IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v452y2021ics030438002100154x.html
   My bibliography  Save this article

An abstract mathematical model for sustainable harvesting of a biological species on the boundary of a protected habitat

Author

Listed:
  • Searle, K.D.
  • van Vuuren, J.H.

Abstract

The objective in this paper is to determine analytically the maximally sustainable pro-rata density-dependent harvest rate of a hypothetical biological species on the spatial boundary of its habitat, which is otherwise a protected zone (i.e. no harvesting of the species is allowed in the interior of its habitat). This is achieved by analysing an abstract mathematical model for the spatio-temporal evolution of the species density over its habitat if it is subjected to a continuum of potential pro-rata density-dependent harvest rates on the spatial boundary. The model takes the form of an initial-boundary value problem involving a reaction-diffusion equation in which the reaction term is a concave function of the population density and Robin boundary conditions are prescribed. A long-time asymptotic analysis of the population density is undertaken by invoking classical results from the theory of eigenproblems. In this way, necessary and sufficient conditions on the pro-rata density-dependent harvest rate are established for the existence of a strictly positive equilibrium attractor of model solutions. Moreover, important necessary properties of this equilibrium attractor are established to guarantee the existence of a density pro-rata harvest rate which maximises the total harvest per unit time at equilibrium.

Suggested Citation

  • Searle, K.D. & van Vuuren, J.H., 2021. "An abstract mathematical model for sustainable harvesting of a biological species on the boundary of a protected habitat," Ecological Modelling, Elsevier, vol. 452(C).
    • Handle: RePEc:eee:ecomod:v:452:y:2021:i:c:s030438002100154x
    DOI: 10.1016/j.ecolmodel.2021.109591
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030438002100154X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2021.109591?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. Brown, Katrina & Adger, W. Neil & Tompkins, Emma & Bacon, Peter & Shim, David & Young, Kathy, 2001. "Trade-off analysis for marine protected area management," Ecological Economics, Elsevier, vol. 37(3), pages 417-434, June.
    2. Emamizadeh, Behrouz & Farjudian, Amin & Liu, Yichen, 2018. "Optimal harvesting strategy based on rearrangements of functions," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 677-690.
    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. K. D. Searle & J. H. Vuuren, 2022. "A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-19, December.
    2. Li, Shangge & Jian, Jinfeng & Poopal, Rama Krishnan & Chen, Xinyu & He, Yaqi & Xu, Hongbin & Yu, Huimin & Ren, Zongming, 2022. "Mathematical modeling in behavior responses: The tendency-prediction based on a persistence model on real-time data," Ecological Modelling, Elsevier, vol. 464(C).

