Abstract
A study of stage structured model of fish population is presented. This model focuse on the anchovy population in the Bay of Biscay (Engraulis encrasicolus L.) is presented. The method of study is based on an intermediate complexity mathematical model, taking into account the spatialisation, the environmental conditions and the stage-structure of the fishes. First, to test the model, we show mathematical properties, such as unicity of the solution of structural stability. Then we provide numerical simulations, to validate the model and to test the dynamics according to the variations of the parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abraham, R. and J. Robbin (1967). Transversal Mappings and Flows. Benjamin, New-York.
Adams, R. (1975). Sobolev spaces, Acad. Press.
Adioui, M., O. Arino, W. Smith and J.P. Treuil (2003). A mathematical analysis of a fish school model. Journal of Differential Equations 188.
Adioui, M., J.P. Treuil and O. Arino (2003). Alignment in a fish school: A mixed Lagrangian-Eulerian approach. Ecological Modelling 167.
Adioui, M. (2002). The interplay between individual based computer simulation and mathematical analysis in a fish school. CARI Proceeding.
Ahmed, N.U. (1991). Semi-group theory with application to system and control. Pitman research notes in mathematics series.
Allain, G. (2004). Modélisation biophysique pour la prévision du recrutement, Ph. D. thesis.
Allain, G., P. Petitgas, P. Grellier and P. Lazure (2003). The selection process from larval to juvenile stages of anchovy (Engraulis encrasicolus) in the Bay of Biscay investigated by Lagrangian simulations and comparative otolith growth. Fischeries Oceanography 12.
Allain, G., P. Petitgas and P. Lazure (2001). The influence of mesoscale ocean processes on anchovy (Engraulis encrasicolus) recruitment in the Bay of Biscay estimated with a three-dimensional hydrodynamic model. Fish. Ocean. 10: 151–163.
Bergeron, J.P. (2000). Effect on strong winds on the nutritional condition of anchovy (Engraulis encrasicolus L.) larvae in the Bay of Biscay, Notheast Atlantic, as inferred from an early field application of the DNA/C index. Journal of the Marine Science 57: 249–255.
Borja, A., A. Uriarte, V. Valencia, L. Motos and Ad. Uriarte (1996). Relationship between anchovy (Engraulis encrasicolus L.) recruitment and the environment in the Bay of Biscay. Scientia Marina 179–192.
Borja, A., A. Uriarte, J. Egaña, L. Motos and V. Valencia (1998). Relationship between anchovy (Engraulis encrasicolus) reruitment and environment in the Bay of Biscay (1967–1996). Fish. Oceanogr 7(3/4): 375–380.
Boussouar, A., S. Le Bihan, O. Arino and P. Prouzet (2001). Mathematical model and numerical simulations of the migration and growth of Biscay Bay anchovy early larval stages. Oceanologica Acta 24(5).
Calaud, V. Hausdorff and fractal dimensions of attractors for a mathematical model for passive oceanic tracers”,, submitted.
Calsina, A. and O. El Idrissi (2002). Asymptotic Behaviour of a semi-linear Age-Structured Population Model with a Dynamics for the Resource. Mathematical and Computer Modelling 35: 403–427.
Crawford, R.J.M. (1981). Distribution, availability and movements of anchovy Engraulis capensis of South Africa, 1964–1976. Fish. Bull. S. Afr. 14: 51–94.
Curry, P. and C. Roy (1989). Optimal environmental window and pelagic fish recruitment success in upwelling areas. Can. J. Fish Aquat Sci. 46: 670–680.
Cushing, D. (1975). Marine ecology and fisheries, Cambridge, UK, Cambridge University Press.
Devaney, R. (1989). An introduction to chaotic dynamical systems. Perseus Book, second edition.
Franks, P. and L. Walstad (1997). Phytoplankton patches at fronts: A model of formation and response to wind events. J. Marine Res. 55: 1–29.
Flament, P., C. Lumpkin and J. Firing (1996). Mean flow and eddy statistics from the Hawaii EEZ inferred from the Pelagic Fisheries drifters array, Report of the eighth meeting of the WOCE/CLIVAR Surface Velocity Programme Planning Committee, 14–16 May 1996, WOCE International Project Office report No. 146/96, 24pp.
