The balance of interaction types determines the assembly and stability of ecological communities


What determines the assembly and stability of complex communities is a central question in ecology. Past work has suggested that mutualistic interactions are inherently destabilizing. However, this conclusion relies on the assumption that benefits from mutualisms never stop increasing. Furthermore, almost all theoretical work focuses on the internal (asymptotic) stability of communities assembled all at once. Here, we present a model with saturating benefits from mutualisms and sequentially assembled communities. We show that such communities are internally stable for any level of diversity and any combination of species interaction types. External stability, or resistance to invasion, is thus an important but overlooked measure of stability. We demonstrate that the balance of different interaction types governs community dynamics. A higher fraction of mutualistic interactions can increase the external stability and diversity of communities as well as species persistence, if mutualistic interactions tend to provide unique benefits. Ecological selection increases the prevalence of mutualisms, and limits on biodiversity emerge from species interactions. Our results help resolve long-standing debates on the stability, saturation and diversity of communities.

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Fig. 1: The balance of interaction types determines the species richness at which communities saturate under the UIM.
Fig. 2: External stability is determined by the proportions of interaction types in the UIM.
Fig. 3: The probability of extinction is determined by the proportions of interaction types in the UIM.
Fig. 4: Species persistence in the UIM is determined by the proportions of interaction types.
Fig. 5: Selection acts to increase Pm and sometimes increase Pe and decrease Pc in the UIM.
Fig. 6: The IIM shows some notable differences from the UIM.

Data availability

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study. All simulation results can be reproduced using the code provided.

Code availability

The model of community assembly was implemented in Python. The simulation code is available at


  1. 1.

    Elton, C. S. The Ecology of Invasions by Animals and Plants (Chapman & Hall, 1958).

  2. 2.

    Pimm, S. L. The complexity and stability of ecosystems. Nature 307, 321–326 (1984).

  3. 3.

    May, R. M. Will a large complex system be stable? Nature 238, 413–414 (1972).

  4. 4.

    May, R. M. C. Stability and Complexity in Model Ecosystems Vol. 6 (Princeton Univ. Press, 2001).

  5. 5.

    Tilman, D. et al. Diversity and productivity in a long-term grassland experiment. Science 294, 843–845 (2001).

  6. 6.

    Tilman, D. & Downing, J. A. Biodiversity and stability in grasslands. Nature 367, 363–365 (1994).

  7. 7.

    Tilman, D. Biodiversity: population versus ecosystem stability. Ecology 77, 350–363 (1996).

  8. 8.

    Ives, A. R. & Carpenter, S. R. Stability and diversity of ecosystems. Science 317, 58–62 (2007).

  9. 9.

    Landi, P., Minoarivelo, H. O., Brannstrom, A., Hui, C. & Dieckmann, U. Complexity and stability of ecological networks: a review of the theory. Popul. Ecol. 60, 319–345 (2018).

  10. 10.

    Mougi, A. & Kondoh, M. Diversity of interaction types and ecological community stability. Science 337, 349–351 (2012).

  11. 11.

    Mougi, A. & Kondoh, M. Stability of competition–antagonism–mutualism hybrid community and the role of community network structure. J. Theor. Biol. 360, 54–58 (2014).

  12. 12.

    Mougi, A. The roles of amensalistic and commensalistic interactions in large ecological network stability. Sci. Rep. 6, 29929 (2016).

  13. 13.

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

  14. 14.

    Coyte, K. Z., Schluter, J. & Foster, K. R. The ecology of the microbiome: networks, competition, and stability. Science 350, 663–666 (2015).

  15. 15.

    Bascompte, J., Jordano, P. & Olesen, J. M. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312, 431–433 (2006).

  16. 16.

    Suweis, S., Grilli, J. & Maritan, A. Disentangling the effect of hybrid interactions and of the constant effort hypothesis on ecological community stability. Oikos 123, 525–532 (2014).

  17. 17.

    Melian, C. J., Bascompte, J., Jordano, P. & Krivan, V. Diversity in a complex ecological network with two interaction types. Oikos 118, 122–130 (2009).

  18. 18.

    Fontaine, C. et al. The ecological and evolutionary implications of merging different types of networks. Ecol. Lett. 14, 1170–1181 (2011).

