Comparative performances of new and existing indices of crown asymmetry: an evaluation using tall trees of Eucalyptus pilularis (Smith)

Over the past 50 years, crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address specific objectives related to tree growth and competition, stand dynamics, stem form, crown structure and treefall risks. Although sharing some similarities, these indices are largely incoherent and non-comparable as they differ not only in the scale but also in the direction of their values in indicating the degree of crown asymmetry. As the first attempt at devising normative measures of crown asymmetry, we adopted a relative scale between 0 for perfect symmetry and 1 for extreme asymmetry. Five existing crown asymmetry indices (CAIs) were brought onto this relative scale after necessary modifications. Eight new CAIs were adapted from measures of circularity for digital images in computer graphics, indices of income inequality in economics, and a bilateral symmetry indicator in plant leaf morphology. The performances of the 13 CAIs were compared over different numbers of measured crown radii for 30 projected crowns of mature Eucalyptus pilularis trees through benchmarking statistics and rank order correlation analysis. For each CAI, the index value based on the full measurement of 36 evenly spaced radii of a projected crown was taken as the true value in the benchmarking process. The index (CAI13) adapted from the simple bilateral symmetry measure proved to be the least biased and most precise. Its performance was closely followed by that of three other CAIs. The minimum number of crown radii that is needed to provide at least an indicative measure of crown asymmetry is four. For more accurate and consistent measures, at least 6 or 8 crown radii are needed. The range of variability in crown morphology of the trees under investigation also needs to be taken into consideration. Although the CAIs are from projected crown radii, they can be readily extended to individual tree crown metrics that are now commonly extracted from LiDAR and other remotely sensed data. Adding a normative measure of crown asymmetry to individual tree crown metrics will facilitate the process of big data analytics and artificial intelligence in forestry wherever crown morphology is among the factors to be considered for decision making in forest management.