Self-regulation and the stability of large ecological networks


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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


  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 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).

  6. 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).

  7. 7.

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

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 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. 12.

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

  13. 13.

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

  14. 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).

  15. 15.

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

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 22.

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

  23. 23.

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

  24. 24.

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

  25. 25.

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

  26. 26.

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

  27. 27.

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

  28. 28.

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

  29. 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).

  30. 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).

  31. 31.

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

  32. 32.

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

  33. 33.

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

  34. 34.

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

  35. 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).

  36. 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).

  37. 37.

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

  38. 38.

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

  39. 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).

  40. 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).

  41. 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).

  42. 42.

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

  43. 43.

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

  44. 44.

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

  45. 45.

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

  46. 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).

  47. 47.

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

  48. 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).

  49. 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).

  50. 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. 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. 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).

  53. 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. 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).

  55. 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).

  56. 56.

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

  57. 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).

  58. 58.

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

  59. 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).

  60. 60.

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

Download references


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

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.

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

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).

Download citation

Further reading