Proximal root diameter as predictor of total root size for fractal branching models

Abstract

In a fractai branching pattern the same rules govern branching at each subsequent level. The initial size (diameter) and the essential branching rules thus contain the information required to construct the whole pattern. If root branching patterns have fractal characteristics, measurement of the proximal root diameter at the stem base and the branching rules as observed anywhere in the root system, would be enough to predict total root length, root diameter distribution and root length per unit dry weight (specific root length).A 'pipe stem' model is used to derive algebraic relations between total root size and proximal root diameter for two classes of branching patterns, determinate and proportionate. To predict total root length from the proximal root diameter, at least information is needed on the minimum root diameter, the average length of internal and external links (segments) and the proportionality factor between total cross sectional areas before and after branching. For the length of the longest root or the specific root length further information on the branching rules is needed, as it is highest for determinate and proportionate branching rules, respectively. Abbreviations:CSA -cross sectional area.

Tree or shrub: a functional branch analysis of Jatropha curcas L.

“…Jatropha roots typically are intermediate in branching pattern between a herringbone and dichotomy pattern (van Noordwijk et al 1994). Herringbone root systems minimise intra-plant root competition so are more effective at resource acquisition, despite their roots being larger, and more resource demanding.…”

“…A high p value indicates that the link cross-sectional area before branching was greater than the sum of the cross-sectional area of links after branching. When added to the fact that one branch had a greater cross sectional area (dominant branch) in comparison with the others (q value 0.76), this indicates a herringbone root branching pattern (van Noordwijk et al 1994). The herringbone pattern for jatropha root had one main axis (mother branch) that started at the base proximal root and branched to form Diameter of middle stem (cm) 9.36 2.23 n.a n.a…”

“…The pipe model hypothesis is that the crosssectional area (sum of squared diameters) of branches is equal to that of the preceding stem or branch. FBA models produce equation coefficients that relate aboveground tree biomass to the stem diameter at breast height (DBH) or root biomass to proximal root diameter (van Noordwijk et al 1994). This eliminates, or at least reduces, the need for destructive sampling to determine biomass.…”

A fractal root model applied for estimating the root biomass and architecture in two tropical legume tree species

“…Van Noordwijk et al [21,25] proposed that fractal geometry combined with parameter estimation based on the pipe model theory [19] could be applied for describing tree root architecture. The pipe model of vascular plants is shown to be a special case of the more general fractal branching and scaling pattern in a 338 E. Salas et al variety of biological systems [26], and it thus is a valid basis for estimating the fractal parameters of a root system.…”

“…Water and nutrient absorbing fine roots are not considered here, as they are functionally different from the water and nutrient transporting coarse roots and may follow different growth patterns [20]. The basic parameters of fractal root models describe the ratio of the sum of root cross-sectional areas after a bifurcation to the cross-sectional area before bifurcation, α, and the distribution of the cross-sectional areas after bifurcation, q [21,25].…”