Geodesic
Oscillations in Functional Structural Plant Growth Models
A. Mathieu1 ; V. Letort2 ; P.H. Cournède2 ; B.G. Zhang3 ; P. Heuret4 ; P. de Reffye5
1 AgroParisTech, UMR EGC (1091), Grignon, France
2 Ecole Centrale Paris, MAS, Châtenay-Malabry, France
3 China Agricultural University, College of Resources and Environmental Sciences, Beijing, China
4 INRA, UMR EcoFoG (745), French Guyana, Kourou, French Guyana
5 CIRAD, UMR AMAP, Montpellier, France
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 6, pp. 47-66.

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The dynamic model of plant growth GreenLab describes plant architecture and functional growth at the level of individual organs. Structural development is controlled by formal grammars and empirical equations compute the amount of biomass produced by the plant, and its partitioning among the growing organs, such as leaves, stems and fruits. The number of organs initiated at each time step depends on the trophic state of the plant, which is evaluated by the ratio of biomass available in plant to the demand of all the organs. The control of the plant organogenesis by this variable induces oscillations in the simulated plant behaviour. The mathematical framework of the GreenLab model allows to compute the conditions for the generation of oscillations and the value of the period according to the set of parameters. Two case-studies are presented, corresponding to emergence of oscillations associated to fructification and branching. Similar alternating patterns are commonly reported by botanists. In this article, two examples were selected: alternate patterns of fruits in cucumber plants and alternate appearances of branches in Cecropia trees. The model was calibrated from experimental data collected on these plants. It shows that a simple feedback hypothesis of trophic control on plant structure allows the emergence of cyclic patterns corresponding to the observed ones.
DOI : 10.1051/mmnp/20127603

A. Mathieu 1 ; V. Letort 2 ; P.H. Cournède 2 ; B.G. Zhang 3 ; P. Heuret 4 ; P. de Reffye 5

1 AgroParisTech, UMR EGC (1091), Grignon, France
2 Ecole Centrale Paris, MAS, Châtenay-Malabry, France
3 China Agricultural University, College of Resources and Environmental Sciences, Beijing, China
4 INRA, UMR EcoFoG (745), French Guyana, Kourou, French Guyana
5 CIRAD, UMR AMAP, Montpellier, France 
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A. Mathieu; V. Letort; P.H. Cournède; B.G. Zhang; P. Heuret; P. de Reffye. Oscillations in Functional Structural Plant Growth Models. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 6, pp. 47-66. doi : 10.1051/mmnp/20127603. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127603/

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