynamics: A Theoretical/Empirical Synthesis (Princeton Univ. Press, Princeton, NJ, 2003).

    Google Scholar 

  13. Flux, J. E. C. Evidence of self-limitation in wild vertebrate populations. Oikos 92, 555–557 (2001).

    Article  Google Scholar 

  14. Skalski, G. T. & Gilliam, J. F. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology 82, 3083–3092 (2001).

    Article  Google Scholar 

  15. Rall, B. C., Guill, C. & Brose, U. Food-web connectance and predator interference dampen the paradox of enrichment. Oikos 117, 202–213 (2008).

    Article  Google Scholar 

  16. Kalinkat, G. et al. Body masses, functional responses and predator–prey stability. Ecol. Lett. 16, 1126–1134 (2013).

    Article  PubMed  Google Scholar 

  17. Jacquet, C. et al. No complexity–stability relationship in empirical ecosystems. Nat. Commun. 7, 12573 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Christensen, V. ECOPATH II—a software for balancing steady-state ecosystem models and calculating network characteristics. Ecol. Model. 61, 169–185 (1992).

    Article  Google Scholar 

  19. Girko, V. L. The circle law. Theory Probab. Appl. 29, 694–706 (1984).

    Article  Google Scholar 

  20. Sommers, H. J., Crisanti, A., Sompolinsky, H. & Stein, Y. Spectrum of large random asymmetric matrices. Phys. Rev. Lett. 60, 1895–1898 (1998).

    Article  Google Scholar 

  21. Bai, Z. & Silverstein, J. W. Spectral Analysis of Large Dimensional Random Matrices (Springer, New York, 2009).

    Google Scholar 

  22. Allesina, S. & Tang, S. Stability criteria for complex ecosystems. Nature 483, 205–208 (2012).

    Article  CAS  PubMed  Google Scholar 

  23. Allesina, S. & Tang, S. The stability-complexity relationship at age 40: a random matrix perspective. Popul. Ecol. 57, 63–75 (2015).

    Article  Google Scholar 

  24. O’Rourke, S. & Renfrew, D. Low rank perturbations of large elliptic random matrices. Electron. J. Probab. 19, 1–65 (2014).

    Google Scholar 

  25. Rogers, T. Universal sum and product rules for random matrices. J. Math. Phys. 51, 093304 (2010).

    Article  Google Scholar 

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

    Book  Google Scholar 

  27. Allesina, S. et al. Predicting the stability of large structured food webs. Nat. Commun. 6, 7842 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Levine, J. M. & HilleRisLambers, J. The importance of niches for the maintenance of species diversity. Nature 461, 254–257 (2009).

    Article  CAS  PubMed  Google Scholar 

  29. Comita, L. S., Muller-Landau, H. C., Aguilar, S. & Hubbell, S. P. Asymmetric density dependence shapes species abundances in a tropical tree community. Science 329, 330–332 (2010).

    Article  CAS  PubMed  Google Scholar 

  30. Metz, M. R., Sousa, W. P. & Valencia, R. Widespread density-dependent seedling mortality promotes species coexistence in a highly diverse Amazonian rain forest. Ecology 91, 3675–3685 (2010).

    Article  PubMed  Google Scholar 

  31. Johnson, D. J., Beaulieu, W. T., Bever, J. D. & Clay, K. Conspecific negative density dependence and forest diversity. Science 336, 904–907 (2012).

    Article  CAS  PubMed  Google Scholar 

  32. Chu, C. & Adler, P. B. Large niche differences emerge at the recruitment stage to stabilize grassland coexistence. Ecology 85, 373–392 (2015).

    Google Scholar 

  33. Arditi, R. & Ginzburg, L. R. How Species Interact—Altering the Standard View on Trophic Ecology (Oxford Univ. Press, Oxford, 2012).

    Book  Google Scholar 

  34. Damuth, J. Population density and body size in mammals. Nature 290, 699–700 (1981).

    Article  Google Scholar 

  35. Schneider, F. D., Brose, U., Rall, B. C. & Guill, C. Animal diversity and ecosystem functioning in dynamic food webs. Nat. Commun. 7, 12718 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Benincà, E., Jöhnk, K. D., Heerkloss, R. & Huisman, J. Coupled predator–prey oscillations in a chaotic food web. Ecol. Lett. 12, 1367–1378 (2009).

    Article  PubMed  Google Scholar 

  37. Gravel, D., Massol, F. & Leibold, M. A. Stability and complexity in model meta-ecosystems. Nat. Commun. 7, 12457 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Huffaker, C. B. Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27, 795–834 (1958).

    Article  Google Scholar 

  39. Hastings, A., Hom, C. L., Ellner, S., Turchin, P. & Godfray, C. J. Chaos in ecology: is Mother Nature a strange attractor? Annu. Rev. Ecol. Syst. 24, 1–33 (1993).

    Article  Google Scholar 

  40. Kendall, B. E., Prendergast, J. & Bjørnstad, O. N. The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles. Ecol. Lett. 1, 160–164 (1998).

    Article  Google Scholar 

  41. Barabás, G., Pigolotti, S., Gyllenberg, M., Dieckmann, U. & Meszéna, G. Continuous coexistence or discrete species? A new review of an old question. Evol. Ecol. Res. 14, 523–554 (2012).

    Google Scholar 

  42. Rohr, R. P., Saavedra, S. & Bascompte, J. On the structural stability of mutualistic systems. Science 345, 1253497 (2014).

