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

Abstract

If root systems have scale-independent branching rules, the total number of links in the root system can be predicted from the ratio of the largest and smallest root diameter. In Paper I we presented an algebraic model for a dicho-syntomous pattern (the simplest form of proportionate branching forming two equal branches at each node) and a herringbone branching model (the simplest form of determinate branching rules). Here, we present a recursive computer model and its results to analyze intermediate patterns, derived from allotomous proportionate branching (with unequal branches). The numerical and algebraic model gave the same results when applied to the same situation and parameter values.For practical applications of the relations found, a test is required on whether or not the underlying assumptions are met. To illustrate such a test, measurements of the branching pattern were made on Mondriaan's Red Tree painting. For patterns such as this tree a slight dependency of the proportionality factor on root diameter and random variability of several parameters may have to be included.

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].…”

“…The objective of our contribution is to research the ways of improving the accuracy of the fractal root model as formulated by van Noordwijk et al [21,25] for describing the architecture of a tree root system, and predicting root biomass and length. We applied the model to two tropical legume trees, Erythrina lanceolata Standley (Papilionaceae: Phaseoleae) and Gliricidia sepium (Jacq.)…”

Below- and aboveground architecture of Androstachys johnsonii prain: topological analysis of the root and shoot systems

“…Finally, assuming Δ=2, the regression through the origin (RTO) of the CSA before branching against total CSA after branching was run by using Equation 5 reported by Spek and van Noordwijk (1994).…”

“…The TI might indicate a non-herringbone branching pattern since A. johnsonii has multiple laterals per stem or taproot node. However, the herringbone mathematical tree based on which TI is calculated, as described by Fitter (1987), , Spek and van Noordwijk (1994), Larkin (1995), van Noordwijk and Purnomosidhi (1995), Richardson and zu Dohna (2003), and Riccardo (2007), has only one lateral per node, and thus, a is equal to μ, as revealed by Fitter (1991), and TI is equal to 1 (Martínez-Sánchez et al 2003). However, the maximum number of laterals per node of A. johnsonii was 4 for the shoot system and 11 for the root system, making μ considerably larger than a, and thus, TI was lesser than 1 and closer to 0.53.…”