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Harvesting and Conversation in a Predator-Prey System

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Author Info
Jeljer Hoekstra (Vrije Universiteit Amsterdam)
Jeroen C.J.M. van den Bergh () (Vrije Universiteit Amsterdam & Autonomous University Barcelona)

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Abstract

Optimal harvesting of prey in a predator-prey ecosystem is studied under the condition that the existence of the predator has value. Predators (birds) and humans (fishers) compete for prey (shellfish). The behavior of the system is studied and conditions for optimal control are deduced. Various optimal harvesting rates are identified for particular ecosystem characteristics, harvesting costs, the discount rate value, and value functions for birds. These optimal harvest rates are constant harvesting, at levels possibly leading to the extinction of birds, or oscillating harvesting, giving rise to oscillating stocks of birds and shellfish. The approach path towards an optimal regime is shown qualitatively and consists of alternating between harvesting maximally and not harvesting at all.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-024/3.

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Date of creation: 26 Feb 2001
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Handle: RePEc:dgr:uvatin:20010024

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Web page: http://www.tinbergen.nl/

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December. [Downloadable!] (restricted)
  2. Tu, Pierre N. V. & Wilman, Elizabeth A., 1992. "A generalized predator- prey model: Uncertainty and management," Journal of Environmental Economics and Management, Elsevier, vol. 23(2), pages 123-138, September. [Downloadable!] (restricted)
  3. Hannesson, Rognvaldur, 1983. "Optimal harvesting of ecologically interdependent fish species," Journal of Environmental Economics and Management, Elsevier, vol. 10(4), pages 329-345, December. [Downloadable!] (restricted)
  4. William A. Brock & Jose Scheinkman, 1975. "The Global Asymptotic Stability of Optimal Control with Applications to Dynamic Economic Theory," Discussion Papers 151, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  5. Wirl Franz, 1995. "The Cyclical Exploitation of Renewable Resource Stocks May Be Optimal," Journal of Environmental Economics and Management, Elsevier, vol. 29(2), pages 252-261, September. [Downloadable!] (restricted)
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