Summary
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.
Similar content being viewed by others
References
Abrams, P. A. (1975) Limiting similarity and the form of the competition coefficient.Theor. Pop. Biol.,8, 356–75.
Abrams, P. A. (1977) Density independent mortality and interspecific competition: a test of Pianka's niche overlap hypothesis.Am. Nat.,111, 539–52.
Abrams, P. A. (1984) Foraging time optimization and interactions in food webs.Am. Nat.,124, 80–96.
Abrams, P. A. (1993) Effect of increased productivity on the abundances of trophic levels.Am. Nat.,141, 351–71.
Abrams, P. A. and Roth, J. (1994) The effects of enrichment on three-species food chains with nonlinear functional responses.Ecology (in press).
Cohen, J. E., Briand, F. R. and Newman, C. M. (1990)Community Food Webs: Data and Theory. Springer Verlag, Berlin, Germany.
DeAngelis, D. A. (1992)Dynamics of Nutrient Cycling and Food Webs. Chapman & Hall, London, UK.
Edelstein-Keshet, L. (1988)Mathematical Models in Biology. Random House, New York.
Fretwell, S. D. (1977) The regulation of plant communities by food chains exploiting them.Persp. Biol. Med.,20, 169–85.
Fretwell, S. D. (1987) Food chain dynamics: the central theory of ecology?Oikos,50, 291–301.
Gilpin, M. E. (1975)Group Selection in Predator—Prey Communities. Princeton University Press, Princeton, NJ, USA.
Gilpin, M. E. and Ayala, F. J. (1973) Global models of growth and competition.Proc. Natl Acad. Sci. USA,70, 3590–3.
Hansson, L. (1987) An interpretation of rodent dynamics as due to trophic interactions.Oikos,50, 308–18.
Hassell, M. P. (1978)The Dynamics of Arthropod Predator—Prey Systems. Princeton University Press, Princeton, NJ, USA.
Hastings, A. and Powell, T. (1991) Chaos in a three-species food chain.Ecology,72, 896–903.
McAllister, C. D., LeBrasseur, R. J. and Parsons, T. R. (1972) Stability of enriched aquatic ecosystems.Science (USA),175, 562–4.
MacArthur, R. H. (1970) Species packing and competitive equilibrium for many species.Theor. Pop. Biol.,1, 1–11.
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.
May, R. M. (1972) Limit cycles in predator—prey communities.Science (USA),177, 900–2.
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.
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.
Oksanen, L. (1983) Trophic exploitation and arctic phytomass patterns.Am. Nat.,122, 45–52.
Oksanen, L. (1988) Ecosystem organization: mutualism and cybernetics or plain Darwinian struggle for existence?Am. Nat.,131, 424–44.
Oksanen, L. (1990) Exploitation ecosystems in seasonal environments.Oikos,57, 14–24.
Oksanen, L. (1992) Evolution of exploitation ecosystems. I. Predation, foraging, ecology, and population dynamics in herbivores.Evol. Ecol.,6, 15–33.
Oksanen, L., Fretwell, S. J., Arruda, J. and Niemela, P. (1981) Exploitation ecosystems in gradients of primary productivity.Am. Nat.,118, 240–61.
Oksanen, T. (1990) Exploitation ecosystems in heterogeneous habitat complexes.Evol. Ecol.,4, 220–34.
Pimm, S. L. (1982)Food Webs. Chapman & Hall, London, UK.
Pimm, S. L. (1991)The Balance of Nature? University of Chicago Press, Chicago, USA.
Power, M. E. (1992) Top-down and bottom-up forces in food webs: do plants have primacy?Ecology,73, 733–46.
Rosenzweig, M. L. (1971) The paradox of enrichment: destabilization of exploitation ecosystems in ecological time.Science (USA),171, 385–7.
Rosenzweig, M. L. (1973) Exploitation in three trophic levels.Am. Nat.,107, 275–94.
Schaffer, W. M. (1981) Ecological abstraction: the consequences of reduced dimensionality in ecological models.Ecol. Monogr.,51, 383–401.
Schoener, T. W. (1974) Some methods for calculating competition coefficients from resource-utilization spectra.Am. Nat.,109, 332–40.
Tilman, G. D. (1982)Resource Competition and Community Structure. Princeton University Press, Princeton, NJ.
Wolfram, S. (1991)Mathematica, 2nd edn. Addison-Wesley, New York, NY, USA.
Wollkind, D. J. (1976) Exploitation in three trophic levels: an extension allowing intraspecies carnivore interaction.Am. Nat.,110, 431–47.
Yodzis, P. (1989)Introduction to Theoretical Ecology. Harper and Row, NY, USA.
Yodzis, P. and Innes, S. (1992) Body size and consumer-resource dynamics.Am. Nat.,139, 1151–75.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abrams, P.A., Roth, J. The responses of unstable food chains to enrichment. Evol Ecol 8, 150–171 (1994). https://doi.org/10.1007/BF01238247
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01238247