Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Modeling Tree Crown Expansion with a Biomass Transport Equation
Robert Beyer

Last modified: 2014-06-12


As a middle way between geometrically detailed organ-based and large scale rigid tree models, we characterize the spatial distribution of a tree's foliage by means of the leaf (area) density.
For a given density, Beer-Lambert's law allows to generically deduce the local light incidence in the crown. A leaf's production of new biomass is proportional to its evaporative flux, which, other things being equal, (i) increases linearly with increasing light incidence and (ii) decreases sigmoidly with decreasing leaf water potential. Leaf water potential, in turn, decreases with (iii) increasing height of the leaf's position, (iv) decreasing soil water potential and with (v) increasing evaporative flux. The unique balance between the two counteracting mechanisms (ii) and (v) can be computed, yielding the local biomass production of foliage as a function of light and water availability.
The gradient of biomass production per leaf area density defines a vector field along which produced biomass is transported before eventually being allocated, thus formalizing a spatial expansion in the locally optimal direction with regard to future biomass production.
Finally, the Pipe Model Theory provides a means to partition available biomass between foliage and (mechanically and hydraulically supporting) sapwood.
We compared the model to long-term experimental data from three stands of European Beech, differing in stand density, to demonstrate its adaptiveness.


Functional-Structural Plant Model, Advection Equation, Optimization, Competition