IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v380y2020ics0096300320302058.html
   My bibliography  Save this article

Collapse and recovery times in non-linear harvesting with demographic stochasticity

Author

Listed:
  • Cuenda, Sara
  • Llorente, Marta
  • Capitán, José A.

Abstract

Recent collapses of many fisheries across the globe have challenged the mathematical approach to these systems through classic bioeconomic models. Decimated populations did not recover as fast as predicted by these models and depensatory effects were introduced to better fit the dynamics at low population abundances. Alternative to depensation, modeling captures by non-linear harvesting functions produces equivalent outcomes at small abundances, and the dynamics undergoes a bifurcation leading to population collapse and recovery once catching efforts are above or below certain thresholds, respectively. The time that a population takes to undergo these transitions has been mostly overlooked in bioeconomic contexts, though. In this work we quantify analytically and numerically the times associated to these collapse and recovery transitions in a model incorporating non-linear harvesting and immigration in the presence and absence of demographic stochasticity. Counterintuitively, although species at low abundances are prone to extinction due to demographic stochasticity, our results show that stochastic collapse and recovery times are upper bounded by their deterministic estimates. This occurs over the full range of immigration rates. Our work may have relevant quantitative implications in the context of fishery management and rebuilding.

Suggested Citation

  • Cuenda, Sara & Llorente, Marta & Capitán, José A., 2020. "Collapse and recovery times in non-linear harvesting with demographic stochasticity," Applied Mathematics and Computation, Elsevier, vol. 380(C).
  • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302058
    DOI: 10.1016/j.amc.2020.125236
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320302058
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2020.125236?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. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    2. Maroto, Jose M. & Moran, Manuel, 2014. "Detecting the presence of depensation in collapsed fisheries: The case of the Northern cod stock," Ecological Economics, Elsevier, vol. 97(C), pages 101-109.
    3. Ransom A. Myers & Boris Worm, 2003. "Rapid worldwide depletion of predatory fish communities," Nature, Nature, vol. 423(6937), pages 280-283, May.
    4. Ragnar Arnason & Leif K. Sandal & Stein Ivar Steinshamn & Niels Vestergaard, 2004. "Optimal Feedback Controls: Comparative Evaluation of the Cod Fisheries in Denmark, Iceland, and Norway," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 531-542.
    5. Gordon R. Munro, 1982. "Fisheries, Extended Jurisdiction and the Economics of Common Property Resources," Canadian Journal of Economics, Canadian Economics Association, vol. 15(3), pages 405-425, August.
    6. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
    Full references (including those not matched with items on IDEAS)

    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. Manuel Pacheco Coelho, 2011. "Hunting Rights and Conservation: The Portuguese Case," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 1(4), pages 164-164.
    2. Julio Peña, 1996. "Regulación Pesquera en Chile: Una Perspectiva Histórica," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 33(100), pages 367-395.
    3. Yi Zhang & Yao Xu & Hao Kong & Gang Zhou, 2022. "Spatial-Temporal Evolution of Coupling Coordination between Green Transformation and the Quality of Economic Development," Sustainability, MDPI, vol. 14(23), pages 1-15, December.
    4. Sethi, Gautam & Costello, Christopher & Fisher, Anthony & Hanemann, Michael & Karp, Larry, 2005. "Fishery management under multiple uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 50(2), pages 300-318, September.
    5. Manning, Dale T. & Uchida, Hirotsugu, 2014. "Are Two Rents Better than None? When Monopoly Harvester Co-ops are Preferred to a Rent Dissipated Resource Sector," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 171628, Agricultural and Applied Economics Association.
    6. Poudel, Diwakar & Sandal, Leif K. & Steinshamn, Stein I. & Kvamsdal, Sturla F., 2012. "Do Species Interactions and Stochasticity Matter to Optimal Management of Multispecies Fisheries?," Discussion Papers 2012/1, Norwegian School of Economics, Department of Business and Management Science.
    7. Yamazaki, Satoshi & Jennings, Sarah & Quentin Grafton, R. & Kompas, Tom, 2015. "Are marine reserves and harvest control rules substitutes or complements for rebuilding fisheries?," Resource and Energy Economics, Elsevier, vol. 40(C), pages 1-18.
    8. Andrés Cisneros-Montemayor & U. Sumaila, 2010. "A global estimate of benefits from ecosystem-based marine recreation: potential impacts and implications for management," Journal of Bioeconomics, Springer, vol. 12(3), pages 245-268, October.
    9. Eisenack, K. & Welsch, H. & Kropp, J.P., 2006. "A qualitative dynamical modelling approach to capital accumulation in unregulated fisheries," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2613-2636, December.
    10. David A Carozza & Daniele Bianchi & Eric D Galbraith, 2017. "Formulation, General Features and Global Calibration of a Bioenergetically-Constrained Fishery Model," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-28, January.
    11. Manuel Pacheco Coelho & José António Filipe, 2021. "Searching for a New Model of Governance in the High Seas: Game Theory Applied to International Commons Management," Mathematics, MDPI, vol. 9(19), pages 1-28, October.
    12. Manuel Francisco Pacheco Coelho, 2009. "Roman Legal Tradition and the Mismanagement of Hunting Resources," Working Papers Department of Economics 2009/29, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    13. Mundt, Matthias, 2012. "The effects of EU fisheries partnership agreements on fish stocks and fishermen: The case of Cape Verde," IPE Working Papers 12/2012, Berlin School of Economics and Law, Institute for International Political Economy (IPE).
    14. Libecap, Gary D., 2007. "The Assignment of Property Rights on the Western Frontier: Lessons for Contemporary Environmental and Resource Policy," The Journal of Economic History, Cambridge University Press, vol. 67(2), pages 257-291, June.
    15. Edwards, Steven F. & Link, Jason S. & Rountree, Barbara P., 2004. "Portfolio management of wild fish stocks," Ecological Economics, Elsevier, vol. 49(3), pages 317-329, July.
    16. Costello, Christopher & Polasky, Stephen, 2008. "Optimal harvesting of stochastic spatial resources," Journal of Environmental Economics and Management, Elsevier, vol. 56(1), pages 1-18, July.
    17. Wilen, Christopher D. & Wilen, James E., 2012. "Fishing down the food chain revisited: Modeling exploited trophic systems," Ecological Economics, Elsevier, vol. 79(C), pages 80-88.
    18. Ragnar Arnason, 2011. "Loss of economic rents in the global fishery," Journal of Bioeconomics, Springer, vol. 13(3), pages 213-232, October.
    19. Michael Finus & Raoul Schneider & Pedro Pintassilgo, 2019. "The Role of Social and Technical Excludability for the Success of Impure Public Good and Common Pool Agreements: The Case of International Fisheries," Graz Economics Papers 2019-12, University of Graz, Department of Economics.
    20. Gary D. Libecap, 2018. "Douglass C. North: Transaction Costs, Property Rights, and Economic Outcomes," NBER Working Papers 24585, National Bureau of Economic Research, Inc.

    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:apmaco:v:380:y:2020:i:c:s0096300320302058. 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/applied-mathematics-and-computation .

    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.