Mathematical Biosciences and Engineering (MBE)

Optimal number of sites in multi-site fisheries with fish stock dependent migrations
Pages: 769 - 783, Volume 8, Issue 3, July 2011

doi:10.3934/mbe.2011.8.769      Abstract        References        Full text (370.8K)           Related Articles

Ali Moussaoui - Université Aboubekr Belkaid, Faculté Des Sciences, Département de Mathématiques, 13000, Tlemcen,, Algeria (email)
Pierre Auger - IRD, UMI 209, UMMISCO, IRD France Nord, F-93143, Bondy, France (email)
Christophe Lett - UMI IRD 209 UMMISCO, Centre de Recherche Halieutique Méditerranéenne et Tropicale, Avenue Jean Monnet, BP 171, 34203 Séte Cedex, France (email)

1 D. K. Arrowsmith and C. M. Place, "Dynamical Systems," in "Differential Equations, Maps and Chaotic Behaviour," Chapman and Hall, London, 1992.       
2 P. Auger, C. Lett, A. Moussaoui and S. Pioch, Optimal number of sites in artificial pelagic multi-site fisheries, Canadian Journal of Fisheries and Aquatic Sciences, 67 (2010), 296-303.
3 P. Auger and J.-C. Poggiale, Emergence of population growth models: Fast migration and slow growth, J. Theor. Biol., 182 (1996), 99-108.
4 P. Auger and J.-C. Poggiale, Aggregation and emergence in systems of ordinary differential equations, Math. Comput. Model., 27 (1998), 1-21.       
5 P. Auger and R. Roussarie, Complex ecological models with simple dynamics: From individuals to population, Acta Biotheor., 42 (1994), 111-136.
6 P. Auger, R. Bravo de la Parra, J.-C. Poggiale, E. Sánchez and T. Nguyen-Huu, Aggregation of variables and applications to population dynamics, in "Structured Population Models in Biology and Epidemiology," Lecture Notes in Mathematics, 1936, Springer, Berlin, 209-263, C. M. Clark, "Mathematical Bioeconomics: The Optimal Management of Renewable Resources," 2nd ed., A. Wiley-Interscience, 2008.       
7 P. Auger, R. Bravo de la Parra, J.-C. Poggiale, E. Sánchez and L. Sanz, Aggregation methods in dynamical systems variables and applications in population and community dynamics, Physics of Life Reviews, 5 (2008), 79-105.
8 H. Belvéze, "Biologie et Dynamique des Populations de Sardine (Sardina Pilchardus Walbaum) Peuplant les CU tes Atlantiques Marocaines et Propositions pour un Aménagement des PIcheries," Ph.D thesis, Bretagne Occidentale University, 1984.
9 J. Carr, "Applications of Centre Manifold Theory," Applied Mathematical Sciences, 35, Springer-Verlag, New York-Berlin, 1981.       
10 D. K. Dao, P. Auger and H. T. Nguyen, Predator density dependent prey dispersal in a patchy environment with a refuge for the prey, South African Journal of Science, 104 (2008), 180-184.
11 T. Dempster and M. Taquet, Fish aggregation device (FAD) research: Gaps in current knowledge and future directions for ecological studies, Reviews in Fish Biology and Fisheries, 14 (2004), 21-42.
12 A. El Abdllaoui, P. Auger, R. Bravo de la Parra, B. Kooi and R. Mchich, Effects of density-dependent migrations on stability of a two-patch predator-prey model, Mathematical Biosciences, 210 (2007), 335-354.       
13 N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana University Mathematical Journal, 21 (1971/1972), 193-226.       
14 A. Fonteneau, J. Ariz, D. Gaertner, T. Nordstrom and P. Pallares, 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, Aquatic Living Resources, 13 (2000), 253-257.
15 C. Girard, S. Benhamou and S. L. Dagorn, FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects, Animal Behaviour, 67 (2004), 319-326.
