Structure and fractal dimensions of root systems of four co-occurring fruit tree species from Botswana

Abstract

-Coarse root systems of four different fruit tree species from southern Africa were completely excavated and semi-automatically digitized. Spatial distributions of root length were determined from the digitally-reconstructed branching systems. Furthermore, the fractal characteristic of the coarse root systems was shown by determining the box-counting dimensions. These quantitative methods revealed architectural differences between the species, probably due to different ecophysiological strategies. For fine root samples, which were taken before digging out the whole systems, fractal analysis of the planar projections showed no significant inter-species differences. Methodologically, the study underlines the usefulness of digital 3-D reconstruction in root research. root / digital reconstruction / fractal / architectural analysis / coarse root Résumé -Structures et dimensions fractales des systèmes racinaires provenant de quatre espèces d'arbres fruitiers de Botswana. Des systèmes de grosses racines, provenant de quatre espèces différentes d'arbres fruitiers d'Afrique du Sud, ont été complètement déterrés et digitalisés semi-automatiquement. Les distributions spatiales des longueurs de racines ont été calculées à partir des maquettes informatiques reconstituées. En outre, le caractère fractal des systèmes de grosses racines a été prouvé par une déter-mination de dimensions utilisant la méthode du comptage de boites. Ces méthodes quantitatives révèlent des différences architecturales entre les espèces, résultant probablement de différentes stratégies écophysiologiques. Pour les échantillons de racines fines, obtenus avant l'excavation des systèmes complets, l'analyse fractale des projections planes n'a pas montré de différences significatives entre les espèces. Concernant la méthode, l'étude fait apparaître l'apport de la reconstruction digitale 3-D dans le domaine de la recherche sur les appareils racinaires. racine / reconstruction digitale / fractal / analyse architectural / racine gros

Enhanced possibilities for analyzing tree structure as provided by an interface between different modelling systems

“…Various definitions of "dimension" and "fractal" are used in the mathematical literature (see Edgar 1990, Peitgen et al 1992). Here we restrict ourselves to box counting dimension as the most commonly used variant for botanical objects (Stoll 1995, Berntson and Stoll 1997, Oppelt et al 2000. Basically, it describes the relationship between the number of equal-sized cubic cells or boxes needed to cover the whole object when it is embedded in a 3-D grid and the resolution at which the object is observed, i.e.…”

A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns

“…Unfortunately, such a technique always under-estimates the actual fractal dimension [13], and so is not accurate. Recently BCM was used on 3D digitized root systems [10]; however, the accuracy of the estimated values could not be evaluated. In this paper, we study the application of the BCM to both artificial and real 3D plant foliage.…”

“…This parameter is of major importance in the study of irregularity: it characterizes the way plants physically occupy space. Most of these studies were carried out using the classical box counting method (BCM) [2] on woody structures, and especially on root systems [8][9][10]. This method consists of immersing the studied object in a grid with uniform cell size and studying the variation of the number of grid cells intercepted by the plant as the size of the cells decreases.…”

A tool to model 3D coarse-root development with annual resolution

“…The Laser ScanArm applied consists of a tactile probe for point measurements. This could be used for additional topological measurements comparable to the digitizer as it was already successfully applied (Danjon et al 1999;Oppelt et al 2000).…”