Abstract
A model for several algal species which compete both for light and for nutrients, and which are also subject to settling and diffusion, is considered. The settling speeds and diffusion coefficients are assumed to be small, in a sense to be made precise later, and a singular perturbation argument is used. In certain cases vertical segregation of the algal species is observed, and the mechanism for this is interpreted biologically.
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Britton, N. F.: Reaction-diffusion equations and their applications to biology. London: Academic Press 1986.
Britton, N. F.: Aggregation and the competitive exclusion principle. J. Theor. Biol. 136, 57–66 (1989)
Britton, N. F.: Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model. SIAM J. Appl. Math. 50, 1663–1688 (1990)
Britton, N. F., Timm, U.: Spatial segregation in competing and shading algae. Proceedings of the 1st European Conference on Mathematics applied to Biology and MedicineGrenoble 1991. (Lect. Notes Biomath.) Berlin Heidelberg New York: Springer 1993.
Conley, C., Gardner, R.: An application of the generalised Morse index to travelling wave solutions of a competitive reaction-diffusion model. Indiana Univ. Math. J. 33, 319–343 (1984)
Gardner, R.: Existence and stability of travelling wave solutions of competition models: a degree theoretic approach. J. Differ. Equations 44, 343–364 (1982)
Ishii, H., Takagi, I.: Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton. dynamics. J. Math. Biol. 16, 1–24 (1982)
Mimura, M.: Patterns, waves and interfaces in excitable reaction-diffusion systems. In: Brown, K. J., Lacey, A. A. (eds.) Reaction-Diffusion Equations, pp. 39–58. Oxford: Oxford University Press 1990
Nielsen, T. G.: Contribution of zooplankton grazing to the decline of a Ceratium bloom. Limnol. Oceanogr. 36, 1091–1106 (1991)
Radach, G., Maier-Reimer, E.: The vertical structure of phytoplankton growth dynamics, a mathematical model. In: Proc. of the Sixth Colloquium on Ocean Hydrodynamics, Liège, 1974. (Mém. Soc. R. Sci. Liege)
Shigesada, N., Okubo, A.: Analysis of the self-shading effect on algal vertical distribution in the natural waters. J. Math. Biol. 12, 311–326 (1981)
Timm, U., Klinck, J. M., Okubo, A.: Self and mutual shading effect of competing algal distribution: biological implications of the model. Ecol. Modell. 59, 11–36 (1991)
Timm, U., Totaro, S., Okubo, A.: Self and mutual shading effect on competing algal distribution. Nonlinear Anal., Theory, Methods Appl. 17, 559–576 (1991)
Volterra, V.: Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. Acad. Lincei 2, 31–113 (1926); translation in Chapman, R. N. Animal ecology. New York: McGraw-Hill 1931; and in Oliveira-Pinto, F., Conolly, B. W. Applicable mathematics of non-physical phenomena. Chichester: Ellis Horwood 1982
Wall, D., Briand, F.: Response of lake phytoplankton communities to in situ manipulations of light intensity and colour. J. Plankton Res. 1, 103–112 (1979)
Wörz-Busekros, A.: Solutions to a degenerate system of parabolic equations from marine biology. J. Math. Biol. 3, 393–406 (1976), J. Math. Biol. 5, 405 (1978)
Zobell, C. E.: Marine Microbiology. Waltham, MA: Chronica Botanica 1946
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Supported by the Danish Natural Science Research Council (Grant No. 11-8321)
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Britton, N.F., Timm, U. Effects of competition and shading in planktonic communities. J. Math. Biol. 31, 655–673 (1993). https://doi.org/10.1007/BF00160418
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DOI: https://doi.org/10.1007/BF00160418