Open Systems & Information Dynamics

, Volume 3, Issue 2, pp 237–254 | Cite as

Dynamics of a food web model of an aquatic ecosystem

  • Morten Liberoth
  • Mikael Barfred
  • Erik Mosekilde
Article
  • 97 Downloads

Abstract

The paper presents a model of an aquatic ecosystem with four species (bacteria, algae, zooplankton and fish) and with three different dead pools (detritus and accessible nutrients in the water column, and nutrients bound to the sediment). The structure of the model is that of a food web with the bacterial population representing the microbial loop. No distinction is made between different nutrients, and all uptake rates are expressed in terms of modified Monod kinetics. Though the model does not explicitly account for shifting abilities of the various species, the modified Monod kinetics enable predators with more than one prey (i.e., zooplankton and fish) to adjust their foraging habits in accordance with the conditions in the system. Simulations of the model show a variety of different solutions, ranging from simple oscillations with the annual periodicity of the external forcing to higher order chaos.

Keywords

Statistical Physic Mechanical Engineer Water Column System Theory Uptake Rate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. C. Allen, Ecological Modeling511, 281 (1990).Google Scholar
  2. [2]
    G. Baier, J. S. Thomsen, and E. Mosekilde, J. Theor. Biol.165, 593 (1993).Google Scholar
  3. [3]
    R. S. K. Barnes and K. H. Mann,Fundamentals of Aquatic Ecology, Blackwell Scientific Publications, 1991.Google Scholar
  4. [4]
    Ø. Bergh, K. Y. Børsheim, G. Bratbak, and M. Heldal, Nature340, 467 (1989).Google Scholar
  5. [5]
    A. T. Bull and J. H. Slater,Microbial Interactions and Communities, Volume 1, Academic Press, New York, 1982.Google Scholar
  6. [6]
    W. L. Ditto and L. M. Pecora, Scientific American8, 62, (1993).Google Scholar
  7. [7]
    F. Doveri, M. Scheffer, S. Rinaldi, S. Muratori, and Y. Kuznetsov, Theoretical Population Biology43, 159 (1993).Google Scholar
  8. [8]
    M. J. Feigenbaum, Los Alamos Science1, 4 (1980).Google Scholar
  9. [9]
    M. E. Gilpin, American Naturalist107, 306 (1979).Google Scholar
  10. [10]
    A. Gnauck, E. Matthäus, M. Straskraba, and I. Affa, System and Modelling Simulation7, 439 (1990).Google Scholar
  11. [11]
    A. Hastings and T. Powell, Ecology72, 896 (1991).Google Scholar
  12. [12]
    M. Inoue and H. Kamifukumoto, Progress of Theoretical Physics71, 930 (1984).Google Scholar
  13. [13]
    Jensen, K. Sand, T. Moth Iversen, and C. Lindegaard,Ferskvandsøkologi (In Danish), Freshwater Biological Laboratory, University of Copenhagen, Denmark, 1983.Google Scholar
  14. [14]
    S. E. Jørgensen,Application of Ecological Modelling in Environmental Management, Part A, Elsevier, 1983.Google Scholar
  15. [15]
    S. E. Jørgensen,Fundamentals of Ecological Modelling, Elsevier, 1986.Google Scholar
  16. [16]
    S. E. Jørgensen,Handbook of Ecological Parameters, Pergamon Press, 1979.Google Scholar
  17. [17]
    S. E. Jørgensen and M. J. Gromiec,Mathematical Submodels in Water Quality Systems, Elsevier, 1989.Google Scholar
  18. [18]
    E. N. Lorenz, Journal of Atm. Physics20, 130 (1963).Google Scholar
  19. [19]
    A. J. Lotka,Elements of Physical Biology, Williams and Wilkins, Baltimore, MD, USA, 1925.Google Scholar
  20. [20]
    R. MacArthur, Ecology36, 533 (1955).Google Scholar
  21. [21]
    H. Malchow, Proc. Roy. Soc. Lond. B.251, 103 (1993).Google Scholar
  22. [22]
    R. M. May, Science186, 645 (1974).Google Scholar
  23. [23]
    R. M. May, Nature261, 459 (1976).Google Scholar
  24. [24]
    R. M. May and G. F. Oster, American Naturalist110, 573 (1976).Google Scholar
  25. [25]
    J. Monod, Ann. Inst. Pasteur79, 390 (1950).Google Scholar
  26. [26]
    B. Moss,Ecology of Fresh Waters, Blackwell Scientific Publication, Oxford, UK., 1988.Google Scholar
  27. [27]
    A. C. Redfield, “On the Proportions of Organic Derivatives in Sea Water and their Relation to the Composition of Plankton”James Johnstone Memorial Volume pp. 176–192, Liverpool University Press, Liverpool, 1934.Google Scholar
  28. [28]
    S. Rinaldi, S. Muratori, and Y. Kuznetsov, Bull. Math. Biol.55, 15 (1993).Google Scholar
  29. [29]
    M. L. Rosenzweig, Science171, 385 (1971).PubMedGoogle Scholar
  30. [30]
    O. E. Rössler, Physics Letters57 A, 397 (1976).Google Scholar
  31. [31]
    O. E. Rössler, Physics Letters71 A, 152 (1979).Google Scholar
  32. [32]
    W. M. Schaffer, Ecology66, 93 (1985).Google Scholar
  33. [33]
    W. M. Schaffer and M. Kot, Trends in Ecological Evolution volume 1, no. 3, 58 (1986).Google Scholar
  34. [34]
    M. Scheffer, J. Plankton Res.13, 1291 (1991).Google Scholar
  35. [35]
    G. Sugihara and R. M. May, Nature344, 734 (1990).Google Scholar
  36. [36]
    V. Volterra, Nature118, 558 (1926).Google Scholar

Copyright information

© Nicholas Copernicus University Press 1995

Authors and Affiliations

  • Morten Liberoth
    • 1
  • Mikael Barfred
    • 1
  • Erik Mosekilde
    • 1
  1. 1.Physics DepartmentThe Technical University of DenmarkLyngbyDenmark

Personalised recommendations