    Article  PubMed  Google Scholar 

  43. Grilli, J. et al. Feasibility and coexistence of large ecological communities. Nat. Commun. 8, 14389 (2017).

    Article  Google Scholar 

  44. Tang, S., Pawar, S. & Allesina, S. Correlation between interaction strengths drives stability in large ecological networks. Ecol. Lett. 17, 1094–1100 (2014).

    Article  PubMed  Google Scholar 

  45. Reinschke, K. J. Multivariable Control—A Graph-theoretic Approach (Lecture Notes in Control and Information Science 108, Springer, Berlin, 1988).

    Book  Google Scholar 

  46. Zander, C. D. et al. Food web including metazoan parasites for a brackish shallow water ecosystem in Germany and Denmark: Ecological Archives E092-174. Ecology 92, 2007–2007 (2011).

    Article  Google Scholar 

  47. Martinez, N. D. Artifacts or attributes? Effects of resolution on the Little Rock Lake food web. Ecol. Monogr. 61, 367–392 (1991).

    Article  Google Scholar 

  48. Mouritsen, K. N., Poulin, R., McLaughlin, J. P. & Thieltges, D. W. Food web including metazoan parasites for an intertidal ecosystem in New Zealand: Ecological Archives E092-173. Ecology 92, 2006–2006 (2011).

    Article  Google Scholar 

  49. Baskerville, E. B. et al. Spatial guilds in the Serengeti food web revealed by a Bayesian group model. PLoS Comp. Biol. 7, e1002321 (2011).

    Article  CAS  Google Scholar 

  50. Christensen, V. et al. Fisheries Ecosystem Model of the Chesapeake Bay: Methodology, Parameterization, and Model Exploration (United States Department of Commerce, National Oceanic and Atmospheric Administration & National Marine Fisheries Service, 2009).

  51. Okey, T. & Pugliese, R. in Fisheries Impacts on North Atlantic Ecosystems: Models and Analyses (eds Guenette, S. et al.) 167–181 (Fisheries Centre, Univ. British Columbia, 2001).

  52. Arias-Gonzalez, J., Delesalle, B., Salvat, B. & Galzin, R. Trophic functioning of the Tiahura reef sector, Moorea Island, French Polynesia. Coral Reefs 16, 231–246 (1997).

    Article  Google Scholar 

  53. Heymans, J. J. & Pitcher, T. J. in Ecosystem Models of Newfoundland for the Time Periods 1995, 1985, 1900 and 1450 (eds Pitcher, T. J. et al.) 5–71 (Fisheries Centre, Univ. British Columbia, 2002).

  54. Walters, C. J., Christensen, V., Martell, S. & Kitchell, J. F. Possible ecosystem impacts of applying MSY policies from single-species assessment. ICES J. Mar. Sci. 62, 558–568 (2005).

    Article  Google Scholar 

  55. Hechinger, R. F., Lafferty, K. D. & McLaughlin, J. P. et al. Food webs including parasites, biomass, body sizes, and life stages for three California/Baja California estuaries: Ecological Archives E092-066. Ecology 92, 791–791 (2011).

    Article  Google Scholar 

  56. Jacob, U. et al. The role of body size in complex food webs: a cold case. Adv. Ecol. Res. 45, 181–223 (2011).

    Article  Google Scholar 

  57. Riede, J. O. et al. Stepping in Elton’s footprints: a general scaling model for body masses and trophic levels across ecosystems. Ecol. Lett. 14, 169–178 (2011).

    Article  PubMed  Google Scholar 

  58. Opitz, S. Trophic Interactions in Caribbean Coral Reefs Technical Report No. 43 (International Center for Living Aquatic Resources Management, 1996).

  59. Thieltges, D. W., Reise, K., Mouritsen, K. N., McLaughlin, J. P. & Poulin, R. Food web including metazoan parasites for a tidal basin in Germany and Denmark: Ecological Archives E092-172. Ecology 92, 2005–2005 (2011).

    Article  Google Scholar 

  60. Jacob, U. Trophic Dynamics of Antarctic Shelf Ecosystems: Food Webs and Energy Flow Budgets. PhD thesis, Univ. Bremen (2005).

Download references

Acknowledgements

We thank A. Celani, J. Grilli, M. Marsili, T. Rogers and E. Sander for discussions, as well as D. Gravel and C. Guill for their valuable input and thorough reading of earlier versions of the paper. This work was supported by the National Science Foundation (#1148867) and United States Department of Education grant P200A150101.

Author information

Authors and Affiliations

  1. Division of Theoretical Biology, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-58183, Linköping, Sweden

    György Barabás

  2. Department of Ecology and Evolution, University of Chicago, 1101 East 57th Chicago, Chicago, IL, 60637, USA

    György Barabás, Matthew J. Michalska-Smith & Stefano Allesina

  3. Computation Institute, University of Chicago, 1101 East 57th Chicago, Chicago, IL, 60637, USA

    Stefano Allesina

  4. Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, 60208, USA

    Stefano Allesina

Authors
  1. György Barabás
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthew J. Michalska-Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefano Allesina
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.B. wrote the paper and Supplementary Information, performed the analytical calculations and produced the figures. M.J.M.-S. performed the simulations and produced the figures. S.A. performed the simulations. All authors contributed to devising the study and editing the manuscript.

Corresponding author

Correspondence to György Barabás.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Supplementary Information

Description of all analytical calculations and numerical methods used to obtain the results. Supplementary Figures 1–39, Supplementary Tables 1–3, Supplementary References

Life Sciences Reporting Summary

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barabás, G., Michalska-Smith, M.J. & Allesina, S. Self-regulation and the stability of large ecological networks. Nat Ecol Evol 1, 1870–1875 (2017). https://doi.org/10.1038/s41559-017-0357-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41559-017-0357-6

This article is cited by

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