Southern pine stem form defined through principal component analysis

Abstract

Principal component analysis, a multivariate statistical procedure, was used to develop equations for defining stem taper of loblolly (Pinustaeda L.) and slash pine (P. elliottii Engelm.) in Louisiana, U.S.A. Four sets of data were used (three of loblolly and one of slash pine). Data included individual tree diameter measurements at the ground line, 0.02, 0.04, 0.06, 0.08, and at each 0.1 of total height. Thus each data-set i included ni trees, each with 14 diameter measurements. Principal component analysis was applied to each data set and in every case a single eigenvalue absorbed more than 99% of the total variance. A graph of the elements of the eigenvector associated with the principal eigenvalue, plotted over the appropriate proportional height, resembled the mean stem taper of the trees in the data set. Within a data set, no differences were found in stem form among diameter at breast height (dbh) or height classes but trees with crown ratios greater than 0.51 did appear to have more taper in the upper 0.3 of the bole. Apparent differences in stem form were noted among trees growing in different areas of the state, and between the two species when growing in the same area. The first eigenvector can be interpolated by various methods to obtain a model for stem taper. We used a regression technique, with the first eigenvector as the dependent variable, and the corresponding proportional heights and their powers as independent variables. The equations thus developed are useful for determining volumes. We believe that the curve of the eigenvector for the first principal component is, at least, an approximation of a descriptive law of stem taper.