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An Analytical Foundation of the Ratio-Dependent Predator-Prey Model

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  • Thomas Eichner
  • Rüdiger Pethig

Abstract

Predator-prey models of the Lotka-Volterra type and their refinements describe predator-prey interactions taking populations as basic units of analysis. In contrast to these macro models we derive interdependent population growth functions of a predator and a prey species from a micro ecosystem model whose basic entities are representative prey and predator organisms which behave as if they maximize their net offspring under constraints. In the short-run periods prices (scarcity indicators) coordinate and determine all biomass transactions and net offspring which directly translates into population growth and thus constitutes the dynamics of the predator-prey relations. For a specific parametric version our model offers a theoretical foundation of the ratio-dependent predator-prey model with Michaelis-Menten type functional response.
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  • Thomas Eichner & Rüdiger Pethig, 2006. "An Analytical Foundation of the Ratio-Dependent Predator-Prey Model," Journal of Bioeconomics, Springer, vol. 8(2), pages 121-132, August.
    • Handle: RePEc:kap:jbioec:v:8:y:2006:i:2:p:121-132
    DOI: 10.1007/s10818-006-0005-8
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    1. Thomas Eichner & Rüdiger Pethig, 2003. "The impact of scarcity and abundance in food chains on species population dynamics," Volkswirtschaftliche Diskussionsbeiträge 109-03, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
    2. Swanson, Timothy M, 1994. "The Economics of Extinction Revisited and Revised: A Generalised Framework for the Analysis of the Problems of Endangered Species and Biodiversity Losses," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 800-821, Supplemen.
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    1. Waters, Edward K. & Sidhu, Harvinder S. & Sidhu, Leesa A. & Mercer, Geoffry N., 2015. "Extended Lotka–Volterra equations incorporating population heterogeneity: Derivation and analysis of the predator–prey case," Ecological Modelling, Elsevier, vol. 297(C), pages 187-195.
    2. Thomas Eichner & Rüdiger Pethig, 2007. "Harvesting in an integrated general equilibrium model," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(1), pages 233-252, May.
    3. Eric Nævdal, 2008. "Animal rationality and implications for resource management: the case of biological reserves for moose and pine," Journal of Bioeconomics, Springer, vol. 10(2), pages 145-163, August.
    4. Francisco Vázquez & Richard Watt, 2011. "Copyright piracy as prey–predator behavior," Journal of Bioeconomics, Springer, vol. 13(1), pages 31-43, April.
    5. Thomas Christiaans, 2004. "Population Dynamics in a Microfounded Predator-Prey Model," Volkswirtschaftliche Diskussionsbeiträge 118-04, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.

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    More about this item

    Keywords

    predator; prey; ratio-dependence; Q29;
    All these keywords.

    JEL classification:

    • Q29 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Other

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