Fractal analysis of foliage distribution in loblolly pine crowns

Abstract

A new method for estimating fractal characteristics (fractal dimension and foliage density) of a single crown or its portions is developed. The proposed method operates with volume and mass of natural units of the crown, such as shoots and branches, rather than with numbers of regular cubes. Fractal dimension alone is not sufficient to describe foliage distribution in the crown because it says nothing about the density of foliage at a given point. The density is defined as the ratio of foliage mass to fractal volume it occupies. Fortunately, the intercept of the regression, which contains fractal dimension as the slope, provides a measure of foliage density. Thus the method makes it possible to separate purely spatial factors represented by fractal dimension from ecophysiological effects characterized by foliage density. Application of the method showed that neither fractal dimension nor foliage density of the studied loblolly pines (Pinus taeda L.) correlates with current diameter increment. At the same time, there is a pronounced negative correlation between fractal dimension and crown size. These results suggest that as crowns become larger, the amount of foliage located at the crown periphery increases in proportion to the foliage amount inside the crown. As a spin-off of this analysis, a method for estimating relative foliage density (defined as the ratio of actual to maximal foliage mass for a given branch) is developed.