, Volume 65, Issue 1, pp 101–107 | Cite as

A universal law of the characteristic return time near thresholds

  • C. Wissel
Original Papers


Dramatic changes at thresholds in multiple stable ecosystems may be irreversible if caused by man. The characteristic return time to an equilibrium increases when a threshold is approached. A universal law for this increase is found, which may be used to forecast the position of a threshold by extrapolation of empirical data. Harvesting experiments on populations are proposed that can be used to verify the method. Preliminary harvesting experiments on rotifer populations display a good agreement with the theory.


Empirical Data Return Time Stable Ecosystem Characteristic Return Rotifer Population 
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  1. Agnew TT (1979) Optimal exploitation of a fishery employing a nonlinear harvesting functions. Ecol Modelling 6:47Google Scholar
  2. Anderson RM (1979) The influence of parasitic infection on the dynamics of host population growth. In Population Dynamics; Anderson RM, Turner BD, Taylor LR (eds), Symp Brit Ecol Soc, Blackwell Scient Publ pp 245Google Scholar
  3. Brauer F, Soudack AC (1979) Stability regions and transition phenomena for harvested predator-prey systems. J Math Biol 7:319Google Scholar
  4. Clark WC, Holling CS (1979) Process models, equilibrium structures, and population dynamics: On the formulation and testing of realistic theory in ecology. In: Population Ecology, Halbach U, Jacobs J, Fortschritte der Zoologie 25:(2/3) Symposium, Mainz, 1978Google Scholar
  5. De Angelis DL, Goldstein RA, O'Neill RV (1975) A model for trophic interaction. Ecology 56:881Google Scholar
  6. Diamond JM (1975) Assembly of species communities. In: Ecology and evolution of communities Cody ML, Diamond JM (eds)Google Scholar
  7. Goel NS, Richter-Dyn N (1974) Stochastic models in biology. Academic PressGoogle Scholar
  8. Gulland JA (1975) The stability of fish stocks. J Cons int Explor Mer 37:199Google Scholar
  9. Halbach U (1979) Strategies in population research exemplified by rotifer population dynamics. In: Population Ecology, Symposium Mainz, 1978. Halbach U, Jacobs J, (eds) Fortschr d Zool 25 (2/3), 1Google Scholar
  10. Janzen DH (1970) Herbivores and the number of tree species in tropical forests. Am Natur 104:501CrossRefGoogle Scholar
  11. Le Creen ED, Kipling C, McCormack JC (1972) Windermere: Effects of exploitation and eutrophication on the salmonid community. J Fish Res Bd Can 29:819Google Scholar
  12. Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: The spruce budworm and forest. J Anim Ecol 47:315Google Scholar
  13. May RM (1977a) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269:471Google Scholar
  14. May RM (1977b) Togetherness among schistosomes: Its effects on the dynamics of the infection. Math Biosc 35:301Google Scholar
  15. McQueen DJ (1975) Multiple stability and maximum stability in a model population. Can J Zool 53:1844Google Scholar
  16. Ming Chen Wang, Uhlenbeck GE (1945) On the theory of the Brownian Motion II. Rev Mod Phys 17:323Google Scholar
  17. Peterman RM, Clark WC, Holling CS (1979) The dynamics of resilience; Shifting stability domains in fish and insect systems. In: Population Dynamics Anderson RM, Turner BD, Taylor LR (eds) 20. Symp Brit Ecol Soc, Blackwell Scient PublGoogle Scholar
  18. Russell BD, Talbot FH, Domm S (1974) Patterns of colonization of artificial reefs by coral reef fishes. Proc Z Int Symp Coral Reefs 1:207Google Scholar
  19. Sasaba T, Kiritani K (1975) A system model: a computer simulation of the green rice leafhopper populations in control programs. Res Pop Ecol 16:231Google Scholar
  20. Schoener TW (1978) Effects of density-restricted food encounter on some single-level competition models. Theor Pop Biol 13:365Google Scholar
  21. Simenstad CA, Estes JA, Kenyon KW (1978) Aleuts, sea otters, and alternate stable state communities. Science 200:403Google Scholar
  22. Sutherland JP (1974) Multiple stable points in natural communities. Am Natur 108:859CrossRefGoogle Scholar
  23. Van Nguyen V, Wood EF (1979) On the morphology of summer algae dynamics in non-stratified lakes. Ecol Mod 6:117Google Scholar
  24. Whittaker RH (1975) The design and stability of plant communities. Proc Int Congr Ecol The Hague 1974Google Scholar
  25. Wissel C, Beuter K, Halbach U (1981) Correlation functions for the evaluation of repeated time series with fluctuations. ISEM Journal 3:(1–2) 11–29Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • C. Wissel
    • 1
  1. 1.Fachbereich Physik der UniversitätMarburgFederal Republic of Germany

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