Live Crown Ratio Models for Loblolly Pine (Pinus taeda) with Beta Regression

The growth and production potential of a tree depends on its crown dimensions as these are closely related to a tree’s photosynthetic capacity. However, tree crowns have been studied less compared to their main stems because of their lower market value and because the measurement of crown dimensions, such as crown volume or surface area, is difficult. Frequently, an individual tree’s live crown ratio (LCR) is predicted by linear or nonlinear models that are a function of easy-to-measure dendrometric variables using ordinary least-squares techniques. Using the long-term data from established genetic and spacing trials, we developed and evaluated the predictive performance of three nonlinear models and introduced a new generalized linear model for predicting LCR. The nonlinear models were fit using exponential, Weibull, and Richards functions. The generalized linear model was based on beta regression. This resulted in a slightly smaller error than the other models in predicting the LCR of loblolly pine trees used in this study. Crown ratio is measured in percentage unit and should be modeled using generalized linear models that assume a beta distribution for error terms.