Size-dependent Allometry of Tree Height, Diameter and Trunk-taper

Abstract

The allometry of tree height with respect to trunk diameter and the allometry of trunk diameter with respect to distance from the top of the tree (i.e. trunk taper) were determined for 27 Robinia pseudoacacia trees differing in age and size growing in an open field. The allometric (scaling) exponent for height was > 1 for small and young trees and decreased to 2/3 and then 1/2 as tree size and age increased. Similarly, the exponent for taper was > 1 near the tips of young and old trunks and converged onto values of 2/3 and 1/2 toward the base of mature tree trunks. These observations indicate that a single 'optimal mechanical design principle' (i.e. elastic, stress or geometric self-similarity) neither holds true throughout the lifetime of R. pseudoacacia trees, nor does a single design principle govern the taper of a trunk throughout its entire length. Rather, over the course of growth and development, the allometry of R. pseudoacacia tree height and trunk taper progressively changes, complying with geometric self-similarity for young plants (and young portions of old plants) and subsequently giving the appearance of elastic or stress self-similarity as plants (or portions of plants) get older and therefore larger. Analyses of published (and new) data suggest that the conclusions drawn for R. pseudoacacia trees are likely to hold true for other tree species because stem growth in diameter is 'indeterminate' whereas growth in overall tree height is asymptotic and therefore essentially 'determinate'.