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A Micro-Level 'Consumer Approach' to Species Population Dynamics

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  • Thomas Christiaans
  • Thomas Eichner
  • Rüdiger Pethig

Abstract

In this paper we develop a micro ecosystem model whose basic entities are representative organisms which behave as if maximizing their net offspring under constraints. Net offspring is increasing in prey biomass intake, declining in the loss of own biomass to predators and Allee’s Law applies. The organism’s constraint reflects its perception of how scarce its own biomass and the biomass of its prey is. In the short-run periods prices (scarcity indicators) coordinate and determine all biomass transactions and net offspring which directly translates into population growth functions. We are able to explicitly determine these growth functions for a simple food web when specific parametric net offspring functions are chosen in the micro-level ecosystem model. For the case of a single species our model is shown to yield the well-known Verhulst-Pearl logistic growth function. With two species in predator-prey relationship, we derive differential equations whose dynamics are completely characterized and turn out to be similar to the predator-prey model with Michaelis-Menten type functional response. With two species competing for a single resource we find that coexistence is a knife-edge feature confirming Tschirhart’s (2002) result in a different but related model.

Suggested Citation

  • Thomas Christiaans & Thomas Eichner & Rüdiger Pethig, 2005. "A Micro-Level 'Consumer Approach' to Species Population Dynamics," CESifo Working Paper Series 1530, CESifo.
  • Handle: RePEc:ces:ceswps:_1530
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    References listed on IDEAS

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    1. Eichner, Thomas & Pethig, Rudiger, 2006. "Economic land use, ecosystem services and microfounded species dynamics," Journal of Environmental Economics and Management, Elsevier, vol. 52(3), pages 707-720, November.
    2. John Tschirhart, 2003. "Ecological Transfers in Non-Human Communities Parallel Economic Markets in a General Equilibrium Ecosystem Model," Journal of Bioeconomics, Springer, vol. 5(2), pages 193-214, May.
    3. Thomas Eichner & Rüdiger Pethig, 2003. "A Microfoundation of Predator-Prey Dynamics," Volkswirtschaftliche Diskussionsbeiträge 110-03, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
    4. David Finnoff & John Tschirhart, 2003. "Protecting an Endangered Species While Harvesting Its Prey in a General Equilibrium Ecosystem Model," Land Economics, University of Wisconsin Press, vol. 79(2), pages 160-180.
    5. Thomas Crocker & John Tschirhart, 1992. "Ecosystems, externalities, and economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 2(6), pages 551-567, November.
    6. Finnoff, David & Tschirhart, John, 2003. "Harvesting in an eight-species ecosystem," Journal of Environmental Economics and Management, Elsevier, vol. 45(3), pages 589-611, May.
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    Cited by:

    1. Christiaans, Thomas & Eichner, Thomas & Pethig, Rudiger, 2007. "Optimal pest control in agriculture," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3965-3985, December.
    2. Kai Konrad & Stergios Skaperdas, 2012. "The market for protection and the origin of the state," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 417-443, June.
    3. John Tschirhart, 2012. "Biology as a Source of Non-convexities in Ecological Production Functions," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 51(2), pages 189-213, February.
    4. 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.
    5. Eichner, Thomas & Pethig, Rüdiger, 2009. "Pricing the ecosystem and taxing ecosystem services: A general equilibrium approach," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1589-1616, July.

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    Keywords

    species; growth; extinction; predator-prey relations; resource competition;
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