Hydrobiological Bulletin

, Volume 23, Issue 1, pp 73–83 | Cite as

Alternative stable states in eutrophic, shallow freshwater systems: A minimal model

  • M. Scheffer


A simple mathematical model was constructed, describing the relationships between pike, bream, aquatic macrophytes and the nutrient loading of shallow lakes. The model is analyzed with the use of zero-isoclines. It is concluded that, over a certain range of nutrient concentrations, the ecological relations incorporated in the model can give rise to the existence of two alternative stable equilibria;viz. a turbid bream-dominated one, and a clear state in which pike and aquatic vegetation are abundant. Under oligotrophic conditions, the clear-water state represents the only stable equilibrium; however, at high nutrient levels, the clear state is absent, or only locally stable. The response of the model to both increase and decrease of the nutrient level is characterised by hysteresis. The results indicate that manipulation of fish densities as a measure to improve water quality is only likely to produce long-term results when the nutrient level is below a certain threshold.


model fish vegetation eutrophication stability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BACKIEL, T. and E.D. LE CREN, 1978. Some density relationships for fish population parameters. In: S.D. Gerking, Ed., Ecology of Freshwater Fish Production, p. 279–302. Blackwell, Oxford.Google Scholar
  2. BENNDORF, J., 1987. Food web manipulation without nutrient control: a useful strategy in lake restoration? Schweiz. Z. Hydrol., 49: 237–248.Google Scholar
  3. CAZEMIER, W.G., 1982. The growth of bream (Abramis brama L.) in relation to habitat and population density. Hydrobiol. Bull., 16: 269–277.Google Scholar
  4. CRONBERG, G., 1982. Phytoplankton changes in Lake Trummen induced by restoration. Folia Limnologica Scandinavica, 18: 1–119.Google Scholar
  5. DE BOER, R.J., 1983. GRIND Great Integrator Differential Equations. Bioinformatics group, University of Utrecht.Google Scholar
  6. DE NIE, H.W., 1987. The decrease in aquatic vegetation in Europe and its consequences for fish populations. EIFAC/CECPI, occasional paper no. 19, 52 pp.Google Scholar
  7. GASCON, D. and W.C. LEGGET, 1977. Distribution, abundance and resource utilization of littoral zone fishes in response to a nutrient/production gradient in Lake Memphremagog. J. Fish. Res. Board Can., 34: 1105–1117.Google Scholar
  8. GERKING, S. D., Ed., 1978. Ecology of Freshwater Fish Production. Blackwell, Oxford.Google Scholar
  9. GRIMM, M.P., 1981. The composition of northern pike (Esox lucius L.) populations in four shallow waters in The Netherlands with special reference to factors influencing O+ pike biomass. Fish. Management, 12: 61–79.Google Scholar
  10. GRIMM, M.P., 1983. Regulation of biomasses of small (<41 cm) northern pike (Esox lucius L.), with special reference to the contribution of individuals stocked as fingerlings (4–6 cm). Fish. Management, 14: 115–133.Google Scholar
  11. GRIMM, M.P., 1985. Pike. In: pike, pike perch, and bream: biology, population development and control. Report of the working party on the evaluation of control methods. OVB, Nieuwegein. (In Dutch).Google Scholar
  12. HAKKARI, L. and P. BAGGE, 1985. On fry densities of pike (Esox lucius L.) in Lake Sainaa, Finland. Verh. Internat. Verein. Limnol., 22: 2560–2565.Google Scholar
  13. HASSEL, M.P., J.H. LAWTON and J.R. BEDDINGTON, 1977. Sigmoid functional responses by invertebrate predators and parasitoïds. J. Anim. Ecol., 46: 249–262.Google Scholar
  14. HILL, D., R. WRIGHT and M. STREET, 1986. Survival of mallard ducklings (Anas platyrhynchos) and competition with fish for invertebrates on a flooded gravel quarry in England. Ibis, 129: 159–167.Google Scholar
