On the impossibility of increasing the MSY in a multisite Schaefer fishing model

Pierre Auger; Tri Nguyen-Huu; Doanh Nguyen-Ngoc; Pierre Auger; Tri Nguyen-Huu; Doanh Nguyen-Ngoc

doi:10.3934/mbe.2025016

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 2: 415-430. doi: 10.3934/mbe.2025016

Previous Article Next Article

Research article Special Issues

On the impossibility of increasing the MSY in a multisite Schaefer fishing model

1.
IRD, Sorbonne Université, Unité de Modélisation Mathématique et Informatique des Systèmes Complexes, UMMISCO, F-93143, Bondy, France
2.
IXXI, ENS Lyon, 46 allée d'Italie, Lyon 69007, France
3.
College of Engineering and Computer Science and Center for Environmental Intelligence, VinUniversity, Vietnam

Received: 18 November 2024 Revised: 17 January 2025 Accepted: 23 January 2025 Published: 11 February 2025

Here, we consider a multisite Schaefer fishing model. The fishery resource grows logistically on each site and is exploited with different fishing efforts. We showed that the Maximum Sustainable Yield (MSY) of the multisite network, when the sites are connected, is always less than or equal to the sum of the MSY of the isolated sites. Equality occurred when the fish population is spatially distributed according to the ideal free distribution (IFD). In this case, the fish had the same access to the resource at each site. We generalized the known result for two sites and the same fishing effort to any number of sites and different fishing efforts. We also discussed how the creation of Marine Protected Areas impacts the fishing efforts. We showed that to minimize the fishing effort to reach the MSY, it is necessary to deploy the entire fishing fleet to the site where the fish is most abundant, the other sites being Marine Protected Areas.

Keywords:

Citation: Pierre Auger, Tri Nguyen-Huu, Doanh Nguyen-Ngoc. On the impossibility of increasing the MSY in a multisite Schaefer fishing model[J]. Mathematical Biosciences and Engineering, 2025, 22(2): 415-430. doi: 10.3934/mbe.2025016

Related Papers:

[1]	Thomas Torku, Abdul Khaliq, Fathalla Rihan . SEINN: A deep learning algorithm for the stochastic epidemic model. Mathematical Biosciences and Engineering, 2023, 20(9): 16330-16361. doi: 10.3934/mbe.2023729
[2]	Giorgos Minas, David A Rand . Parameter sensitivity analysis for biochemical reaction networks. Mathematical Biosciences and Engineering, 2019, 16(5): 3965-3987. doi: 10.3934/mbe.2019196
[3]	Tianfang Hou, Guijie Lan, Sanling Yuan, Tonghua Zhang . Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate. Mathematical Biosciences and Engineering, 2022, 19(4): 4217-4236. doi: 10.3934/mbe.2022195
[4]	Linda J. S. Allen, P. van den Driessche . Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences and Engineering, 2006, 3(3): 445-458. doi: 10.3934/mbe.2006.3.445
[5]	Sheng-I Chen, Chia-Yuan Wu . A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions. Mathematical Biosciences and Engineering, 2020, 17(4): 2984-2997. doi: 10.3934/mbe.2020169
[6]	Shengnan Zhao, Sanling Yuan . A coral reef benthic system with grazing intensity and immigrated macroalgae in deterministic and stochastic environments. Mathematical Biosciences and Engineering, 2022, 19(4): 3449-3471. doi: 10.3934/mbe.2022159
[7]	David F. Anderson, Tung D. Nguyen . Results on stochastic reaction networks with non-mass action kinetics. Mathematical Biosciences and Engineering, 2019, 16(4): 2118-2140. doi: 10.3934/mbe.2019103
[8]	Yangjun Ma, Maoxing Liu, Qiang Hou, Jinqing Zhao . Modelling seasonal HFMD with the recessive infection in Shandong, China. Mathematical Biosciences and Engineering, 2013, 10(4): 1159-1171. doi: 10.3934/mbe.2013.10.1159
[9]	Damilola Olabode, Jordan Culp, Allison Fisher, Angela Tower, Dylan Hull-Nye, Xueying Wang . Deterministic and stochastic models for the epidemic dynamics of COVID-19 in Wuhan, China. Mathematical Biosciences and Engineering, 2021, 18(1): 950-967. doi: 10.3934/mbe.2021050
[10]	Hermann Mena, Lena-Maria Pfurtscheller, Jhoana P. Romero-Leiton . Random perturbations in a mathematical model of bacterial resistance: Analysis and optimal control. Mathematical Biosciences and Engineering, 2020, 17(5): 4477-4499. doi: 10.3934/mbe.2020247