    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. K. D. Searle & J. H. Vuuren, 2022. "A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-19, December.
    2. Amrullah Rosadi & Paul Dargusch & Taryono Taryono, 2022. "Understanding How Marine Protected Areas Influence Local Prosperity—A Case Study of Gili Matra, Indonesia," IJERPH, MDPI, vol. 19(20), pages 1-19, October.
    3. Heinze, Alan & Bongers, Frans & Ramírez Marcial, Neptalí & García Barrios, Luis E. & Kuyper, Thomas W., 2022. "Farm diversity and fine scales matter in the assessment of ecosystem services and land use scenarios," Agricultural Systems, Elsevier, vol. 196(C).
    4. Ester Comas Argemí & Àngela D. Bosch Serra & Mamen Cuéllar Padilla & Gonzalo Gamboa Jiménez, 2012. "Sostenibilidad de la producción porcina en Cataluña (España). Aplicación del análisis multicriterio," Revista Iberoamericana de Economía Ecológica, Red Iberoamericana de Economía Ecológica, vol. 18, pages 1-19, Abril.
    5. Grafeld, Shanna & Oleson, Kirsten & Barnes, Michele & Peng, Marcus & Chan, Catherine & Weijerman, Mariska, 2016. "Divers' willingness to pay for improved coral reef conditions in Guam: An untapped source of funding for management and conservation?," Ecological Economics, Elsevier, vol. 128(C), pages 202-213.
    6. Hojatollah Khedrigharibvand & Hossein Azadi & Dereje Teklemariam & Ehsan Houshyar & Philippe Maeyer & Frank Witlox, 2019. "Livelihood alternatives model for sustainable rangeland management: a review of multi-criteria decision-making techniques," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 21(1), pages 11-36, February.
    7. Hooper, Tara & Austen, Melanie, 2013. "Tidal barrages in the UK: Ecological and social impacts, potential mitigation, and tools to support barrage planning," Renewable and Sustainable Energy Reviews, Elsevier, vol. 23(C), pages 289-298.
    8. Lucrezi, Serena & Milanese, Martina & Markantonatou, Vasiliki & Cerrano, Carlo & Sarà, Antonio & Palma, Marco & Saayman, Melville, 2017. "Scuba diving tourism systems and sustainability: Perceptions by the scuba diving industry in two Marine Protected Areas," Tourism Management, Elsevier, vol. 59(C), pages 385-403.
    9. Hajkowicz, Stefan, 2007. "Allocating scarce financial resources across regions for environmental management in Queensland, Australia," Ecological Economics, Elsevier, vol. 61(2-3), pages 208-216, March.
    10. Upham, Paul & Shackley, Simon & Waterman, Holly, 2007. "Public and stakeholder perceptions of 2030 bioenergy scenarios for the Yorkshire and Humber region," Energy Policy, Elsevier, vol. 35(9), pages 4403-4412, September.
    11. Stefan Hajkowicz & Kerry Collins, 2007. "A Review of Multiple Criteria Analysis for Water Resource Planning and Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(9), pages 1553-1566, September.
    12. Tammi, Ilpo & Kalliola, Risto, 2014. "Spatial MCDA in marine planning: Experiences from the Mediterranean and Baltic Seas," Marine Policy, Elsevier, vol. 48(C), pages 73-83.
    13. Grippo, Valeria & Vastola, Antonella, 2018. "Evaluation Of Bran Use Through Multi Criteria Analysis," 2018 Seventh AIEAA Conference, June 14-15, Conegliano, Italy 275646, Italian Association of Agricultural and Applied Economics (AIEAA).
    14. Foa, Roberto, 2009. "Social and governance dimensions of climate change : implications for policy," Policy Research Working Paper Series 4939, The World Bank.
    15. Hung, Ming-Lung & Yang, Wan-Fa & Ma, Hwong-Wen & Yang, Ya-Mei, 2006. "A novel multiobjective programming approach dealing with qualitative and quantitative objectives for environmental management," Ecological Economics, Elsevier, vol. 56(4), pages 584-593, April.
    16. Estévez, Rodrigo A. & Gelcich, Stefan, 2015. "Participative multi-criteria decision analysis in marine management and conservation: Research progress and the challenge of integrating value judgments and uncertainty," Marine Policy, Elsevier, vol. 61(C), pages 1-7.
    17. Kenyon, Wendy, 2007. "Evaluating flood risk management options in Scotland: A participant-led multi-criteria approach," Ecological Economics, Elsevier, vol. 64(1), pages 70-81, October.
    18. George Panagopoulos & George Bathrellos & Hariklia Skilodimou & Faini Martsouka, 2012. "Mapping Urban Water Demands Using Multi-Criteria Analysis and GIS," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(5), pages 1347-1363, March.
    19. Farid Dahdouh-Guebas, 2002. "The Use of Remote Sensing and GIS in the Sustainable Management of Tropical Coastal Ecosystems," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 4(2), pages 93-112, June.
    20. De La Fuente, G. & Asnaghi, V. & Chiantore, M. & Thrush, S. & Povero, P. & Vassallo, P. & Petrillo, M. & Paoli, C., 2019. "The effect of Cystoseira canopy on the value of midlittoral habitats in NW Mediterranean, an emergy assessment," Ecological Modelling, Elsevier, vol. 404(C), pages 1-11.

    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:ecomod:v:452:y:2021:i:c:s030438002100154x. 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: http://www.journals.elsevier.com/ecological-modelling .

    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.