16 R. Hilborn and P. Medley, Tuna purse-seine fishing with Fish-Aggregating Devices (FAD)- Models of tuna FAD interactions, Canadian Journal of Fisheries and Aquatic Sciences, 46 (1989), 28-32.
17 R. Hilborn, F. Micheli and G. A. De Leo, Integrating marine protected areas with catch regulation, Canadian Journal of Fisheries and Aquatic Sciences, 63 (2006), 642-649.
18 M. W. Hirsch, C. C. Pugh and M. Shub, Invariant manifolds, Bull. Am. Math. Soc., 76 (1970), 1015-1019.       
19 Y. Iwasa, V. Andreasen and S. A. Levin, Aggregation in model ecosystems I. Perfect aggregation, Ecological Modelling, 37 (1987), 287-302.
20 Y. Iwasa, S. A. Levin and V. Andreasen, Aggregation in model ecosystems. II. Approximate aggregation, IMA Journal of Mathematics Applied in Medicine and Biology, 6 (1989), 1-23.       
21 H. Kakimoto, Artificial fishing reef studies and effects, Japanese Institute of Technology on Fishing Ports, Grounds and Communities (JIFIC), in Japanese, II (2004), 150-178.
22 C. H. Lan and C. Y. Hsui, The deployment of artificial reef ecosystem: Modelling, simulation and application, Simulation Modelling Practice and Theory, 14 (2006), 673-675.
23 R. Mchich, P. Auger and J.-C. Poggiale, Effect of predator density dependent dispersal of prey on stability of a predator-prey system, Mathematical Biosciences, 206 (2007), 343-356.       
24 R. Mchich, P. Auger, R. Bravo de la Parra and N. Raïssi, Dynamics of a fishery on two fishing zones with fish stock dependent migrations: Aggregation and control, Ecol. Model., 158 (2002), 51-62.
25 J. Michalski, J.-C. Poggiale, R. Arditi and P. Auger, Macroscopic dynamic effects of migrations in patchy predator-prey systems, J. Theor. Biol., 185 (1997), 459-474.
26 G. Moreno, L. Dagorn, G. Sancho and D. Itano, Fish behaviour from fishers' knowledge: The case study of tropical tuna around Drifting Fish Aggregating Devices (DFADs), Canadian Journal of Fisheries and Aquatic Sciences, 64 (2007), 1517-1528.
27 A. Moussaoui, Effect of a toxicant on the dynamics of a spatial fishery, African Diaspora Journal of Mathematics, 10 (2010), 122-134.
28 P. A. Nelson, Marine fish assemblages associated with Fish Aggregating Devices (FADs): Effects of fish removal, FAD size, fouling communities, and prior recruits, Fishery Bulletin, 101 (2003), 835-850.
29 S. Levin and S. Pacala, Theories of simplification and scaling of spatially distributed processes, in "Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions" (eds. D. Tilman and P. Kareiva), Princeton University Press, Princeton, (1997), 204-232.
30 S. Pioch, "Les 'Habitats Artificiels': Élément de Stratégie pour une Gestion Intégrée des Zones Côtières? Essai de Méthodologie d'Aménagement en 325 Ré cifs Artificiels Adapté à la Pêche Artisanale Côtière," Ph.D. thesis, Paul Valery University, Montpellier, Tokyo University of Marine Science and Technology, Tokyo, in French, 2008.
31 J.-C. Poggiale, "Applications des Variétés Invariantes a la Modélisation de l'Hétèrogén éité en Dynamique des Populations," Ph.D. thesis, Bourgogne University, Dijon, in French, 1994.
32 J.-C. Poggiale and P. Auger, Impact of spatial heterogeneity on a predator-prey system dynamics, Comptes Rendus Biologies, 327 (2004), 1058-1063.
33 R. A. Rountree, Association of fishes with fish aggregating devices: Effects of structure size on fish abundance, Bulletin of Marine Science, 44 (1989), 960-972.
34 K. Sakamoto, Invariant manifolds in singular perturbations problems for ordinary differential equations, Proc. Roy. Soc. Ed. Sect. A, 116 (1990), 45-78.       

Go to top