This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE’s governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model.
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Alfaro-Shigueto J, Mangel JC, Pajuelo M, Dutton PH, Seminoff JA, Godley BJ (2010) Where small can have a large impact: structure and characterization of small-scale fisheries in Peru. Fish Res 106:8–17
Auger P, de la Parra RB (2000) Methods of aggregation of variables in population dynamics. C R Acad Sci 323:665–674
Auger P, de la Parra RB, Poggiale JC, Snchez E, Nguyen Huu T (2008a) 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. Springer, Berlin, pp 209–263
Auger P, de la Parra RB, Poggiale JC, Snchez E, Sanz L (2008b) Aggregation methods in dynamical systems variables and applications in population and community dynamics. Phys Life Rev 5:79–105
Auger P, Mchich R, Raissi N, Koii B (2010) Effects of market price on the dynamics of a spatial fishery model: over-exploited fishery/traditional fishery. Ecol Complex 7(1):13–20
Bonnin M, Le Tixerant M, Ly I, Ould Zein A (2013) Atlas cartographique du droit de l’environnement marin: Senegal, Mauritania, Guinea. CSRP-IUCN, Research report, January. http://www.spcsrp.org/Atlas+cartographique. Accessed 19 Jan 2016
Brehmer P, Guillard J, Guenngan Y, Bigot J-L, Liorzou B (2006) Evidence of a variable “unsampled” biomass along the shallow water (\(< 20\) m) coastline in small pelagic fish stock assessment methods. ICES J Mar Sci 63:444–451
Charouki N, Rassi N, Auger P, Mchich R, Atmani H (2011) A management oriented competitive model with two time scales: the case of sardine fishery along the Atlantic coast between Cantin Cape and Blanc Cape. Ecol Model 222(6):1253–1261
Clark CM (1990) Mathematical bioeconomics: the optimal management of renewable resources, 2nd edn. A Wiley-Interscience, Hoboken
Clark CW, Clarke FH, Munro GR (1979) The optimal management of renewable resources stocks: problem of irreversible investment. Econometrica 47:25–47
Conand F (1977) Oeufs et larves de la sardinelle ronde (Sardinella aurita) au Sénégal: distribution, croissance, mortalité, variations d’abondance de 1971 à 1976. Cah ORSTOM Sér Océanogr 15:201–214
Cury P, Bakun A, Crawford RJ, Jarre A, Quinones RA, Shannon LJ, Verheye HM (2000) Small pelagics in upwelling systems: patterns of interaction and structural changes in “wasp-waist” ecosystems. ICES J Mar Sci J du Cons 57:603
Estrade P, Marchesiello P, De Verdire AC, Roy C (2008) Cross-shelf structure of coastal upwelling: a two dimensional extension of Ekman’s theory and a mechanism for innershelf upwelling shut down. J Mar Res 66:589616
Kooi BW (2003) Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment. Acta Biotheor 51:189222
Lafrance JT (1985) Linear demand functions in theory and practice. J Econ Theory 37:147166
Mchich R, Auger PM, de la Parra RB, Raïssi N (2002) Dynamics of a fishery on two fishing zones with fish stock dependent migrations: aggregation and control. Ecol Model 158(1–2):51–62
Mchich R, Auger P, Raïssi N (2005) The stabilizability of a controlled system describing the dynamics of a fishery. C R Biol 328(4):337–350
Metian AGJTM (2009) Fishing for feed or fishing for food: increasing global competition for small pelagic forage fish. AMBIO J Hum Environ 38:294302
Michalski J, Poggiale JC, Arditi R, Auger PM (1997) Macroscopic dynamic effects of migrations in patchy predator-prey systems. J Theor Biol 185:459–474
Pauly D, Watson R, Alder J (2005) Global trends in world fisheries: impacts on marine ecosystems and food security. Philos Trans R Soc B Biol Sci 360:512
Srinivasan UT, Cheung WWL, Watson R, Sumaila UR (2010) Food security implications of global marine catch losses due to overfishing. J Bioecon 12:183200
Tacon AGJ (2004) Use of fish meal and fish oil in aquaculture: a global perspective. Aquat Resour Cult Dev 1:314
Tacon AGJ, Metian M (2009) Fishing for aquaculture: non-food use of small pelagic forage fish—a global perspective. Rev Fish Sci 17:305–317
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Mchich, R., Brochier, T., Auger, P. et al. Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach. Acta Biotheor 64, 479–493 (2016). https://doi.org/10.1007/s10441-016-9299-7
- Fishery model
- Industrial and artisanal fisheries
- Aggregation of variables
- Parameters identification measures
- National policy management