Acta Biotheoretica

, Volume 66, Issue 4, pp 257–278 | Cite as

A 3D Individual-Based Model to Study Effects of Chemotaxis, Competition and Diffusion on the Motile-Phytoplankton Aggregation

  • Ilhem BouderbalaEmail author
  • Nadjia El Saadi
  • Alassane Bah
  • Pierre Auger
Regular Article


In this paper, we develop a 3D-individual-based model (IBM) to understand effect of various small-scale mechanisms in phytoplankton cells, on the cellular aggregation process. These mechanisms are: spatial interactions between cells due to their chemosensory abilities (chemotaxis), a molecular diffusion and a demographical process. The latter is considered as a branching process with a density-dependent death rate to take into account the local competition on resources. We implement the IBM and simulate various scenarios under real parameter values for phytoplankton cells. To quantify the effects of the different processes quoted above on the spatial and temporal distribution of phytoplankton, we used two spatial statistics: the Clark–Evans index and the group belonging percentage. Our simulation study highlights the role of the branching process with a weak-to-medium competition in reinforcing the aggregating structure that forms from attraction mechanisms (under suitable conditions for diffusion and attraction forces), and shows by contrast that aggregations cannot form when competition is high.


Individual-based model Phytoplankton aggregation Density-dependent mortality model Chemosensory ability Simulation Nearest-neighbor index Group belonging percentage 



We thank the editor and the two anonymous reviewers for their valuable comments which helped us to improve the manuscript’s quality. We also thank GAMA team, especially Patrick Taillandier, Ahmed Laatabi and Quang Nghi Huynh for their help and assistance in the programming part. We are grateful to Coralie Fritsch for her help and advices in the conception of our IBM and to Santosh Sathe for his precious biological explanations.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Ilhem Bouderbala
    • 1
    • 2
    • 3
    Email author
  • Nadjia El Saadi
    • 2
  • Alassane Bah
    • 4
  • Pierre Auger
    • 1
    • 3
  1. 1.IRDUMI 209, UMMISCOBondyFrance
  2. 2.Laboratoire de Modélisation de Phénomènes Stochastiques (LAMOPS)ENSSEAAlgiersAlgeria
  3. 3.Sorbonne Université, UMMISCO, UMI 209ParisFrance
  4. 4.UMI 209, UMMISCO (IRD-Sorbonne Université), ESP-UCADDakarSenegal

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