  19. 19.

    May, R. M. in Theoretical Ecology: Principles and Applications (ed. May, R. M.) 78–104 (Blackwell Scientific, 1976).

  20. 20.

    Holland, J. N. in Mutualism (ed. Bronstein, J. L.) 133–158 (Oxford Univ. Press, 2015).

  21. 21.

    Holland, J. N., Okuyama, T. & De Angelis, D. L. Comment on “Asymmetric coevolutionary networks facilitate biodiversity maintenance”. Science 313, 1887 (2006).

  22. 22.

    Okuyama, T. & Holland, J. N. Network structural properties mediate the stability of mutualistic communities. Ecol. Lett. 11, 208–216 (2008).

  23. 23.

    Holland, J. N., DeAngelis, D. L. & Bronstein, J. L. Population dynamics and mutualism: functional responses of benefits and costs. Am. Nat. 159, 231–244 (2002).

  24. 24.

    Thebault, E. & Fontaine, C. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329, 853–856 (2010).

  25. 25.

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

  26. 26.

    Gross, T., Rudolf, L., Levin, S. A. & Dieckmann, U. Generalized models reveal stabilizing factors in food webs. Science 325, 747–750 (2009).

  27. 27.

    Bastolla, U. et al. The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009).

  28. 28.

    Kawatsu, K. & Kondoh, M. Density-dependent interspecific interactions and the complexity–stability relationship. Proc. R. Soc. B 285, 20180698 (2018).

  29. 29.

    Holling, C. S. The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Entomol. 91, 293–320 (1959).

  30. 30.

    Jeschke, J. M., Kopp, M. & Tollrian, R. Consumer–food systems: why type I functional responses are exclusive to filter feeders. Biol. Rev. 79, 337–349 (2004).

  31. 31.

    McCann, K., Hastings, A. & Huxel, G. R. Weak trophic interactions and the balance of nature. Nature 395, 794–798 (1998).

  32. 32.

    Case, T. J. Invasion resistance arises in strongly interacting species-rich model competition communities. Proc. Natl Acad. Sci. USA 87, 9610–9614 (1990).

  33. 33.

    Law, R. & Morton, R. D. Permanence and the assembly of ecological communities. Ecology 77, 762–775 (1996).

  34. 34.

    Maynard, D. S., Servan, C. A. & Allesina, S. Network spandrels reflect ecological assembly. Ecol. Lett. 21, 324–334 (2018).

  35. 35.

    Tokita, K. & Yasutomi, A. Emergence of a complex and stable network in a model ecosystem with extinction and mutation. Theor. Popul. Biol. 63, 131–146 (2003).

  36. 36.

    Kokkoris, G. D., Troumbis, A. Y. & Lawton, J. H. Patterns of species interaction strength in assembled theoretical competition communities. Ecol. Lett. 2, 70–74 (1999).

  37. 37.

    Hui, C. et al. Defining invasiveness and invasibility in ecological networks. Biol. Invasions 18, 971–983 (2016).

  38. 38.

    Hui, C. & Richardson, D. M. How to invade an ecological network. Trends Ecol. Evol. 32, 121–131 (2018).

  39. 39.

    Fridley, J. D. et al. The invasion paradox: reconciling pattern and process in species invasions. Ecology 88, 3–17 (2007).

  40. 40.

    Roberts, A. The stability of a feasible random ecosystem. Nature 251, 607–608 (1974).

  41. 41.

    Stone, L. The Google matrix controls the stability of structured ecological and biological networks. Nat. Commun. 7, 12857 (2016).

  42. 42.

    Stone, L. The feasibility and stability of large complex biological networks: a random matrix approach. Sci. Rep. 8, 8246 (2018).

  43. 43.

    Barabás, G., Michalska-Smith, M. J. & Allesina, S. Self-regulation and the stability of large ecological networks. Nat. Ecol. Evol. 1, 1870–1875 (2017).

  44. 44.

    Afkhami, M. E., Rudgers, J. A. & Stachowicz, J. J. Multiple mutualist effects: conflict and synergy in multispecies mutualisms. Ecology 95, 833–844 (2014).

  45. 45.

    Burrows, R. L. & Pfleger, F. L. Arbuscular mycorrhizal fungi respond to increasing plant diversity. Can. J. Bot. 80, 120–130 (2002).

