IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p555-d746790.html
   My bibliography  Save this article

Coupling of Bio-Reactors to Increase Maximum Sustainable Yield

Author

Listed:
  • Pierre Auger

    (Institut de Recherche Pour Développement (IRD), UMMISCO, Sorbonne Université, F-93143 Bondy, France)

  • Ali Moussaoui

    (Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Department of Mathematics, Faculty of Science, University of Abou Bekr Belkaïd, Tlemcen 13000, Algeria)

Abstract

In the field of fisheries management, the objective is to obtain an optimal catch while maintaining the fishery resource at a sufficiently high level to avoid the extinction of the exploited species. In mathematical fishery models, the fishing effort that must be implemented to have a sustainable fishery with a maximum harvest rate in the long term is sought. This goal is called the “Maximum Sustainable Yield” (MSY). In the chemostat, the substrate can be seen as prey of which the predator is the product. MSY search is thus extended to the classical chemostat model with a Monod function. There exists a dilution rate that maximizes the product synthesis. The study is extended to the case of the gradostat with fast substrate and product exchanges between two coupled bioreactors. The existence of two time scales makes it possible to apply methods of aggregation of variables to derive a reduced model governing a few global variables describing the dynamics of the complete system at the slow time scale. The analysis of the mathematical aggregated model is performed. Existence of equilibria as well as local and global stability are studied. The overall product yield in the system of coupled bioreactors may be greater than the sum of the yields of the two uncoupled bioreactors, i.e., if they functioned without connection between them. The increase in product yield is all the more important as the distribution of the substrate and of the product is asymmetrical between the two coupled bioreactors. The model is applied to fish farming by considering the coupling of two breeding sites. Here again, the model makes it possible to find the fast fish exchanges that must be established between the two breeding basins to optimize the overall yield of the farm.

Suggested Citation

  • Pierre Auger & Ali Moussaoui, 2022. "Coupling of Bio-Reactors to Increase Maximum Sustainable Yield," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:555-:d:746790
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/555/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/4/555/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Legović, Tarzan & Geček, Sunčana, 2012. "Impact of maximum sustainable yield on mutualistic communities," Ecological Modelling, Elsevier, vol. 230(C), pages 63-72.
    2. Kar, T.K. & Ghosh, Bapan, 2013. "Impacts of maximum sustainable yield policy to prey–predator systems," Ecological Modelling, Elsevier, vol. 250(C), pages 134-142.
    3. Legović, Tarzan & Geček, Sunčana, 2010. "Impact of maximum sustainable yield on independent populations," Ecological Modelling, Elsevier, vol. 221(17), pages 2108-2111.
    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. Auger, Pierre & Kooi, Bob & Moussaoui, Ali, 2022. "Increase of maximum sustainable yield for fishery in two patches with fast migration," Ecological Modelling, Elsevier, vol. 467(C).
    2. Woodall, Hannah & Bullock, James M. & White, Steven M., 2014. "Modelling the harvest of an insect pathogen," Ecological Modelling, Elsevier, vol. 287(C), pages 16-26.
    3. Ghosh, Bapan & Kar, T.K., 2014. "Sustainable use of prey species in a prey–predator system: Jointly determined ecological thresholds and economic trade-offs," Ecological Modelling, Elsevier, vol. 272(C), pages 49-58.
    4. Móréh, Ágnes & Endrédi, Anett & Piross, Sándor Imre & Jordán, Ferenc, 2021. "Topology of additive pairwise effects in food webs," Ecological Modelling, Elsevier, vol. 440(C).
    5. Das, Debabrata & Kar, T.K. & Pal, Debprasad, 2023. "The impact of invasive species on some ecological services in a harvested predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 66-90.
    6. Kar, T.K. & Ghosh, Bapan, 2013. "Impacts of maximum sustainable yield policy to prey–predator systems," Ecological Modelling, Elsevier, vol. 250(C), pages 134-142.
    7. Violaine Tarizzo & Eric Tromeur & Olivier Thébaud & Richard Little & Sarah Jennings & Luc Doyen, 2018. "Risk averse policies foster bio-economic sustainability in mixed fisheries," Cahiers du GREThA (2007-2019) 2018-07, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    8. Tromeur, Eric & Doyen, Luc & Tarizzo, Violaine & Little, L. Richard & Jennings, Sarah & Thébaud, Olivier, 2021. "Risk averse policies foster bio-economic sustainability in mixed fisheries," Ecological Economics, Elsevier, vol. 190(C).
    9. Paul, Prosenjit & Kar, T.K., 2016. "Impacts of invasive species on the sustainable use of native exploited species," Ecological Modelling, Elsevier, vol. 340(C), pages 106-115.
    10. Legović, Tarzan & Geček, Sunčana, 2012. "Impact of maximum sustainable yield on mutualistic communities," Ecological Modelling, Elsevier, vol. 230(C), pages 63-72.
    11. Paul, Prosenjit & Kar, T.K. & Ghorai, Abhijit, 2016. "Ecotourism and fishing in a common ground of two interacting species," Ecological Modelling, Elsevier, vol. 328(C), pages 1-13.
    12. Adrien Lagarde & Abdoul Ahad-Cissé & Sophie Gourguet & Olivier Le Pape & Olivier Thébaud & Nathalie Caill-Milly & Gilles Morandeau & Claire Macher & Luc Doyen, 2017. "How MMEY mitigates bio-economic impacts of climate change on mixed fisheries," Cahiers du GREThA (2007-2019) 2017-22, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    13. Helene Gomes & Luc Doyen & Fabian Blanchard & Adrien Lagarde, 2021. "Viable and ecosystem-based management for tropical small-scale fisheries facing climate change," Bordeaux Economics Working Papers 2021-24, Bordeaux School of Economics (BSE).
    14. Ji, Guilin & Ge, Qing & Xu, Jiabo, 2016. "Dynamic behaviors of a fractional order two-species cooperative systems with harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 51-55.
    15. Aleksandr Abakumov & Yuri Izrailsky, 2022. "Optimal Harvest Problem for Fish Population—Structural Stabilization," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    16. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.
    17. Lagarde, A. & Doyen, L. & Ahad-Cissé, A. & Caill-Milly, N. & Gourguet, S. & Pape, O. Le & Macher, C. & Morandeau, G. & Thébaud, O., 2018. "How Does MMEY Mitigate the Bioeconomic Effects of Climate Change for Mixed Fisheries," Ecological Economics, Elsevier, vol. 154(C), pages 317-332.
    18. Choirul Basir & Asep Kuswandi Supriatna & Sukono & Jumadil Saputra, 2023. "Prey–Predator Mathematics Model for Fisheries Insurance Calculations in the Search of Optimal Strategies for Inland Fisheries Management: A Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-14, August.
    19. Animesh Mahata & Sankar Prasad Mondal & Banamali Roy & Shariful Alam, 2021. "Study of two species prey-predator model in imprecise environment with MSY policy under different harvesting scenario," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(10), pages 14908-14932, October.
    20. Barnes, Belinda & Sidhu, Harvinder, 2013. "The impact of marine closed areas on fishing yield under a variety of management strategies and stock depletion levels," Ecological Modelling, Elsevier, vol. 269(C), pages 113-125.

    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:gam:jmathe:v:10:y:2022:i:4:p:555-:d:746790. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.