Abstract
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.
Similar content being viewed by others
Abbreviations
- CSA:
-
cross sectional area
References
Bell, A D, Roberts, D and Smith, A 1979 Branching patterns: the simulation of plant architecture. J. Theor. Biol. 81, 351–375.
Brown, S, Gillespie, A J R and Lugo, A E 1989 Biomass estimation procedures for tropical forests with applications to forest inventory data. For. Sci. 35, 889–902.
Cayley, A 1875 On the analytical forms called trees. Philos. Mag. 18, 374–378.
De Willigen P and Van Noordwijk M 1987 Roots for plant production and nutrient use efficiency, Doctoral thesis Agricultural University, Wageningen, 282 p.
Ericsson, T 1981 Effects of varied nitrogen stress on growth and nutrition of three Salix clones. Physiol. Plant. 51, 423–429.
Fitter, A H 1988 The topology and geometry of plant root systems: influence of watering rate on root system topology in Trifolium pratense. Ann. Bot. 58, 91–101.
Fitter, A H, Nicholas, R and Harvey, M L, 1988 Root system architecture in relation to life history and nutrient supply. Funct. Ecol. 2, 345–351.
Fitter, A H 1991 Characteristics and functions of root systems. In Plant Roots, the Hidden Half. Eds. Y.Waisel, A.Eshel and U.Kafkafi. pp 3–25 Marchel Dekker Inc, New York.
Fitter, A H and Stickland, T R 1991 Architectural analysis of plant root systems 2. Influence of nutrient supply on architecturally contrasting plant species. New Phytol. 118, 383–389.
Fitter, A H and Stickland, T R 1992 Fractal characterization of root architecture. Funct. Ecol. 6, 632–635.
Kuiper L C, Bakker A J J and Van Dijk G J E 1990 Stem and crown parameters related to structural root systems of Douglas fir. Wageningen Agric. Univ. Papers 90–6, 57–67.
Lyford, W H 1975 Rhizography of non-woody roots of trees in the floor. pp 179–197. In The Development and Function of Roots. Eds. J GTorrey and D TClarkson. Third Cabot symposium, Academic Press, London.
Mandelbrot, B B 1983 The Fractal Geometry of Nature. Freeman, New York.
Marcelis-VanAcker, C A M, Keijzer, C J and Van dePol, P A 1993 Xylem pathways in rose plants in relation to basal shoot development. Acta Bot. Neerl. 42, 313–318.
Milburn, J A 1979 Water Flow in Plants, Longman, London.
Pagès, L and Kervella, J 1990 Growth and development of root systems: geometrical and structural aspects. Acta Biotheor. 38, 289–302.
Rayner, R J 1983 New observations on Sawdonia ornata from Scotland. Trans. R. Soc. Edinburgh: Earth Sciences 74, 79–93.
Rayner, R J 1984 New finds of Drepanophycus spinaeformis Goppert from the Lower Devonian of Scotland. Trans. R. Soc. Edinburgh: Earth Sciences 75, 353–363.
Spek, L Y and VanNoordwijk, M 1994 Proximal root diameter as predictor of total root system size for fractal branching models. II. Numerical model. Plant and Soil 164, 119–127.
Sugihara, G and May, R M 1990 Applications of fractals in ecology. Trends Ecol. Evol. 5, 79–86.
Tatsumi, J T, Yamauchi, A and Kono, Y 1989 Fractal analysis of plant root systems. Ann. Bot. 64, 499–503.
Van Noordwijk M 1987 Methods for quantification of root distribution pattern and root dynamics in the field. pp 263–281. 20th Colloq Intern Potash Inst, Bern.
VanNoordwijk, M and DeWilligen, P 1991 Root functions in agricultural systems. In Plant Roots and their Environment. Eds. HPersson and B LMcMichael. pp 381–395, Elsevier, Amsterdam.
VanNoordwijk, M, Hairiah, K, Syekhfani, M S and Flach, B 1991 Peltophorum pterocarpa a tree with a root distribution suitable for alley cropping. In Plant Roots and their Environment. Eds. HPersson and B LMcMichael. pp 526–532, Elsevier, Amsterdam.
Waring, R H and Schlesinger, W H 1985 The carbon balance of trees. In Forest Ecosystems, Concepts and Management. Academic Press, Orlando, Florida.
Werner, C and Smart, J S 1973 Some new methods of topologic classification of channel networks. Geogr. Anal. 5, 271–295.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Noordwijk, M., Spek, L.Y. & de Willigen, P. Proximal root diameter as predictor of total root size for fractal branching models. Plant Soil 164, 107–117 (1994). https://doi.org/10.1007/BF00010116
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00010116