Plant and Soil 209: 167–180, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. 167 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 Harry Ozier-Lafontaine ∗ , François Lecompte and Jean François Sillon INRA Centre Antilles-Guyane, Unit´ e Agrop´ edoclimatique de la Zone Caraïbe Domaine Duclos, 97170 Petit-Bourg, Guadeloupe, France Received 16 March 1998. Accepted in revised form 29 December 1998 Key words: alley cropping, self similarity, pipe model theory, three dimensional root architecture model Abstract 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 α and q — the proportionality factor α 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 α 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. Introduction In agroforestry systems, below ground complementar- ity between root systems is now considered as a key issue for a successful exploitation of soil resources. It is hence of great interest to develop accurate methods allowing a good knowledge of tree — crop root spa- tial distribution and functioning so as to explore the best rooting configuration to optimize the competition for water and nutrients (Huxley, 1996). It is also re- cognized that deep tree root systems are usually more difficult to assess than those of shorter-lived crops. However, among the various soil or plant-based ap- proaches devoted to the study of root systems (Box, ∗ FAX No: +590 941663. E-mail: ozier@antilles.inra.fr 1996), recent advances in root architecture modeling offer new possibilities for the analysis and the know- ledge of tree root systems (Van Noordwijk and Van de Geijn, 1996). On the one hand, the simulation of three- dimensional distribution of roots has been enhanced by the development of morphogenetic models such as ROOTMAP (Diggle, 1988), the model of Pagès et al. (1989), SimRoot (Nielsen et al., 1994), and the model of Clausnitzer and Hopmans (1994), provided that information about root appearance, growth, tra- jectories and branching rules is available. In these models, the influence of a variety of soil environ- mental factors such as soil strength, aeration, and temperature may be considered (Lynch and Nielsen, 1996). These approaches are, however, very exacting