  46. 46.

    Gustafson, D. J. & Casper, B. B. Differential host plant performance as a function of soil arbuscular mycorrhizal fungal communities: experimentally manipulating co-occurring glomus species. Plant Ecol. 183, 257–263 (2006).

  47. 47.

    Palmer, T. M. et al. Synergy of multiple partners, including freeloaders, increases host fitness in a multispecies mutualism. Proc. Natl Acad. Sci. USA 107, 17234–17239 (2010).

  48. 48.

    Stachowicz, J. J. & Whitlatch, R. B. Multiple mutualists provide complementary benefits to their seaweed host. Ecology 86, 2418–2427 (2005).

  49. 49.

    McKeon, C. S., Stier, A. C., McIlroy, S. E. & Bolker, B. M. Multiple defender effects: synergistic coral defense by mutualist crustaceans. Oecologia 169, 1095–1103 (2012).

  50. 50.

    Tu, C., Suweis, S., Grilli, J., Formentin, M. & Maritan, A. Reconciling cooperation, biodiversity and stability in complex ecological communities. Sci. Rep. 9, 5580 (2019).

  51. 51.

    Bascompte, J. & Jordano, P. Plant–animal mutualistic networks: the architecture of biodiversity. Annu. Rev. Ecol. Evol. Syst. 38, 567–593 (2007).

  52. 52.

    Butler, S. & O’Dwyer, J. P. Stability criteria for complex microbial communities. Nat. Commun. 9, 2970 (2018).

  53. 53.

    Butler, S. & O’Dwyer, J. P. Cooperation and stability for complex systems in resource limited environments. Preprint at (2020).

  54. 54.

    Momeni, B., Xie, L. & Shou, W. Lotka–Volterra pairwise modeling fails to capture diverse pairwise microbial interactions. eLife 6, e25051 (2017).

  55. 55.

    Cornell, H. V. & Lawton, J. H. Species interactions, local and regional processes, and limits to the richness of ecological communities: a theoretical perspective. J. Anim. Ecol. 61, 1–12 (1992).

  56. 56.

    Alroy, J. Limits to species richness in terrestrial communities. Ecol. Lett. 21, 1781–1789 (2018).

  57. 57.

    Cornell, H. V. Unsaturation and regional influences on species richness in ecological communities: a review of the evidence. Ecoscience 6, 303–315 (1999).

  58. 58.

    Mouquet, N., Munguia, P., Kneitel, J. M. & Miller, T. E. Community assembly time and the relationship between local and regional species richness. Oikos 103, 618–626 (2003).

  59. 59.

    Loreau, M. Are communities saturated? On the relationship between α, β and γ diversity. Ecol. Lett. 3, 73–76 (2000).

  60. 60.

    Valone, T. J. & Hoffman, C. D. Effects of regional pool size on local diversity in small-scale annual plant communities. Ecol. Lett. 5, 477–480 (2002).

  61. 61.

    MacArthur, R. H. & Wilson, E. O. The Theory of Island Biogeography Vol. 1 (Princeton Univ. Press, 1967).

  62. 62.

    Bruno, J. F., Stachowicz, J. J. & Bertness, M. D. Inclusion of facilitation into ecological theory. Trends Ecol. Evol. 18, 119–125 (2003).

  63. 63.

    Hairer, E., Norsett, S. P., & Wanner, G. Solving Ordinary Differential Equations Vol. 1 (Springer, 1991).

  64. 64.

    Harper, M. et al. python-ternary: ternary plots in Python. Zenodo 12, 17 (2015);

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We thank A. Tilman, J. Van Cleve, L. Stone and G. Barabás for helpful comments regarding the manuscript. J.J.Q. was funded by the Roy and Diana Vagelos Scholars Program in the Molecular Life Sciences at the University of Pennsylvania.

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Both authors designed the study. J.J.Q. constructed the model, and both authors provided the analysis. Both authors contributed substantially to writing the manuscript. Both authors gave the final approval for publication.

Correspondence to Erol Akçay.

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Qian, J.J., Akçay, E. The balance of interaction types determines the assembly and stability of ecological communities. Nat Ecol Evol 4, 356–365 (2020).

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