Variation of leaf shape with tree size: a case study using Decne.

The Montgomery equation (ME) assumes that leaf area () is proportional to the product of leaf length () and width (). Leaf shape is found to determine the ME's proportionality coefficient, i.e., the Montgomery parameter (MP). However, prior work seldom reported the influence of tree size (reflected by the diameter at breast height, DBH) on leaf shape and size. In the present study, we sampled 840 leaves from six trees of , with 140 leaves for each tree. Three leaf-shape indices were measured for each leaf, viz. the width to length ratio (/), a leaf roundness index which indicates the extent to which the leaf shape approaches a circular leaf, and the centroid ratio, defined as /, where is the distance from the leaf base to the point on the leaf length axis where the leaf width is a maximum. For each tree, the ME was investigated in two ways, one being that was assumed to be proportional to the product of and , and the second being a power-law equation which assumed an allometric relationship between and , i.e., (), where α is a constant to be estimated. The centroid ratio slightly decreased with increasing DBH, indicating that larger trees tend to have more ovate leaves than elliptical leaves. However, DBH did not significantly affect the ratio / nor the leaf roundness index. The estimated MP for the pooled data was 0.6466, and it was not statistically affected by DBH. The numerical value of α was found to approximate unity. The percent error between ME and the power-law equation was smaller than 5%, which means that there is no need to use the power-law equation to describe the relationship between and . ME is valid for the calculation of at the individual tree level and for the pooled data of all trees. The present study indicates that the influence of DBH on MP can be neglected when calculating , and any easily accessible trees can be selected to examine the versus isometric relationship.