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Top predator persistence in differential equation models of food chains: The effects of omnivory and external forcing of lower trophic levels

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Abstract

Persistence criteria are given for the highest trophic level predator in ordinary differential equation models of food chains exhibiting arbitrary omnivory and external supplementation of food source or an intermediate predator. The results are expressed in terms of inequalities involving the bounds on the intrinsic growth and interaction rates. Whether omnivory or external forcing enhances persistence is discussed, particularly for the examples of three-, four-, and five-link Lotka-Volterra food chains.

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References

  1. Batschelet, E.: Introduction to mathematics for life scientists. 3rd. ed. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  2. Brody, S.: Bioenergetics and growth. New York: Reinhold 1945

    Google Scholar 

  3. Gard, T. C.: Persistence in food webs: Holling-type food chains. Math. Biosc. 49, 61–67 (1980a)

    Google Scholar 

  4. Gard, T. C.: Persistence in food chains with general interactions. Math. Biosc. 51, 165–174 (1980b)

    Google Scholar 

  5. Gard, T. C., Hallam, T. G.: Persistence in food webs. I. Lotka-Volterra food chains. Bull. Math. Biol. 41, 877–891 (1979)

    Google Scholar 

  6. Lassiter, R. R.: Microcosms as ecosystems for testing ecological models. State-of-the-Art in Ecological Modelling, Vol. 7, pp. 127–161. Proceedings of the 1st International Conference on Ecological Modelling, (Jørgensen, S. E., ed.) ISEM, Copenhagen, 1978

    Google Scholar 

  7. Pimm, S.: The structure of food webs. Theoret. Pop. Biol. 16, 144–158 (1979)

    Google Scholar 

  8. Pimm, S.: Properties of food webs. Ecology 61, 219–225 (1980)

    Google Scholar 

  9. Pimm, S., Lawton, J.: On feeding on more than one trophic level. Nature 275, 542–544 (1978)

    Google Scholar 

  10. Rosenzweig, M. L.: Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time. Science 171, 385–387 (1971)

    Google Scholar 

  11. Wiegert, R.: Population models: Experimental tools for analysis of ecosystems. Analysis of ecological systems (Horn, D. J., Stairs, G. R., Mitchell, R. D., eds.) pp. 233–279. Ohio: Ohio State University Press, 1979

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, 30602, Athens, Georgia, USA

    Thomas C. Gard

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  1. Thomas C. Gard
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Gard, T.C. Top predator persistence in differential equation models of food chains: The effects of omnivory and external forcing of lower trophic levels. J. Math. Biology 14, 285–299 (1982). https://doi.org/10.1007/BF00275394

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  • DOI: https://doi.org/10.1007/BF00275394

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