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Moment approximation of individual-based models. Application to the study of the spatial dynamics of phytoplankton populations

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  • Bordj, Naziha
  • Saadi, Nadjia El

Abstract

The objective of this paper is to analyze the efficiency of a spatial moments model (SMM) in approximating an individual-based model (IBM) dedicated to the study of the aggregation phenomenon in a phytoplankton population. The dynamic system of spatial moments consists of a system of integro-differential equations derived from a phytoplankton IBM. The later is built on the basis of stochastic processes describing the dynamics of phytoplankton cells and their interactions. These processes are: (1) the movement of cells, which takes into account the random dispersion of cells in water and the attraction between cells due to their chemosensory abilities, (2) the demographical process (cell division or cell death) in which, the effect of local competition for nutrient resources on the cell’s division process is taken into account through the use of density dependent division rate.

Suggested Citation

  • Bordj, Naziha & Saadi, Nadjia El, 2022. "Moment approximation of individual-based models. Application to the study of the spatial dynamics of phytoplankton populations," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006780
    DOI: 10.1016/j.amc.2021.126594
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    References listed on IDEAS

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    1. El Saadi, N. & Bah, A., 2007. "An individual-based model for studying the aggregation behavior in phytoplankton," Ecological Modelling, Elsevier, vol. 204(1), pages 193-212.
    2. Bruno Bonté & Jean-Denis Mathias & Raphaël Duboz, 2012. "Moment Approximation of Infection Dynamics in a Population of Moving Hosts," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-10, December.
    3. U. Dieckmann & T. Herben & R. Law, 1997. "Spatio-Temporal Processes in Plant Communities," Working Papers ir97026, International Institute for Applied Systems Analysis.
    4. Bouderbala, Ilhem & El Saadi, Nadjia & Bah, Alassane & Auger, Pierre, 2019. "A simulation study on how the resource competition and anti-predator cooperation impact the motile-phytoplankton groups’ formation under predation stress," Ecological Modelling, Elsevier, vol. 391(C), pages 16-28.
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