Topology, scaling relations and Leonardo's rule in root systems from African tree species

Aspects of root architecture, including topology, link length, diameter and scaling relations, were analyzed in excavated coarse root systems of three field-grown fruit tree species (Strychnos cocculoides Bak., Strychnos spinosa Lam. and Vangueria infausta Burch) and the fruit-bearing shrub Grewia flava DC. We investigated the root systems using semi-automatic digitizing and computer-based 3-D reconstruction techniques. Topological analysis was carried out to investigate branching patterns as basic determinants of root architecture. New topological indices were developed and revealed significant differences among the species. The different architectural strategies can be explained in terms of cost-benefit relations and efficiency in soil resource exploration and exploitation. In addition, some well-known hypotheses about geometry and scaling, most of them previously unverified by empirical observations on root systems, were tested. For practical applications, the main emphasis is on the relationship between proximal root diameter, an easily determined parameter, and several parameters describing the size of the whole root system. We also tested the "pipe stem" theory, essentially dating back to Leonardo da Vinci, which underlies many models and which we found conformed to our measurement data with reasonable accuracy. A physiological consequence of the "constant cross-sectional area rule" may be a certain homogeneity of hydraulic architecture throughout root systems.