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Thresholds and breakpoints in ecosystems with a multiplicity of stable states

Nature volume 269, pages 471–477 (1977)Cite this article

Abstract

Theory and observation indicate that natural multi-species assemblies of plants and animals are likely to possess several different equilibrium points. This review discusses how alternate stable states can arise in simple 1- and 2-species systems, and applies these ideas to grazing systems, to insect pests, and to some human host–parasite systems.

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References

  1. Monod, J. Chance and Necessity: an Essay on the Natural Philosophy of Modern Biology (Knopf, New York, 1971).

    Google Scholar 

  2. Weinberg, S. The First Three Minutes: a Modern View of the Origin of the Universe (Basic Books, New York, 1977).

    Google Scholar 

  3. Hawking, S. W. Sci. Am. 236, 34–40 (1977).

    Article  ADS  Google Scholar 

  4. Layzer, D. Sci. Am. 233, 56–69 (1975).

    Article  Google Scholar 

  5. Blatt, J. M. Prog. theor. Phys. 22, 745–756 (1959).

    Article  ADS  Google Scholar 

  6. Simpson, G. G. The Major Features of Evolution (Columbia University Press, New York, 1953).

    Book  Google Scholar 

  7. Raup, D. M. Am. Sci. 65, 50–57 (1977).

    CAS  ADS  PubMed  Google Scholar 

  8. MacArthur, R. H. Geographical Ecology (Harper and Row, New York, 1972).

    Google Scholar 

  9. May, R. M. in Progress in Theoretical Biology 3 (eds Rosen, R. & Snell, F.) 1–50 (Academic. New York, 1974).

    Book  Google Scholar 

  10. Sutherland, J. P. Am. Nat. 108, 859–873 (1974).

    Article  Google Scholar 

  11. Levin, S. A. A. Rev. ecol. Syst. 7, 287–310 (1976).

    Article  Google Scholar 

  12. Connell, J. H. & Slatyer, R. O. Am. Nat. (in the press).

  13. Austin, M. P. & Cook, B. G. J. theor. Biol. 45, 435–458 (1974).

    Article  CAS  PubMed  Google Scholar 

  14. Case, T. J. & Gilpin, M. E. Nature 26l, 40–42 (1976).

    Google Scholar 

  15. Holling, C. S. A. Rev. ecol. Syst. 4, 1–23 (1973).

    Article  Google Scholar 

  16. Lewontin, R. C. in Diversity and Stability in Ecological Systems 13–24 (US National Bureau of Standards, Springfield, Virginia, 1969).

    Google Scholar 

  17. May, R. M. Stability and Complexity in Model Ecosystems 2nd ed, (Princeton University Press, Princeton, 1974).

    Google Scholar 

  18. Orians, G. H. in Unifying Concepts in Ecology (eds van Dobben, W. H. & Lowe-McConnell. R. H.) 139–150 (W. Junk, The Hague, 1975).

    Book  Google Scholar 

  19. Margalef, R. in Unifying Concepts in Ecology (op. cit.) 151–160.

    Chapter  Google Scholar 

  20. May, R. M. in Unifying Concepts in Ecology (op. cit.) 161–168.

    Chapter  Google Scholar 

  21. Whittaker, R. H. in Unifying Concepts in Ecology (op. cit.) 169–181.

    Chapter  Google Scholar 

  22. Grumm, H. R. IIASA Publicalion RR-76-005 (2361 Laxenburg, Austria, 1976).

  23. Noy-Meir, I. J. Ecol. 63, 459–481 (1975).

    Article  Google Scholar 

  24. Caughley, G. in Theoretical Ecology: Principles and Applications (ed. May. R. M.) 94–113 (Blackwell, Oxford, 1976).

    Google Scholar 

  25. Holling, C. S. Mem. ent. Soc. Can. 45, 3–60 (1965).

    Google Scholar 

  26. Hassell, M. P., Lawton, J. H. & Beddington, J. R. J. Anim. Ecol. 46, 249–262 (1977).

    Article  Google Scholar 

  27. Murdoch, W. W. & Oaten, A. Adv. ecol. Res. 9, 1–131 (1975).

    Article  Google Scholar 

  28. Hassell, M. P. Arthropod Predator-Prey Systems (Princeton University Press, Princeton, in the press).

  29. Macdonald, G. Trans. R. Soc. trop. Med. Hyg. 59, 489–506 (1965).

    Article  CAS  PubMed  Google Scholar 

  30. Brougham, R. W. Aust. J. agric. Res. 6, 804–812 (1955).

    Article  Google Scholar 

  31. Brougham, R. W. N. Z. J. Sci. Technol. A 38, 78–87 (1956).

    Google Scholar 

  32. Davidson, J. L. & Donald, C. M. Aust. J. agric. Res. 9, 53–72 (1958).

    Article  Google Scholar 

  33. Willoughby, W. M. Aust. J. agric. Res. 10, 248–268 (1959).

    Article  Google Scholar 

  34. Arnold, G. W. in Grazing in Terrestrial and Marine Environments (ed. Crisp. D. J.) 133–154 (Blackwell, Oxford, 1963).

