Evolutionary Ecology

, Volume 8, Issue 2, pp 150–171 | Cite as

The responses of unstable food chains to enrichment

  • Peter A. Abrams
  • James Roth


This article investigates the mean abundances of trophic levels in simple models of two- and three-level food chains as a function of the rate of input of nutrients. The analysis concentrates on cases in which the equilibrium point with all species present is unstable. In most of the models, the instability arises because the consumer species become satiated when food density is high. In unstable two-level systems, bottom level abundance generally increases with increased nutrient input. The abundance of the second level may decrease with increased input. Changes in the intrinsic rate of increase and carrying capacity of the bottom level can have qualitatively opposite effects on trophic level abundances. Refuges for or immigration of the bottom level usually cause both levels to increase in mean abundance with an increased carrying capacity. A variety of different predator—prey models are discussed briefly and the results suggest that increased nutrient input will often increase the abundance of both levels; however, several circumstances can cause the top level to decrease. In three-level systems, an increased carrying capacity can cause extinction of the top level. Extinction may or may not be conditional on the initial densities of the three levels. These results may help explain the observed lack of correlation between productivity and the number of trophic levels in natural food webs, as well as the lack of very long food chains. The results suggest that patterns of abundances across productivity gradients cannot be used to assess the importance of top-down vs bottom-up effects.


