A 3D Individual-Based Model to Study Effects of Chemotaxis, Competition and Diffusion on the Motile-Phytoplankton Aggregation
- 144 Downloads
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.
KeywordsIndividual-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.
- Bowie GL, Mills WB, Porcella DB, Campbell CL, Pagenkopf JR, Rupp GL, Johnson KM, Chan P, Gherini SA, Chamberlin CE (1985) Rates, constants, and kinetics formulations in surface water quality modeling, vol 600. US Environmental Protection Agency, Washington, D.C.Google Scholar
- Campillo F, Joannides M (2009) A spatially explicit Markovian individual-based model for terrestrial plant dynamics, pp 1–31. arXiv:09043632
- DeAngelis DL, Grimm V (2013) Individual-based models in ecology after four decades. F1000prime reports 6:39–39Google Scholar
- El Saadi N (2004) Modélisation et études mathématique et informatique de populations structurées par des variables aléatoires. Application à l’agrégation du phytoplancton. Ph.D. thesis, École Doctorale des Sciences Exactes et de leurs Applications, Université de Pau et des pays de l’AdourGoogle Scholar
- El Saadi N, Arino O (2006) A stochastic modelling of phytoplankton aggregation. ARIMA 5:80–94Google Scholar
- El Saadi N, Bah A (2012) Numerical treatment of a nonlocal model for phytoplankton aggregation. Appl Math Comput 218(17):8279–8287Google Scholar
- Fritsch C, Campillo F (2017) Models of chemostat. https://github.com/coraliefritsch/modelsOfChemostat. Accessed 16 Feb 2017
- Grignard A, Taillandier P, Gaudou B, Vo DA, Huynh NQ, Drogoul A (2013) Gama 1.6: advancing the art of complex agent-based modeling and simulation. In: Boella G, Elkind E, Savarimuthu BTR, Dignum F, Purvis MK (eds) Proceedings of 16th international conference on PRIMA 2013: principles and practice of multi-agent systems, Dunedin, New Zealand, 1–6 Dec 2013. Springer, Berlin, pp 117–131Google Scholar
- Grünbaum D, Okubo A (1994) Modelling social animal aggregations. In: Levin SA (ed) Frontiers in Mathematical Biology. Lecture Notes in Biomath, vol 100. Springer, Berlin, pp 296–325Google Scholar
- Smoluchowski V (1917 ) Versuch einer mathematischen theroie der koagulationskinetik kollider losungen. Z Phys Chem 92:129–168 Google Scholar