The theory of tree bole and branch form

Working from the general postulate that natural selection of plant form operates so as to maximize the survival potential of a species, this paper examines the hypothesis that the mechanical support of tree foliage must approach optimality in the use of wood, i.e., that tree stems and branches will have "optimal form" with respect to the amount of support tissue. Mathematical models of bole and branch form are presented, based on the proposition that either wind or gravity are the primary limiting factors for tree size and shape. Predictions of trunk and branch diameter as a function of tree size were tested with dimensional measurements of Populus tremuloides. The individual stems were selected from close-grown stands of differing ages. For small and intermediate trees, trunk diameter is such that stems have only 1.6 times as much wood as the minimum required to keep the tree from buckling under its own weight due to elastic instability. Branch diameters are shown to be close to the minimum required to maintain the spatial position of growing branches, as well as withstand wind forces. This minimal branch cost not only reduces the load which the stem must support against elastic instability, but allows the crown to flex in high winds. The flexing, in turn, reduces the drag force exerted by the wind on the trunk. Thus, the hypothesis that the observed tree form is an optimal design cannot be rejected on the basis of these results. Additional studies are planned with respect to optimal foliage distribution.