Journal of Mathematical Biology

, Volume 12, Issue 3, pp 311–326 | Cite as

Analysis of the self-shading effect on algal vertical distribution in natural waters

  • Nanako Shigesada
  • Akira Okubo


Self-shading of light by algae growing in a column of water plays an important role in the dynamics of algal blooms. Thus without self-shading the algal concentration would increase more rapidly, making the nutrient limitation too strong. Apart from the practical importance of self-shading, its inherent nonlinearity in the growth dynamics leads to an interesting mathematical problem, which warrants detailed analytical investigation. Our mathematical model for the self-shading effect includes vertical diffusion, algal settling, gross production, and collective losses of algae. Steady-state solutions of the model equation are investigated in detail by the phase plane method, and their stability examined. Finally we discuss the vertical profile of algal concentration.

Key words

Self-shading Nonlinear diffusion and reaction Algal vertical distribution 


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Nanako Shigesada
    • 1
  • Akira Okubo
    • 1
  1. 1.Marine Sciences Research CenterState University of New YorkStony BrookUSA

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