Abstract

References

[1]	H. I. Freedman, P. Waltman, Mathematical models of population interactions with dispersal. Ⅰ. Stability of two habitats with and without a predator, SIAM J. Appl. Math., 32 (1977), 631–648. https://doi.org/10.1137/0132052 doi: 10.1137/0132052
[2]	R. T. Holt, Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution, Theor. Popul. Biol., 28 (1985), 181–208. https://doi.org/10.1016/0040-5809(85)90027-9 doi: 10.1016/0040-5809(85)90027-9
[3]	J. C Poggiale, P. Auger, D. Nérini, C. Manté, F. Gilbert, Global production increased by spatial heterogeneity in a population dynamics model, Acta Biotheor., 53 (2005), 359–370.
[4]	R. Arditi, C. Lobry, T. Sari, Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation, Theor. Popul. Biol., 106 (2015), 45–59. https://doi.org/10.1016/j.tpb.2015.10.001 doi: 10.1016/j.tpb.2015.10.001
[5]	R. Arditi, C. Lobry, T. Sari, Asymmetric dispersal in the multi-patch logistic equation, Theor. Popul. Biol., 120 (2018), 11–15. https://doi.org/10.1016/j.tpb.2017.12.006 doi: 10.1016/j.tpb.2017.12.006
[6]	B. Elbetch, T. Benzekri, D. Massart, T. Sari, The multi-patch logistic equation, Discrete Contin. Dyn. Syst. Ser. B, 25 (2021), 1–20. https://doi.org/10.3934/dcdsb.2021025 doi: 10.3934/dcdsb.2021025
[7]	D. L. DeAngelis, B. Zhang, Effects of dispersal in a non-uniform environment on population dynamics and competition: a patch model approach, Discrete Contin. Dyn. Syst. Ser. B., 19 (2014), 3087–3104. https://doi.org/10.3934/dcdsb.2014.19.3087 doi: 10.3934/dcdsb.2014.19.3087
[8]	D. L. DeAngelis, W. M. Ni, B. Zhang, Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems, Theor. Ecol., 9 (2016), 443–453.
[9]	B. Zhang, A. Kula, K. M. L. Mack, L. Zhai, A. L. Ryce, W. M. Ni, et al., Carrying capacity in a heterogeneous environment with habitat connectivity, Ecol. Lett., 20 (2017), 1–11. https://doi.org/10.1111/ele.12807 doi: 10.1111/ele.12807
[10]	P. Auger, B. Kooi, A. Moussaoui, Increase of maximum sustainable yield for fishery in two patches with fast migration, Ecol. Model., 467 (2022), 109898. https://doi.org/10.1016/j.ecolmodel.2022.109898 doi: 10.1016/j.ecolmodel.2022.109898
[11]	P. Auger, R. B. de la Parra, J. Poggiale, E. Sánchez, L. Sanz, Aggregation methods in dynamical systems and applications in population and community dynamics, Phys. Life Rev., 5 (2008), 75–105. https://doi.org/10.1016/j.plrev.2008.02.001 doi: 10.1016/j.plrev.2008.02.001
[12]	P. Auger, R. B. de la Parra, J. C. Poggiale, E. Sánchez, T. Nguyen-Huu, Aggregation of variables and applications to population dynamics, Structured Population Models in Biology and Epidemiology, Berlin, Heidelberg: Springer Berlin Heidelberg, 1936 (2008), 209–263.
[13]	M. B. Schaefer, Some considerations of population dynamics and economics in relation to the management of the commercial marine fisheries, J. Fish. Res. Board Can., 14 (1957), 669–681.
[14]	D. Nguyen-Ngoc, T. Nguyen-Huu, P. Auger, Connectivity between two fishing sites can lead to an emergence phenomenon related to Maximum Sustainable Yield, J. Theor. Biol., 595 (2024), 111913. https://doi.org/10.1016/j.jtbi.2024.111913 doi: 10.1016/j.jtbi.2024.111913
[15]	C. Chu, W. Liu, G. Lv, A. Moussaoui, P. Auger, Optimal harvest for predator-prey fishery models with variable price and marine protected area, Commun. Nonlinear Sci. Numer. Simul., 134 (2024), 107992. https://doi.org/10.1016/j.cnsns.2024.107992 doi: 10.1016/j.cnsns.2024.107992
[16]	A. Ghouali, A.Moussaoui, P. Auger, T. Nguyen-Huu, Optimal placement of marine protected areas to avoid the extinction of the fish stock, J. Biol. Syst., 30 (2022), 323–337. https://doi.org/10.1142/S0218339022500115 doi: 10.1142/S0218339022500115
[17]	A. Moussaoui, P. Auger, C. Lett, Optimal number of sites in multi-site fisheries with fish stock dependent migrations, Math. Biosci. Eng., 8 (2011), 769–783. https://doi.org/10.3934/mbe.2011.8.769 doi: 10.3934/mbe.2011.8.769
[18]	P. Auger, C. Lett, A. Moussaoui, S. Pioch, Optimal number of sites in artificial pelagic multisite fisheries, Can. J. Fish. Aquat. Sci., 67 (2010), 296–303. https://doi.org/10.1139/F09-188 doi: 10.1139/F09-188
[19]	R. B. de la Parra, J. C. Poggiale, P. Auger, The effect of connecting sites in the environment of a harvested population, Math. Model. Nat. Phenom., 18 (2023). https://doi.org/10.1051/mmnp/2023004 doi: 10.1051/mmnp/2023004

