IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v83y2013icp123-135.html
   My bibliography  Save this article

Optimal policies aimed at stabilization of populations with logistic growth under human intervention

Author

Listed:
  • Cruz-Rivera, Erica
  • Vasilieva, Olga

Abstract

This work examines both positive and negative impacts that economic growth may have on the ecological dynamics and stability of a single biological species. Local extinction of the species may force the social planner to implement defensive expenditures aimed at conservation of the species population by means of habitat protection. The latter may lead to an ecological equilibrium that will be different from the natural equilibrium that would have arisen in the absence of human intervention. Moreover, the existence of such equilibrium is formally demonstrated and its stability properties are revised. Additionally, optimal-choice decision policies are constructed on the basis of Pontryagin’s maximum principle. Under such policies together with initial abundance of the species, the growth trajectories will move the system towards the fixed point of maximum species abundance.

Suggested Citation

  • Cruz-Rivera, Erica & Vasilieva, Olga, 2013. "Optimal policies aimed at stabilization of populations with logistic growth under human intervention," Theoretical Population Biology, Elsevier, vol. 83(C), pages 123-135.
    • Handle: RePEc:eee:thpobi:v:83:y:2013:i:c:p:123-135
    DOI: 10.1016/j.tpb.2012.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580912000822
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2012.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    2. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, December.
    3. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    4. Seierstad, Atle & Sydsaeter, Knut, 1977. "Sufficient Conditions in Optimal Control Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 367-391, June.
    5. Viscusi, W Kip & Evans, William N, 1990. "Utility Functions That Depend on Health Status: Estimates and Economic Implications," American Economic Review, American Economic Association, vol. 80(3), pages 353-374, June.
    6. Kraus, Alan & Litzenberger, Robert H, 1975. "Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility," Journal of Finance, American Finance Association, vol. 30(5), pages 1213-1227, December.
    7. Alexander, Robert R., 2000. "Modelling species extinction: the case for non-consumptive values," Ecological Economics, Elsevier, vol. 35(2), pages 259-269, November.
    8. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. Timothy M. Swanson, 1994. "The Economics of Extinction Revisited and Revised," Palgrave Macmillan Books, in: The International Regulation of Extinction, chapter 3, pages 45-76, Palgrave Macmillan.
    11. Li, Chuan-Zhong & Lã–Fgren, Karl-Gustaf, 1998. "A dynamic model of biodiversity preservation," Environment and Development Economics, Cambridge University Press, vol. 3(2), pages 157-172, May.
    12. Armsworth, Paul R. & Kendall, Bruce E. & Davis, Frank W., 2004. "An introduction to biodiversity concepts for environmental economists," Resource and Energy Economics, Elsevier, vol. 26(2), pages 115-136, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cruz-Rivera, Erica & Vasilieva, Olga & Svinin, Mikhail, 2013. "Optimal short-term policies for protection of single biological species from local extinction," Ecological Modelling, Elsevier, vol. 263(C), pages 273-280.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bertram, Christine, 2010. "Integrating biodiversity indices into a multi-species optimal control model," Kiel Working Papers 1662, Kiel Institute for the World Economy (IfW Kiel).
    2. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    3. Alexander, Robert R. & Shields, David W., 2002. "Using Land As A Control Variable In Density-Dependent Bioeconomic Models," Discussion Papers in Natural Resource and Environmental Economics 23694, Massey University, Centre for Applied Economics and Policy Studies.
    4. 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.
    5. Fleming, Christopher M. & Alexander, Robert R., 2002. "The Economic Implications of a Multiple Species Approach to Bioeconomic Modelling," 2002 Conference (46th), February 13-15, 2002, Canberra, Australia 125082, Australian Agricultural and Resource Economics Society.
    6. Marggraf, R., 2001. "Wie effizient ist die Integration von naturschutzbezogenen Handelsbeschränkungen in die Regeln der WTO?," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 37.
    7. van den Bergh, Jeroen C.J.M., 2008. "Optimal diversity: Increasing returns versus recombinant innovation," Journal of Economic Behavior & Organization, Elsevier, vol. 68(3-4), pages 565-580, December.
    8. Barbier, Edward B. & Bulte, Erwin H., 2004. "Introduction to the symposium on trade, renewable resources and biodiversity," Journal of Environmental Economics and Management, Elsevier, vol. 48(2), pages 883-890, September.
    9. Leroux, Anke D. & Creedy, John, 2007. "Optimal land conversion and growth with uncertain biodiversity costs," Ecological Economics, Elsevier, vol. 61(2-3), pages 542-549, March.
    10. Erwin Bulte & Edward Barbier, 2005. "Trade and Renewable Resources in a Second Best World: An Overview," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 30(4), pages 423-463, April.
    11. Alexander, Robert R. & Shields, David W., 1999. "Bioeconomic Modelling Of Endangered Species Conservation," Discussion Papers in Natural Resource and Environmental Economics 23692, Massey University, Centre for Applied Economics and Policy Studies.
    12. Messer, Kent D., 2010. "Protecting endangered species: When are shoot-on-sight policies the only viable option to stop poaching?," Ecological Economics, Elsevier, vol. 69(12), pages 2334-2340, October.
    13. Kassar, Ilhem & Lasserre, Pierre, 2004. "Species preservation and biodiversity value: a real options approach," Journal of Environmental Economics and Management, Elsevier, vol. 48(2), pages 857-879, September.
    14. Naoto Jinji, 2006. "International trade and terrestrial open-access renewable resources in a small open economy," Canadian Journal of Economics, Canadian Economics Association, vol. 39(3), pages 790-808, August.
    15. Erwin H. Bulte & Charles F. Mason & Richard D. Horan, 2003. "Betting on Extinction: Endangered Species and Speculation," Land Economics, University of Wisconsin Press, vol. 79(4), pages 460-471.
    16. Astrid Zabel & Karen Pittel & Göran Bostedt & Stefanie Engel, 2011. "Comparing Conventional and New Policy Approaches for Carnivore Conservation: Theoretical Results and Application to Tiger Conservation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(2), pages 287-301, February.
    17. Productivity Commission, 2002. "Harnessing private sector conservation of biodiversity," Others 0201004, University Library of Munich, Germany.
    18. Willem H. Buiter, 2003. "James Tobin: An Appreciation of his Contribution to Economics," Economic Journal, Royal Economic Society, vol. 113(491), pages 585-631, November.
    19. Bulte, Erwin H. & Horan, Richard D., 2003. "Habitat conservation, wildlife extraction and agricultural expansion," Journal of Environmental Economics and Management, Elsevier, vol. 45(1), pages 109-127, January.
    20. Birgit Bednar-Friedl & Edwin Muchapondwa & Precious Zikhali & Samson Mukanjari, 2012. "Evaluating the Prospects of Benefit Sharing Schemes in Protecting Mountain Gorillas in Central Africa," Working Papers 321, Economic Research Southern Africa.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:83:y:2013:i:c:p:123-135. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.