Skip to main content
SpringerLink
Log in

A universal law of the characteristic return time near thresholds

  • Original Papers
  • Published:
Oecologia Aims and scope Submit manuscript

Summary

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agnew TT (1979) Optimal exploitation of a fishery employing a nonlinear harvesting functions. Ecol Modelling 6:47

    Google Scholar 

  • 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 245

  • Brauer F, Soudack AC (1979) Stability regions and transition phenomena for harvested predator-prey systems. J Math Biol 7:319

    Google Scholar 

  • 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, 1978

  • De Angelis DL, Goldstein RA, O'Neill RV (1975) A model for trophic interaction. Ecology 56:881

    Google Scholar 

  • Diamond JM (1975) Assembly of species communities. In: Ecology and evolution of communities Cody ML, Diamond JM (eds)

  • Goel NS, Richter-Dyn N (1974) Stochastic models in biology. Academic Press

  • Gulland JA (1975) The stability of fish stocks. J Cons int Explor Mer 37:199

    Google Scholar 

  • 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), 1

  • Janzen DH (1970) Herbivores and the number of tree species in tropical forests. Am Natur 104:501

    Article  Google Scholar 

  • Le Creen ED, Kipling C, McCormack JC (1972) Windermere: Effects of exploitation and eutrophication on the salmonid community. J Fish Res Bd Can 29:819

    Google Scholar 

  • Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: The spruce budworm and forest. J Anim Ecol 47:315

    Google Scholar 

  • May RM (1977a) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269:471

    Google Scholar 

  • May RM (1977b) Togetherness among schistosomes: Its effects on the dynamics of the infection. Math Biosc 35:301

    Google Scholar 

  • McQueen DJ (1975) Multiple stability and maximum stability in a model population. Can J Zool 53:1844

    Google Scholar 

  • Ming Chen Wang, Uhlenbeck GE (1945) On the theory of the Brownian Motion II. Rev Mod Phys 17:323

    Google Scholar 

  • 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 Publ

  • Russell BD, Talbot FH, Domm S (1974) Patterns of colonization of artificial reefs by coral reef fishes. Proc Z Int Symp Coral Reefs 1:207

    Google Scholar 

  • Sasaba T, Kiritani K (1975) A system model: a computer simulation of the green rice leafhopper populations in control programs. Res Pop Ecol 16:231

    Google Scholar 

  • Schoener TW (1978) Effects of density-restricted food encounter on some single-level competition models. Theor Pop Biol 13:365

    Google Scholar 

  • Simenstad CA, Estes JA, Kenyon KW (1978) Aleuts, sea otters, and alternate stable state communities. Science 200:403

    Google Scholar 

  • Sutherland JP (1974) Multiple stable points in natural communities. Am Natur 108:859

    Article  Google Scholar 

  • Van Nguyen V, Wood EF (1979) On the morphology of summer algae dynamics in non-stratified lakes. Ecol Mod 6:117

    Google Scholar 

  • Whittaker RH (1975) The design and stability of plant communities. Proc Int Congr Ecol The Hague 1974

  • Wissel C, Beuter K, Halbach U (1981) Correlation functions for the evaluation of repeated time series with fluctuations. ISEM Journal 3:(1–2) 11–29

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Physik der Universität, Lahnberge, D-3550, Marburg, Federal Republic of Germany

    C. Wissel

Authors
  1. C. Wissel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wissel, C. A universal law of the characteristic return time near thresholds. Oecologia 65, 101–107 (1984). https://doi.org/10.1007/BF00384470

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00384470

Keywords

Search

Navigation