Abstract
We attempted to derive the vertical distribution of annual ring width from the apex to the butt of a stem from the following assumptions: 1) The crown profile of leaves is expressed in terms of the beta distribution as a function of tree height. 2) The photosynthetic substance produced at each position within the crown flows into phloem of the stem according to the beta distribution as a function of time. First, we adopted a generalized random walk with two boundary conditions, one of which is an elastic barrier at the butt and another is an absorbing barrier at roots, for expressing the movement of the substance passing through the phloem. As a next step, we applied a diffusion equation with the third kind of boundary conditions to the movement of the substance. The vertical distribution obtained from these models simulated actual one, which tends to increase downwards in the upper part, decrease in the middle part, and increase in the lower part of the stem.
