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

In a fractal 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.

[1]  L. Pagès,et al.  Growth and development of root systems: Geometrical and structural aspects , 1990 .

[2]  Meine van Noordwijk,et al.  Proximal root diameter as predictor of total root size for fractal branching models , 1994, Plant and Soil.

[3]  Alastair H. Fitter,et al.  Architectural analysis of plant root systems , 1992 .

[4]  Alastair H. Fitter,et al.  Fractal Characterization of Root System Architecture , 1992 .

[5]  A. Bell,et al.  Branching patterns: the simulation of plant architecture. , 1979, Journal of theoretical biology.

[6]  Alastair H. Fitter,et al.  The Topology and Geometry of Plant Root Systems: Influence of Watering Rate on Root System Topology in Trifolium pratense , 1986 .

[7]  T. Ericsson.  Effects of varied nitrogen stress on growth and nutrition in three Salix clones , 1981 .

[8]  R. J. Rayner.  New observations on Sawdonia ornata from Scotland , 1983, Transactions of the Royal Society of Edinburgh: Earth Sciences.

[9]  M. van Noordwijk,et al.  Root functions in agricultural systems , 1991 .

[10]  R. J. Rayner.  New finds of Drepanophycus spinaeformis Göppert from the Lower Devonian of Scotland , 1984, Transactions of the Royal Society of Edinburgh: Earth Sciences.

[11]  Akira Yamauchi,et al.  Fractal Analysis of Plant Root Systems , 1989 .

[12]  John A. Milburn,et al.  Water flow in plants , 1979 .

[13]  M. van Noordwijk,et al.  Peltophorum Pterocarpa (Dc.) Back (Caesalpiniaceae), a Tree with a Root Distribution Suitable for Alley Cropping on Acid Soils in the Humid Tropics , 1991 .

[14]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[15]  C. J. Keijzer,et al.  Xylem pathways in rose plants in relation to basal shoot development , 1993 .

[16]  A. Cayley Esq..  LVIII. On the analytical forms called trees.–Part II , 1859 .

[17]  Alastair H. Fitter,et al.  Characteristics and Functions of Root Systems , 2002 .

[18]  Alastair H. Fitter,et al.  Root system architecture in relation to life history and nutrient supply , 1988 .

[19]  Arthur Cayley,et al.  The Collected Mathematical Papers: On the analytical forms called trees , 1881 .

[20]  Loïc Pagès,et al.  SARAH : modèle de simulation de la croissance, du développement et de l'architecture des systèmes racinaires , 1988 .

[21]  M. van Noordwijk,et al.  Roots, plant production and nutrient use efficiency , 1987 .

[22]  M. Seyfried.  Plant roots: The bidden half. (Books in Soils, Plants, and the Environment), Y. Waisel, A. Eshel, U. Kafkafi (Eds.). Marcel Dekker Inc., New York (1991) , 1993 .

[23]  G Sugihara,et al.  Applications of fractals in ecology. , 1990, Trends in ecology & evolution.