Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-20T00:18:15.180Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Auger, P., Mchich, R., Raïssi, N., Kooi, B.. Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery. Ecol. Complex., 7 (2009), No. 1, 13–20. doi:10.1016/j.ecocom.2009.03.005 CrossRefGoogle Scholar
Auger, P., Poggiale, J.C.. Emergence of population growth models: fast migration and slow growth. J. Theor. Biol., 182 (1996), No. 2, 99–108. doi:10.1006/jtbi.1996.0145. PMID:8944142 CrossRefGoogle Scholar
P. Auger, R. Bravo de la Parra, J.C. Poggiale, E. Sanchez, T. Nguyen-Huu. Aggregation of variables and applications to population dynamics. In Structured population models in biology and epidemiology. Lecture notes in mathematics. Vol. 1936. Edited by P. Magal and S. Ruan. Mathematical Biosciences Subseries (2008) Springer, Berlin., 209–263.
Auger, P., Roussarie, R.. Complex ecological models with simple dynamics: from individuals to population. Acta Biotheor., 42 (1994), No. 2-3, 111–136. doi:10.1007/BF00709485. CrossRefGoogle Scholar
Auger, P., Lett, C., Moussaoui, A., Pioch, S.. Optimal number of sites in artificial pelagic multi-site fisheries. Can. J. Fish. Aquat. Sci., 67 (2010), 296–303. doi:10.1139/F09-188 Google Scholar
Barbier, E.B., Strand, I., Sathirathai, S.. Do open access conditions affect the valuation of an externality? Estimating the welfare effects of mangrove-fishery linkages. Env. Resour. Econ., 21 (2002), 343–367. CrossRefGoogle Scholar
C.W. Clark. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. 2nd ed. Wiley, New York, 1990.
Dagorn, L., Holland, K.N., Itano, D.G.. Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs). Mar. Biol. (Berl.), 151(2) (2007) 595–606. doi:10.1007/s00227-006-0511-1. CrossRefGoogle Scholar
Robert, M., Dagorn, L., Lopez, J., Moreno, G., Deneubourg, J.L.A.. Does social behavior influence the dynamics of aggregations formed by tropical tunas around floating objects ? An experimental approach.. J. Exp. Mar. Biol. Ecol., 440 (2013), 238–243. CrossRefGoogle Scholar
M. de Lara, L. Doyen. Sustainable Management of renewable resources: Mathematical Models and Methods. Springer-Verlag, Berlin Heidelberg, 2008.
Food and Agriculture Organization of the United Nations (FAO). Fishing Technology Equipments Fish Aggregating Device (FAD). Fisheries and Aquaculture Department.
Fonteneau, A., Ariz, J., Gaertner, D., Nordstrom, T., Pallares, P.. Observed changes in the species composition of tuna schools in the Gulf of Guinea between 1981 and 1999, in relation with the fish aggregrating device fishery. Aquat. Living Resour. 13 (2000) 253–257. doi:10.1016/S0990-7440(00)01054-8. CrossRefGoogle Scholar
Girard, C., Benhamou, S., Dagorn, L.. FAD: fish aggregating device or fish attracting device? A new analysis of yellowfin tuna movements around floating objects. Anim. Behav. 67(2) (2004), 319–326. doi:10.1016/j.anbehav.2003.07.007.
Iwasa, Y., Andreasen, V., Levin, S.A.. Aggregation in model ecosystems. I. Perfect aggregation. Ecol. Model., 37 (1987), 287–302. CrossRefGoogle Scholar
Iwasa, Y., Levin, S.A., Andreasen, V.. Aggregation in model ecosystems. II. Approximate aggregation. IMA J. Math. Appl. Med. Biol., 6 (1989), 1–23. CrossRefGoogle Scholar
Kakimoto, H.. Artificial fishing reef studies and effects. Japanese Institute of Technology on Fishing Ports, Grounds and Communities (JIFIC), 2, (2004), 150–178. Google Scholar
L. Kumoro. Notes on the use of FADs in the Papua New Guinea purse seine fishery. Papua New Guinea National Fisheries Authority, Port Moresby, Papua New Guinea, 2003.
Kritzer, J.P., Sale, P.F.. Metapopulation ecology in the sea: from Levins’ model to marine ecology and fisheries science. Fish Fish. 5 (2004), 131–140. CrossRefGoogle Scholar
Lan, C.H., Hsui, C.Y.. The deployment of artificial reef ecosystem: modelling, simulation and application. Simul. Model. Pract. Theory, 14 (2006), No. 5, 663–675. doi:10.1016/j.simpat.2005.10.011. CrossRefGoogle Scholar
Lafrance, J.T.. Linear demand functions in theory and practice. J. Econ. Theory, 37 (1985), 147–166. CrossRefGoogle Scholar
S.A. Levin, S. Pacala. Theories of simplification and scaling of spatially distributed processes, in: D. Tilman, P. Kareiva (Eds.), Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, Princeton University, 1997.
Moreno, G., Dagorn, L., Sancho, G., Itano, D.. Fish behaviour from fishers’ knowledge: the case study of tropical tuna around drifting fish aggregating devices (DFADs). Can. J. Fish. Aquat. Sci. 64(11) (2007) 1517–1528. doi:10.1139/F07-113. CrossRefGoogle Scholar
Ohta, I., Kakuma, S.. Periodic behavior and residence time of yellowfin and bigeye tuna associated with fish aggregating devices around Okinawa Islands, as identified with automated listening stations. Mar. Biol. (Berl.), 146(3) (2005), 581–594. doi:10.1007/s00227-004-1456-x. CrossRefGoogle Scholar
Sanchirico, J.N., Wilen, J.E.. Bioeconomics of spatial exploitation in a patchy environment . J. Environ. Econ. Manag. 37 (1999), 129–150. CrossRefGoogle Scholar
Schaefer, M.B.. Some considerations of population dynamics and economics in relation to the management of the commercial marine fisheries. J. Fish. Res. Board Canada 14 (1957), 669–681. CrossRefGoogle Scholar
Smith, V.L.. Economics of production from natural resources. Am. Econ. Rev., 58 (1968), No. 3, 409–431. Google Scholar
Smith, V.L.. On models of commercial fishing. J. Political Economy, 77 (1969), No. 2, 181–198. CrossRefGoogle Scholar
L. Walras. Elément d’économie Politique Pure. Corbaz, Lausanne, 1874.
Western and Central Pacific Fisheries Commission (WCPFC). Paragraph 24 of CMM 2008-01 FAD management and monitoring. Fifth regular session, Technical and Compliance Committee. WCPFC-TCC5-2009/22 (2009).