Modeling tree crown dynamics with 3D partial differential equations

Robert Beyer (1, 2) , Véronique Letort (1) , Paul-Henry Cournède (3)

1 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
2 DIGIPLANTE - Modélisation de la croissance et de l'architecture des plantes
3 Laboratoire de Mathématiques Appliquées [Paris]

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

Mots clés: crown plasticity; competition for light; Beer-Lambert's law; leaf area density; continuity equation; functional-structural plant model

Domaines: Systèmes dynamiques [math.DS]; Amélioration des plantes

Robert Beyer, Véronique Letort, Paul-Henry Cournède. Modeling tree crown dynamics with 3D partial differential equations. Frontiers in Plant Science, 2014, 5, pp.329. ⟨10.3389/fpls.2014.00329⟩. ⟨hal-01272213⟩