On the shape of trees

Abstract

Answers to questions concerning the broad-scale characteristics of trees are sought in the analytical development of a simple model in which the rate of photosynthesis is controlled by leaf water potential and by access to direct solar radiation. These concepts are introduced first in a simple discussion of the single isolated tree. Later they are applied to the forest-stand situation. Expressions are derived which relate growth rate (per tree and per unit area of ground) to the height, shape, spatial separation and lifetime of the trees; to the environmental conditions such as the average solar elevation, potential evaporation E p and soil moisture content; and to two main physiological factors—the proportionality factor z 0 relating potential drop per unit length of trunk or branch to potential evaporation, and the critical leaf water potential ψ 0 at which net photosynthesis is zero. Accepting the assumptions in the model, the following are examples of its predictions. It is shown that at optimum tree spacing the photosynthesis per unit area of ground may be greatest for the shortest trees (grass ?). It is shown that for a given environment there may be an optimum tree spacing yielding maximum photosynthesis per unit area of ground averaged over the lifetime of the trees; that this maximum decreases with increasing ultimate tree height (which in turn is determined by E p, z 0 and ψ 0); and that this maximum and this optimum spacing decrease with decreasing average soil moisture. It is shown that there can be an optimum leaf distribution which in general is such that leaf density increases radially from the trunk. It is shown how the optimum shape of trees in a forest might be expected to alter with their size. In general it appears that the concepts discussed here may be useful in explaining the evolutionary development of many of the broad features of tree growth.