Acta Biotheoretica

, Volume 62, Issue 3, pp 339–353 | Cite as

Effect of Small Versus Large Clusters of Fish School on the Yield of a Purse-Seine Small Pelagic Fishery Including a Marine Protected Area

  • Nguyen Trong Hieu
  • Timothée Brochier
  • Nguyen-Huu Tri
  • Pierre Auger
  • Patrice Brehmer
Regular Article


We consider a fishery model with two sites: (1) a marine protected area (MPA) where fishing is prohibited and (2) an area where the fish population is harvested. We assume that fish can migrate from MPA to fishing area at a very fast time scale and fish spatial organisation can change from small to large clusters of school at a fast time scale. The growth of the fish population and the catch are assumed to occur at a slow time scale. The complete model is a system of five ordinary differential equations with three time scales. We take advantage of the time scales using aggregation of variables methods to derive a reduced model governing the total fish density and fishing effort at the slow time scale. We analyze this aggregated model and show that under some conditions, there exists an equilibrium corresponding to a sustainable fishery. Our results suggest that in small pelagic fisheries the yield is maximum for a fish population distributed among both small and large clusters of school.


Optimal yield Small pelagic fish Fish school Clusters Marine protected area Aggregation of variables  Three level system 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Nguyen Trong Hieu
    • 1
    • 2
    • 3
  • Timothée Brochier
    • 4
    • 5
  • Nguyen-Huu Tri
    • 1
    • 6
  • Pierre Auger
    • 1
    • 7
  • Patrice Brehmer
    • 4
    • 5
  1. 1.IRD UMI 209 UMMISCOBondy CedexFrance
  2. 2.École doctorale Pierre Louis de santé publiqueUniversité Pierre et Marie CurieParisFrance
  3. 3.Faculty of Mathematics, Informatics and MechanicsVietnam National UniversityHanoiVietnam
  4. 4.IRD UMR195 LemarDakarSenegal
  5. 5.ISRA, CRODTPole de recherche de HannDakarSenegal
  6. 6.IXXIENS LyonFrance
  7. 7.University Cheikh-Anta-DiopDakarSenegal

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