Fractal analysis of the root architecture of Gliricidia sepium for the spatial prediction of root branching, size and mass:: model development and evaluation in agroforestry

Based on fractal and pipe model assumptions, a static three-dimensional model of the Gliricidia sepium root system was developed, in order to provide a basis for the prediction of root branching, size and mass in an alley cropping system. The model was built from observations about the topology, branching rules, link length and diameter, and root orientation, provided by in situ and extracted root systems. Evaluation tests were carried out at the plant level and at the field level. These tests principally concerned coefficients alpha and q - the proportionality factor alpha between total cross-sectional area of a root before and after branching, and allocation parameter q that defines the partitioning of biomass between the new links after a branching event - that could be considered as key variables of this fractal approach. Although independent of root diameter, these coefficients showed a certain variability that may affect the precision of the predictions. When calibrated, however, the model provided suitable predictions of root dry matter, total root length and root diameter at the plant level. At the field level, the simulation of 2D root maps was accurate for root distribution patterns, but the number of simulated root dots was underestimated in the surface layers. Hence recommendations were made to improve the model with regard to alpha and q. This static approach appeared to be well suited to study the root system of adult trees. Compared with explicit models, the main advantage of the fractal approach is its plasticity and ease of use.