Several theories have been put forwarded to explain the variation in taper from tree to tree

Metzger, a German Forester proposed the tree stem as cantilever beam of uniform size against the bending force of the wind

The stem of the tree is built in such a way as, with minimum of material, to offer uniformly the greatest resistance to the stress to which it is subjected. The wind pressure acts on the crown and is conveyed to the lower part of the stem in an increasing measure with the increasing length of the bole. Thus the greatest pressure is exerted at the base and there is a danger of tree snapping at the place

To counteract this tendency, the tree reinforces along the tree stem so that it affords a uniform resistance all along its length to the pressure

As the pressure is in the upper part of the tree is less, due to smaller length of lever in that portion it is allocated lesser growth material than lower part where the pressure gets increased with increased length of bole.

The pressure of wind on crown keeps on changing as the tree is growing in open or crowded portion. Trees growing in complete isolation have larger crowns and so the pressure exerted on them is the greatest.

Mathematically, according to rule of mechanics,

S=(P*l/d³)*32/π

As the P in case of tree consists of components, W = wind pressure per unit area and F = crown area, it will be P=W*F then

S=(W*F*l/d³) *32/π = (W*F*l*32/d³*π)

For a given tree W, S, F can be considered as constant,therefore d³=kl, where k is constant