bottom-up effects food chain functional response limit cycle predator prey stability topdown effects trophic structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abrams, P. A. (1975) Limiting similarity and the form of the competition coefficient.Theor. Pop. Biol.,8, 356–75.Google Scholar
  2. Abrams, P. A. (1977) Density independent mortality and interspecific competition: a test of Pianka's niche overlap hypothesis.Am. Nat.,111, 539–52.Google Scholar
  3. Abrams, P. A. (1984) Foraging time optimization and interactions in food webs.Am. Nat.,124, 80–96.Google Scholar
  4. Abrams, P. A. (1993) Effect of increased productivity on the abundances of trophic levels.Am. Nat.,141, 351–71.Google Scholar
  5. Abrams, P. A. and Roth, J. (1994) The effects of enrichment on three-species food chains with nonlinear functional responses.Ecology (in press).Google Scholar
  6. Cohen, J. E., Briand, F. R. and Newman, C. M. (1990)Community Food Webs: Data and Theory. Springer Verlag, Berlin, Germany.Google Scholar
  7. DeAngelis, D. A. (1992)Dynamics of Nutrient Cycling and Food Webs. Chapman & Hall, London, UK.Google Scholar
  8. Edelstein-Keshet, L. (1988)Mathematical Models in Biology. Random House, New York.Google Scholar
  9. Fretwell, S. D. (1977) The regulation of plant communities by food chains exploiting them.Persp. Biol. Med.,20, 169–85.Google Scholar
  10. Fretwell, S. D. (1987) Food chain dynamics: the central theory of ecology?Oikos,50, 291–301.Google Scholar
  11. Gilpin, M. E. (1975)Group Selection in Predator—Prey Communities. Princeton University Press, Princeton, NJ, USA.Google Scholar
  12. Gilpin, M. E. and Ayala, F. J. (1973) Global models of growth and competition.Proc. Natl Acad. Sci. USA,70, 3590–3.PubMedGoogle Scholar
  13. Hansson, L. (1987) An interpretation of rodent dynamics as due to trophic interactions.Oikos,50, 308–18.Google Scholar
  14. Hassell, M. P. (1978)The Dynamics of Arthropod Predator—Prey Systems. Princeton University Press, Princeton, NJ, USA.Google Scholar
  15. Hastings, A. and Powell, T. (1991) Chaos in a three-species food chain.Ecology,72, 896–903.Google Scholar
  16. McAllister, C. D., LeBrasseur, R. J. and Parsons, T. R. (1972) Stability of enriched aquatic ecosystems.Science (USA),175, 562–4.Google Scholar
  17. MacArthur, R. H. (1970) Species packing and competitive equilibrium for many species.Theor. Pop. Biol.,1, 1–11.Google Scholar
  18. Matson, P. A. and Hunter, M. D. (1992) The relative contributions of top-down and bottom-up forces in population and community ecology.Ecology,73, 723–65.Google Scholar
  19. May, R. M. (1972) Limit cycles in predator—prey communities.Science (USA),177, 900–2.Google Scholar
  20. Mittelbach, G. G., Osenberg, C. W. and Leibold, M. A. (1988) Trophic relations and ontogenetic niche shifts in aquatic ecosystems. InSize Structured Populations (B. Ebenman and L. Persson, eds), pp. 219–35. Springer Verlag, Berlin, Germany.Google Scholar
  21. Neill, W. E. (1988) Complex interactions in oligotrophic lake food webs: responses to nutrient enrichment. InComplex Interactions in Lake Communities (S. R. Carpenter, ed.) pp. 31–44. Springer Verlag, New York, USA.Google Scholar
  22. Oksanen, L. (1983) Trophic exploitation and arctic phytomass patterns.Am. Nat.,122, 45–52.Google Scholar
  23. Oksanen, L. (1988) Ecosystem organization: mutualism and cybernetics or plain Darwinian struggle for existence?Am. Nat.,131, 424–44.Google Scholar
  24. Oksanen, L. (1990) Exploitation ecosystems in seasonal environments.Oikos,57, 14–24.Google Scholar
  25. Oksanen, L. (1992) Evolution of exploitation ecosystems. I. Predation, foraging, ecology, and population dynamics in herbivores.Evol. Ecol.,6, 15–33.Google Scholar
  26. Oksanen, L., Fretwell, S. J., Arruda, J. and Niemela, P. (1981) Exploitation ecosystems in gradients of primary productivity.Am. Nat.,118, 240–61.Google Scholar
  27. Oksanen, T. (1990) Exploitation ecosystems in heterogeneous habitat complexes.Evol. Ecol.,4, 220–34.Google Scholar
  28. Pimm, S. L. (1982)Food Webs. Chapman & Hall, London, UK.Google Scholar
  29. Pimm, S. L. (1991)The Balance of Nature? University of Chicago Press, Chicago, USA.Google Scholar
  30. Power, M. E. (1992) Top-down and bottom-up forces in food webs: do plants have primacy?Ecology,73, 733–46.Google Scholar
  31. Rosenzweig, M. L. (1971) The paradox of enrichment: destabilization of exploitation ecosystems in ecological time.Science (USA),171, 385–7.Google Scholar
  32. Rosenzweig, M. L. (1973) Exploitation in three trophic levels.Am. Nat.,107, 275–94.Google Scholar
  33. Schaffer, W. M. (1981) Ecological abstraction: the consequences of reduced dimensionality in ecological models.Ecol. Monogr.,51, 383–401.Google Scholar
  34. Schoener, T. W. (1974) Some methods for calculating competition coefficients from resource-utilization spectra.Am. Nat.,109, 332–40.Google Scholar
  35. Tilman, G. D. (1982)Resource Competition and Community Structure. Princeton University Press, Princeton, NJ.Google Scholar
  36. Wolfram, S. (1991)Mathematica, 2nd edn. Addison-Wesley, New York, NY, USA.Google Scholar
  37. Wollkind, D. J. (1976) Exploitation in three trophic levels: an extension allowing intraspecies carnivore interaction.Am. Nat.,110, 431–47.Google Scholar
  38. Yodzis, P. (1989)Introduction to Theoretical Ecology. Harper and Row, NY, USA.Google Scholar
  39. Yodzis, P. and Innes, S. (1992) Body size and consumer-resource dynamics.Am. Nat.,139, 1151–75.Google Scholar

Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • Peter A. Abrams
    • 1
  • James Roth
    • 1
  1. 1.Department of Ecology, Evolution, and BehaviorUniversity of MinnesotaSt PaulUSA

Personalised recommendations