Gurney, W., D. Speirs, S. Wood, E. Clarke and M. Heath (2001). Simulating spatially and physiologically structured populations. Journal of Animal Ecology 70.
Gill, A.E. (1982). Atmosphere-ocean dynamics. Academic Press.
Heijmans, H.J.A.M. (1985). Dynamics of structured populations, PhD thesis, University of Amsterdam.
Hinrichsen, H.H., U. Bttcher, F.W. Kster, A. Lehmann and St. John M.A. (2003). Modelling the influence of atmospheric forcing conditions on Baltic cod early life stages: Distributin and drift. Journal of Sea Research 49: 187–201.
Hutchings, L., M. Barange, S.F. Bloomer, A.J. Boyd, R.J.M. Crawford, J.A. Huggett, M. Kerstan, J.L. Korrubel, J.A.A. De Oliveira, S.J. Painting, A.J. Richardson, L.J. Shannon, F.H. Schülen, C.D. Van der Lingen and Verheye H.M. (1998). Multiple factors affecting South african anchovy recruitment and the spawning, transport and nursery areas. S. Afr. Mar Sci. 19: 211–225.
Irwin, M. (1980). Smooth Dynamical Systems. Academic Press.
Jégou, A.M., F. Dumas and P. Lazure (2001). Modelling the Adour plume with a 3D hydrodynamic model. In Actes du VII Colloque International Océanographique du Golfe de Gascogne, d'Elbée, J. Prouzet, P. (Eds.), Editions Ifremer, Actes Colloq. 31.
Lazure, P. and A.M. Jégou (1998). 3D modelling of seasonal evolution of Loire and Gironde plumes on Biscay Bay continental shelf. Oceanol. Ata, 21.
Leslie, P.H. (1945). On the use of matrices in certain population mathematics. Biometrika 33: 183–212.
Lehodey, P., J.M. André, M. Bertignac, J. Hampton, A. Stoens, C. Menkès, L. Mémery and N. Grima (1998). Predicting skipjack tuna forage distributions in the equatorial pacific using a coupled dynamical bio-geochemical. Fish Oceanogr 7.
Lévy, M., L. Mémery and J.M. André (1998). Simulation of primary production and export fluxes in the NW Mediterranean Sea J. Mar. Res. 197–238.
Lewandowski, R. (1997). Analyse mathématique et océanographie. Masson.
Metz, J.A.J. and O. Diekmann (1986). The dynamics of physiologically structured populations, Lecture notes in Biomathematics 68. Springer-Verlag, Berlin.
Mich, R., P. Auger, R. Bravo de la Parra and N. Raissi (2002). Dynamics of fishery on two fishing zones with fish stock dependent migrations: Aggregation and control. Ecol model. 158: 51–62.
Pedlovsky, J. (1979). Geophysical Fluid Dynamics. Springer-Verlag.
Peterman, R.M., M.J. Bradford, N.H.C. Lo and R.D. Methot (1988). Contribution of early life stages to interannual variability in recruitment of Northern Anchovy. Can. J. Fish. Aquat. Sci. 45: 8–16
Palis, J. and W. De Melo (1982). Geometric Theory of Dynamical Systems. An Introdution. Springer-Verlag.
Plounevez, S. and G. Champalbert (1999). Feeding behaviour environment of Engraulis encrasicolus (L). in the bay of biscay. Estuarine. Coastal and Shelf Science 49: 177–191.
Sinclair, M. (1988). Marine population: An essay on population regulation and speciation. Seattle, WA, University of Washington Press.
Thom, R. (1991). Prédire n'est pas expliquer (éd). Eshel, coll. la Question, Paris.
Thompson, R.W. and D.A. Cauley (1979). A population balance model for fish population dynamics. J. Theor. Biol. 81: 289–307.
Xiao, Y. (2000). A general theory of fish stock assessment models. Ecol. Model. 128: 165–180.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Calaud, V., Lagadeuc, Y. Structural Stability of a Stage Structured Model of Fish: The Case of the Anchovy (Engraulis Encrasicolus L.) in the Bay of Biscay. Acta Biotheor 53, 341–358 (2005). https://doi.org/10.1007/s10441-005-4889-9
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10441-005-4889-9