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A Model of a Multi-Site Fishery with Variable Price: fromOver-Exploitation to Sustainable Fisheries

Published online by Cambridge University Press:  28 November 2013

S. Ly ,
F. Mansal ,
M. Baldé ,
T. Nguyen-Huu  and
P. Auger
S. Ly
Affiliation:
Université Cheikh-Anta-Diop, Dakar, Sénégal
F. Mansal
Affiliation:
Université Cheikh-Anta-Diop, Dakar, Sénégal
M. Baldé
Affiliation:
Université Cheikh-Anta-Diop, Dakar, Sénégal
T. Nguyen-Huu*
Affiliation:
IRD UMI IMMISCO, 32 av. Henri Varagnat, 93140 Bondy cedex, France
P. Auger
Affiliation:
Université Cheikh-Anta-Diop, Dakar, Sénégal IXXI, ENS Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon Cedex 07
*
⋆Corresponding author. E-mail: [email protected]
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Abstract

We present a mathematical model of a fishery on several sites with a variable price. Themodel takes into account the evolution during the time of the resource, fishes and boatsmovements between the different sites, fishing effort and price that varies with respectto supply and demand. We suppose that boats and fishes movements as well as pricesvariations occur at a fast time scale. We use methods of aggregation of variables in orderto reduce the number of variables and we derive a reduced model governing two globalvariables, respectively the biomass of the resource and the fishing effort of the wholefishery. We look for the existence of equilibria of the aggregated model. We show that theaggregated model can have 1, 2 or 3 non trivial equilibria. We show that a variation ofthe total number of sites can induce a switch from over-exploitation to sustainablefisheries.

Keywords

dynamical systemsmulti-site fisheryvariable pricedemand functionequilibriumstabilityoptimum capture
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 6: Ecology , 2013 , pp. 130 - 142
Copyright
© EDP Sciences, 2013

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