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Beyer R, Letort V, Cournède PH. Modeling tree crown dynamics with 3D partial differential equations. Front Plant Sci. 2014;5:329doi: 10.3389/fpls.2014.00329.
Beyer, R., Letort, V., & Cournède, P. H. (2014). Modeling tree crown dynamics with 3D partial differential equations. Frontiers in plant science, 5329. https://doi.org/10.3389/fpls.2014.00329
Beyer, Robert, et al. "Modeling tree crown dynamics with 3D partial differential equations." Frontiers in plant science vol. 5 (2014): 329. doi: https://doi.org/10.3389/fpls.2014.00329
Beyer R, Letort V, Cournède PH. Modeling tree crown dynamics with 3D partial differential equations. Front Plant Sci. 2014 Jul 21;5:329. doi: 10.3389/fpls.2014.00329. eCollection 2014. PMID: 25101095; PMCID: PMC4104424.
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Front Plant Sci. 2014 Jul 21;5:329. doi: 10.3389/fpls.2014.00329. eCollection 2014.

Modeling tree crown dynamics with 3D partial differential equations.

Frontiers in plant science

Robert Beyer, Véronique Letort, Paul-Henry Cournède

Affiliations

  1. Ecole Centrale Paris, Applied Mathematics and Systems Laboratory Châtenay-Malabry, France.

PMID: 25101095 PMCID: PMC4104424 DOI: 10.3389/fpls.2014.00329

Abstract

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.

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

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