Predicting Tree Height-Diameter Relationship from Relative Competition Levels Using Quantile Regression Models for Chinese Fir (Cunninghamia lanceolata) in Fujian Province, China

The importance of the height-diameter (H-D) relationship in forest productivity is well known. The general nonlinear regression model, based on the mean regression technical, is not able to give a complete description of the H-D relationship. This study aims to evaluate the H-D relationship among relative competition levels and develop a quantile regression (QR) model to fully describe the H-D relationship. The dominance index was applied to determine the relative competition levels of trees for the Chinese fir. Based on the basic Weibull growth model, the mean regression for five relative competition levels and 11 QR models was constructed with 10-fold cross-validation. We have demonstrated that the H-D relationship for the Chinese fir strongly correlated with relative competition states, but the five curves from mean regression models did not show a notable difference between the trends of H-D relationship under different competition levels. Similar regression results were found in QR models of the specific quantiles; the average tree height of five competition levels varied between 5.78% and 17.65% (i.e., about 0.06 and 0.18 quantiles). In addition, some special curves of the H-D relationship such as the QR models of the 0.01 and 0.99 quantile showed the H-D relationship under certain conditions. These findings indicate that the QR models not only evaluated the rates of change of the H-D relationships in various competition levels, but also described their characteristics with more information, like the upper and lower boundary of the conditional distribution of responses. Although the flexible QR curves followed the distribution of the data and showed more information about the H-D relationships, the H-D curves may not intersect with each other, even when the trees reached their maximum height. Hence, the QR model requires further practice in assessing the growth trajectory of the tree's diameter or tree height to gain better results.