AUTHOR=Beyer Robert , Letort Véronique , Cournède Paul-Henry TITLE=Modeling tree crown dynamics with 3D partial differential equations JOURNAL=Frontiers in Plant Science VOLUME=5 YEAR=2014 URL=https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2014.00329 DOI=10.3389/fpls.2014.00329 ISSN=1664-462X 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.