  15. HOSPER, S.H., 1989. Biomanipulation, new perspectives for restoration of shallow eutrophic lakes in The Netherlands. Hydrobiol. Bull., 23: 5–10.Google Scholar
  16. KIPLING, C., 1983. Changes in the population of pike (Esox lucius) in Windermere from 1944 to 1981. J. Anim. Ecol., 52: 989–999.Google Scholar
  17. MANN, R.H.K., 1982. The annual food consumption and prey preferences of pike (Esox lucius) in the river Frome, Dorset. J. Animal. Ecol., 51: 81–95.Google Scholar
  18. MAY, R.M., 1976. Theoretical ecology. Blackwell, London.Google Scholar
  19. McALLISTER, C.D., R.J. LEBRASSEUR and T.R. PARSONS, 1972. Stability of enriched aquatic ecosystems. Science, 175: 562–564.Google Scholar
  20. McQUEEN, D.J. and J.R. POST, 1988. Cascading trophic interactions: uncoupling at the zooplankton-phytoplankton link. Hydrobiologia, 159: 277–296.Google Scholar
  21. MEIJER, M.-L., A.J.P. RAAT and R.W. DOEF, 1989. Restoration by biomanipulation of the Dutch shallow, eutrophic Lake Bleiswijkse Zoom, first results. Hydrobiol. Bull., 23: 49–57.Google Scholar
  22. MILLS, E.L., J.L. FORNEY and K.J. WAGNER, 1987. Fish predation and its cascading effect on the Oneida Lake food chain. In: W.C. Kerfoot and A. Sih, Eds., Predation, direct and indirect impacts on aquatic communities, p. 118–131 University Press of New England, Hanover.Google Scholar
  23. MOHN, R.K. and R.J. MILLER, 1987. A ration-based model of a seaweed/sea urchin community. Ecological Modelling, 37, 249–267.Google Scholar
  24. PARTRIDGE, D. and P. LOPEZ, 1984. Computer programs as theories in biology. J. theor. Biol., 108: 539–564.Google Scholar
  25. POPOVA, O.A., 1978. The role of predacious fish in ecosystems. In: S.D. Gerking, Ed., Ecology of freshwater fish production, p. 215–249 Blackwell, Oxford.Google Scholar
  26. RAAT, A.J.P., 1988. Synopsis of biological data on the northern pike,Esox lucius L. FAO Fisheries Synopsis No. 30 Rev. 2. FAO, Rome.Google Scholar
  27. ROSE, M.R. and R. HARMSEN, 1981. Ecological outbreak dynamics and the cusp catastrophe. Acta Biotheoretica, 30: 229–253.Google Scholar
  28. ROSENZWEIG, M.L., 1971. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science, 171: 385–387.Google Scholar
  29. ROSENZWEIG, M.L., 1972. Stability of enriched ecosystems; a reply. Science, 175: 564–565.Google Scholar
  30. SHAPIRO, J., 1980. The importance of trophic-level interactions, to the abundance and species composition of algae in lakes. In: J. Barica and R. Mur, Eds., Developments in Hydrobiology, Vol. 2, Hypertrophic ecosystems, pp. 105–116.Google Scholar
  31. SPENCE, D.H.N., 1982. The zonation of plants in freshwater lakes, 12: 37–125.Google Scholar
  32. TEN WINKEL, E.H. and J.T. MEULEMANS, 1984. Effects of fish upon submerged vegetation. Hydrobiol. Bull., 18: 157–158.Google Scholar
  33. TIMMS, R.M. and B. MOSS, 1984. Prevention of growth of potentially dense phytoplankton, populations by zooplankton grazing in the presence of zooplanktivorous fish in a shallow wetfand ecosystem. Limnol. Oceanogr., 29: 472–486.Google Scholar
  34. VAN DONK, E., R.D. GULATI, and M.P. GRIMM, 1989. Food web manipulation in Lake Zwemjust: positive and negative effects during the first two years. Hydrobiol. Bull., 23: 19–34.Google Scholar
  35. WILLEMSEN, J., 1980. Fishery aspects of eutrophication. Hydrobiol. Bull., 14: 12–21.Google Scholar
  36. WRIGHT, R., 1987. The pike population of the A.R.C. Wildfowl reserve. In: The Game conservancy, Annual review 1986, p. 139–141 Fordingbridge.Google Scholar

Copyright information

© Netherlands Hydrobiological Society 1989

Authors and Affiliations

  • M. Scheffer
    • 1
  1. 1.Institute for Inland Water Management and Waste Water Treatment Lelystad, The NetherlandsLelystadThe Netherlands

Personalised recommendations