Acta Biotheoretica

, Volume 62, Issue 3, pp 305–323 | Cite as

A Mathematical Model of a Fishery with Variable Market Price: Sustainable Fishery/Over-exploitation

  • Fulgence Mansal
  • Tri Nguyen-Huu
  • Pierre Auger
  • Moussa Balde
Regular Article

Abstract

We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource.

Keywords

Dynamical systems Fishery Variable price Market price equation Demand function Equilibrium Stability Sustainable exploitation/overexploitation 

References

  1. Auger P, Mchich R, Raïssi N, Kooi B (2010) Effects of market price on the dynamics of a spatial fishery model: over-exploited fishery/traditional fishery. Ecol Complex 7:13–20CrossRefGoogle Scholar
  2. Auger P, Bravo de la Parra R (2000) Methods of aggregation of variables in population dynamics. C R Acad Sci 323:665–674CrossRefGoogle Scholar
  3. Auger P, Ducrot A (2009) A model of fishery with fish stock involving delay equations. Philos Trans R Soc A 367:4907–4922CrossRefGoogle Scholar
  4. Auger P, Bravo de la Parra R, Poggiale JC, Sánchez E, Nguyen-Huu T (2008) Aggregation of variables and applications to population dynamics. In: Magal P, Ruan S (eds) Structured population models in biology and epidemiology. Lecture notes in mathematics, Vol. 1936, Mathematical Biosciences Subseries, Springer, Berlin, pp 209–263Google Scholar
  5. Auger P, Lett C, Moussaoui A, Pioch S (2010) Optimal number of sites in artificial pelagic multi-site fisheries. Can J Fish Aquat Sci 67:296–303CrossRefGoogle Scholar
  6. Barbier EB, Strand I, Sathirathai S (2002) Do open access conditions affect the valuation of an externality? Estimating the welfare effects of mangrove-fishery linkages. Env Resour Econ 21:343–367CrossRefGoogle Scholar
  7. Boudouresque CF, Gadiou G, Le Direac’h L (2005) Marine protected areas: a tool for costal areas management. In: Levner E, Linkov I, Proth JM (eds) Strategic management of marine Ecosystems. Springer, Dordrecht, pp 29–52CrossRefGoogle Scholar
  8. Clark CW (1990) Mathematical bioeconomics: the optimal management of renewable resources, 2nd edn. Wiley, New YorkGoogle Scholar
  9. Clark CW (1985) Bioeconomic modelling and fisheries management. Wiley, New YorkGoogle Scholar
  10. Clark CW (2006) Fisheries bioeconomics: why is it so widely misunderstood? Popul Ecol 48(2):95–98Google Scholar
  11. De Lara M, Doyen L (2008) Sustainable management of renewable resources: mathematical models and methods. Springer, BerlinGoogle Scholar
  12. Doyen L, Cissé A, Gourguet S, Mouysset L, Hardy PY, Béné C, Blanchard F, Jiguet F, Pereau JC, Thébaud O (2013) Ecological-economic modelling for the sustainable management of biodiversity. Comput Manag Sci 10(4):353–364Google Scholar
  13. Ekouala L (2013) Le développement durable et le secteur des pêches et de l’aquaculture au Gabon: une étude de la gestion durable des ressources halieutiques et de leur écosystème dans les provinces de l’Estuaire et de l’Ogoué Maritime. PhD Thesis, Université du Littoral Côte d’OpaleGoogle Scholar
  14. Iwasa Y, Andreasen V, Levin SA (1987) Aggregation in model ecosystems. I. Perfect aggregation. Ecol Model 37:287–302CrossRefGoogle Scholar
  15. Iwasa Y, Levin SA, Andreasen V (1989) Aggregation in model ecosystems. II. Approximate aggregation. IMA J Math Appl Med Biol 6:1–23CrossRefGoogle Scholar
  16. Lafrance JT (1985) Linear demand functions in theory and practice. J Econ Theory 37:147–166CrossRefGoogle Scholar
  17. Mankiw NG (2011) Principles of economics, 5th edn. South-Western Cengage Learning, BostonGoogle Scholar
  18. Ly S, Mansal F, Balde M, Nguyen-Huu T, Auger P (2014) A model of a multi-site fishery with variable price: from over-exploitation to sustainable fisheries. Mathematical Modelling of Natural Phenomena (in press)Google Scholar
  19. Meuriot E (1987) Les modèles bio-économiques d’exploitation des pêcheries. Démarches et enseignements. Rapports économiques et juridiques de l’IFREMER N 4Google Scholar
  20. Moussaoui A, Auger P, Lett C (2011) Optimal number of sites in multi-site fisheries with fish stock dependent migrations. Math Biosci Eng 8:769–783CrossRefGoogle Scholar
  21. Prellezo R, Accadia P, Andersen JL, Andersen BS, Buisman E, Little A, Nielsen JR, Poos JJ, Powell J, Rockmann C (2012) A review of EU bio-economic models for fisheries: the value of a diversity of models. Mar Policy 36:423–431CrossRefGoogle Scholar
  22. Robert M, Dagorn L, Filmalter JD, Deneubourg JL, Itano D, Holland K (2013) Intra-individual behavioral variability displayed by tuna at fish aggregating devices (FADs). Mar Ecol-Prog Ser (in press)Google Scholar
  23. Randall JE (1963) An analysis of the fish populations of artificial and natural reefs in the virgin islands. Caribb J Sci 3(1):31–47Google Scholar
  24. Robert M, Dagorn L, Lopez J, Moreno G, Deneubourg JLA (2013) Does social behavior influence the dynamics of aggregations formed by tropical tunas around floating objects ? An experimental approach. J Exp Mar Biol Ecol 440:238–243CrossRefGoogle Scholar
  25. Smith VL (1968) Economics of production from natural resources. Am Econ Rev 58(3):409–431Google Scholar
  26. Smith VL (1969) On models of commercial fishing. J Polit Econ 77(2):181–198CrossRefGoogle Scholar
  27. Sow FN, Thiam N, Samb B (2011) Diagnostic de l’état d’exploitation du stock de mérou Epinephelus aeneus(Geoffroy St. Hilaire, 1809) au Sénégal par l’utilisation des fréquences des tailles. J Sci Hal Aquat 3:82–88Google Scholar
  28. Walras L (1874) Éléments d’économie Politique Pure. Corbaz, LausanneGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Fulgence Mansal
    • 1
  • Tri Nguyen-Huu
    • 2
    • 3
    • 4
  • Pierre Auger
    • 1
    • 2
    • 4
  • Moussa Balde
    • 1
  1. 1.Département de mathématiques et informatique, Faculté des Sciences et techniques, UMI IRD 209, UMMISCO, IRDUniversité Cheikh Anta DiopDakarSenegal
  2. 2.UMI IRD 209, UMMISCOBondy CedexFrance
  3. 3.IXXIENS LyonLyonFrance
  4. 4.UPMC, Sorbonne UniversityParisFrance

Personalised recommendations