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On mathematical modelling of complex ecosystems: Application to marine planktonic patchiness
Helgoländer wissenschaftliche Meeresuntersuchungen volume 30, pages 76–82 (1977)
Abstract
Mathematical modeling of complex ecosystems is very difficult due to the very large number of components in the real ecosystem. Conceptual subdivision into interacting sub-systems is necessarily subjective and is made in view of explaining a particular aspect of the reality. In this paper, the North Sea planktonic ecosystem is reduced to a rather simple mathematical model with the purpose of showing the possibility of a spontaneous spatial emergence of plankton patches by diffusive instability. Due to the dependence of diffusion coefficients on the differential diameters of phytoplankton and herbivorous zooplankton patches, respectively, the spatially homogeneous steady state is unstable for spatial perturbations with wavelengths belonging to a certain range of values. As a consequence, these perturbations amplify leading to spatial heterogeneity.
Literature Cited
Dubois, D. M., 1975. A model of patchiness for prey-predator plankton populations. Ecol. Modeling1, 67–80.
— 1976a. Modelling and simulation of the mesoscale mosaic structure of the lower marine trophic levels. Springer, Berlin, 407–418 (Lecture notes in computer science. Vol. 40).
Dubois, D. M., 1976b. On temporal and spatial structure in model systems and application to ecological patchiness. In: Analyse de systèmes et ses orientations nouvelle. IRIA, 599–613.
— & Adam, Y., 1976. Spatial structuration of diffusive prey-predator biological populations: simulation of the horizontal distribution of plankton in the North Sea. In: System simulation in water resources. Ed. by G. C. Vansteenkiste. North-Holland, Amsterdam, 343–356.
— & Closset, P. L., 1976. Patchiness in primary and secondary production in the Southern Bight: a mathematical theory. In: Proceedings of the 10th European Symposium on Marine Biology. Ed. by G. Persoone & E. Jaspers. University Press, Wetteren,2, 211–229.
— & Mayzaud, P., 1976. Experimental and theoretical approach of the production and transformation of organic matter in a semi-enclosed basin. In: Proceedings of the 10th European Symposium on Marine Biology. Ed. by G. Persoone & E. Jaspers. University Press, Wetteren,2, 231–245.
Glansdorff, P. & Prigogine, I., 1974. Thermodynamic theory of structure, stability and fluctuations. Wiley-Interscience, London,306 pp.
Levin, S. A., 1976. Population dynamic models in heterogeneous environments. Ann. Rev. Ecol. Syst.7, 287–310.
Thom, R., 1972. Structural stability and morphogenesis. Benjamin, Reading, Mass., 362 pp.
—, 1974. Modèles mathématiques de la morphogénèse. Collection 10/18, UGE, Paris, 319 pp.
Turing, A. M., 1952, The chemical basis of morphogenesis. Proc. R. Soc.,Lond. (B)237, 37–72
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Dubois, D.M. On mathematical modelling of complex ecosystems: Application to marine planktonic patchiness. Helgolander Wiss. Meeresunters 30, 76–82 (1977). https://doi.org/10.1007/BF02207826
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DOI: https://doi.org/10.1007/BF02207826