    Google Scholar 

  35. Allden, W. G. Proc. Aust. Soc. Anim. Prod. 4, 163–166 (1962).

    Google Scholar 

  36. Morley, F. H. W. Proc. N. Z. Soc. Anim. Prod. 26, 8–21 (1966).

    Google Scholar 

  37. Brauer, F. & Sanchcez, D. A. Theor. Pop. Biol. 8, 12–31 (1975).

    Article  CAS  Google Scholar 

  38. Beddington, J. R. & May, R. M. Science 197, 463 (1977).

    Article  CAS  ADS  PubMed  Google Scholar 

  39. Goh, B. S. Math. Biosci. 33, 359 (1977).

    Article  Google Scholar 

  40. Huberman, G. Theor. Pop. Biol. (in the press).

  41. Clark, C. W. Mathematical Bioeconomics (Wiley, New York, 1976).

    MATH  Google Scholar 

  42. Takahashi, F. Res. Pop. Ecol. 6, 28–36 (1964).

    Article  Google Scholar 

  43. Watt, K. E. F. Ecology and Resource Management (McGraw-Hill, New York, 1968).

    Google Scholar 

  44. Southwood, T. R. E. & Comins, H. N. J. Anim. Ecol. 45, 949–966 (1976).

    Article  Google Scholar 

  45. Southwood, T. R. E. in Proceedings of XV International Congress of Entomology (ed. Packer, J. S.) 36–51 (Entomological Society of America, College Park, Maryland, 1977).

    Google Scholar 

  46. Southwood, T. R. E. Am. Sci. 65, 30–39 (1977).

    CAS  ADS  PubMed  Google Scholar 

  47. Southwood, T. R. E. in The Origins of Pest, Parasite, Disease and Weed Problems (eds Cherrett, J. M. & Sagar, G. R.) (Blackwell, Oxford, 1977).

    Google Scholar 

  48. May, R. M. Nature 264, 211–212 (1976).

    Article  ADS  Google Scholar 

  49. Conway, G. R. in Theoretical Ecology: Principles and Applications (op. cit.) 257–281.

  50. Conway, G. R. Nature (in the press).

  51. Morris, R. Mem. ent. Soc. Can. 31, 1–332 (1963).

    Article  Google Scholar 

  52. Holling, C. S., Dantzig, G., Baskerville, C., Jones, D. & Clark, W. Proc. Int.(Canadian) Conference on Applied Systems Analysis, 1975 (in the press).

  53. Levandowsky, M. & White, B. S. Evol. Biol. (in the press).

  54. Macdonald, G. The Epidemiology and Control of Malaria (Oxford University Press, London, 1957).

    Google Scholar 

  55. Macdonald, G. Dynamics of Tropical Disease (Oxford University Press, London, 1973).

    Google Scholar 

  56. Nasell, I. & Hirsch, W. M. Comm. pure appl. Math. 26, 395–453 (1973).

    Article  MathSciNet  Google Scholar 

  57. Nasell, I. Theor. Pop. Biol. 10, 133–144 (1976).

    Article  CAS  MathSciNet  Google Scholar 

  58. May, R. M. Math. Biosci. (in the press).

  59. Bradley, D. J. & May, R. M. Trans. R. Soc. trop. Med. Hyg. (in the press).

  60. May, R. M. & Oster, G. F. Am. Nat. 110, 573–599 (1976).

    Article  Google Scholar 

  61. May, R. M. Nature 261, 459–467 (1976).

    Article  CAS  ADS  Google Scholar 

  62. Guckenheimer, J., Oster, G. F. & Ipaktchi, A. Theor. Pop. Biol. (in the press).

  63. Rossler, O. E. Z. Naturforsch 31 a, 1664–1670 (1976).

    Article  ADS  Google Scholar 

  64. Gilbert, L. E. in Coerolution of Animals and Plants (eds Gilbert, L. E. & Raven, P. H.) (Texas University Press, Austin, 1975).

    Google Scholar 

  65. Lawton, J. H. Nature 264, 138–139 (1976).

    Article  ADS  Google Scholar 

Download references

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  1. Biology Department, Princeton University, Princeton, New Jersey, 08540

    Robert M. May

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  1. Robert M. May
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May, R. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269, 471–477 (1977). https://doi.org/10.1038/269471a0

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