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

A 'pipe-stem' model was used to derive algebraic relations between total root size and proximal root diameter for determinate and proportionate branching patterns. To predict root length from the proximal root diameter 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