A similarity law in botanic. The case of hydraulic conductivity of trees

Abstract

The hydraulic conductivity of xylem vascular systems is modelled via the Verhulst differential equation with the introduction of relevant dimensionless quantities. Sap pressure is scaled to the geometrical and elastic properties of the xylem tubes, and cavitation events are considered as a limited growth process. The self-similar solution of Verhulst equation is a sigmoidal function, that is the same empirical correlation used to fit the experimental data. An important result of this approach is to reveal the existence of a control parameter. This number, which embodies morphological and physicochemical properties of vascular system, characterizes the discharge of tense fluids.The theoretical predictions are in good agreement with experimental data.