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

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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.
- multi-site fishery,
- maximum sustainable yield,
- ideal free distribution,
- fish habitat connectivity,
- marine protected area,
- aggregation of variables
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

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Abstract

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.

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