This article has been cited by:

1.	Amy D. Hagerman, Bruce A. McCarl, Jianhong Mu, 2010, 9780471761303, 10.1002/9780470087923.hhs696
2.	Jose Faro, Bernardo von Haeften, Rui Gardner, Emilio Faro, A Sensitivity Analysis Comparison of Three Models for the Dynamics of Germinal Centers, 2019, 10, 1664-3224, 10.3389/fimmu.2019.02038
3.	S. Pant, B. Fabrèges, J-F. Gerbeau, I. E. Vignon-Clementel, A methodological paradigm for patient-specific multi-scale CFD simulations: from clinical measurements to parameter estimates for individual analysis, 2014, 30, 20407939, 1614, 10.1002/cnm.2692
4.	H. T. Banks, Sava Dediu, Stacey L. Ernstberger, Franz Kappel, Generalized sensitivities and optimal experimental design, 2010, 18, 0928-0219, 10.1515/jiip.2010.002
5.	H.T. Banks, Kathleen Holm, Nathan C. Wanner, Ariel Cintrón-Arias, Grace M. Kepler, Jeffrey D. Wetherington, A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system, 2009, 50, 08957177, 959, 10.1016/j.mcm.2009.02.007
6.	H. T. Banks, S. Dediu, S. L. Ernstberger, Sensitivity functions and their uses in inverse problems, 2007, 15, 0928-0219, 10.1515/jiip.2007.038
7.	H.T. Banks, Jared Catenacci, Shuhua Hu, Stochastic vs. Deterministic Models for Systems with Delays, 2013, 46, 14746670, 61, 10.3182/20130925-3-FR-4043.00022
8.	H. Thomas Banks, Marie Davidian, John R. Samuels, Karyn L. Sutton, 2009, Chapter 11, 978-90-481-2312-4, 249, 10.1007/978-90-481-2313-1_11
9.	Chloe Audebert, Petru Bucur, Mohamed Bekheit, Eric Vibert, Irene E. Vignon-Clementel, Jean-Frédéric Gerbeau, Kinetic scheme for arterial and venous blood flow, and application to partial hepatectomy modeling, 2017, 314, 00457825, 102, 10.1016/j.cma.2016.07.009
10.	Sanjay Pant, Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems, 2018, 15, 1742-5689, 20170871, 10.1098/rsif.2017.0871
11.	Chloe Audebert, Irene E. Vignon-Clementel, Model and methods to assess hepatic function from indocyanine green fluorescence dynamical measurements of liver tissue, 2018, 115, 09280987, 304, 10.1016/j.ejps.2018.01.008
12.	A comparison of computational efficiencies of stochastic algorithms in terms of two infection models, 2012, 9, 1551-0018, 487, 10.3934/mbe.2012.9.487
13.	H. T. Banks, M. Davidian, Shuhua Hu, Grace M. Kepler, E. S. Rosenberg, Modelling HIV immune response and validation with clinical data, 2008, 2, 1751-3758, 357, 10.1080/17513750701813184
14.	Tejas Ghadiyali, Kalpesh Lad, Jayesh Dhodiya, 2018, Chapter 6, 978-981-10-6601-6, 51, 10.1007/978-981-10-6602-3_6
15.	Multiple endemic states in age-structured $SIR$ epidemic models, 2012, 9, 1551-0018, 577, 10.3934/mbe.2012.9.577
16.	H. T. Banks, Jared Catenacci, Shuhua Hu, A Comparison of Stochastic Systems with Different Types of Delays, 2013, 31, 0736-2994, 913, 10.1080/07362994.2013.806217
17.	Nonlinear stochastic Markov processes and modeling uncertainty in populations, 2012, 9, 1551-0018, 1, 10.3934/mbe.2012.9.1
18.	Mohammad Munir, Generalized sensitivity analysis of the minimal model of the intravenous glucose tolerance test, 2018, 300, 00255564, 14, 10.1016/j.mbs.2018.03.014
19.	Angelie Reandelar Ferrolino, Victoria May Paguio Mendoza, 2019, 2192, 0094-243X, 060008, 10.1063/1.5139154
20.	D. F. Yusupov, G. Abdullayeva, O. Aliev, S. Hamrayeva, 2021, 2402, 0094-243X, 050002, 10.1063/5.0071987
21.	José Faro, Emilio Faro, 2022, Chapter 10, 978-1-0716-1735-9, 111, 10.1007/978-1-0716-1736-6_10

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)