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

Abstract

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.

Estimated biomass carbon in thinned Cunninghamia lanceolate plantations at different stand-ages

“…At the same time, the increasing rate between height and DBH in the medium density always remained constant throughout the four ages. These results concur with those from a recent study where changes of height-DBH relationship were found among different competitions that were derived from stand density (Zhang et al 2020). However, the height-DBH relationship among different densities needs to be tested in more regions to further confirm the response of regression coefficients to the variation of densities.…”

Stochastic Models to Qualify Stem Tapers

“…In this study, the developed models are nondeterministic models that consider both the symmetric and asymmetric diffusions of stem diameter at a particular height [21]. Multiple regression models that describe stem tapers have been proposed, traditionally incorporating the diameter at breast height and tree height as the independent variables [14][15][16][17][18][19] or using additional independent variables such as the density [18], crown ratio [33], and many more [34,35]. The newly developed SDE models are affected by the probability density function of the relative diameter, which changes among the relative heights.…”

“…For the illustration plan, three stems from the complete dataset, corresponding to large, medium, and small trees were selected. Quantile regression is a method used to estimate the full conditional distribution of dependent variables [35,38]. Information about the distribution of diameters at any specified height is useful, for example, in understanding tree diameter dynamics against the tree height for the prediction of stem abnormality and for production management.…”

“…The SDE stem taper models enables one to define any moment of stem diameter evolution. The main characteristics of the stem taper process focus on the mean function, defined by Equations (21)- (28), and the p-quantile (0 < p < 1) functions, which, for Models 1 and 3, can be formulated in the following forms, respectively: Quantile regression is a method used to estimate the full conditional distribution of dependent variables [35,38]. Information about the distribution of diameters at any specified height is useful, for example, in understanding tree diameter dynamics against the tree height for the prediction of stem abnormality and for production management.…”

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

“…To achieve reliable predictions of tree height, European forest statisticians have applied different techniques, such as generalized height-diameter models that include additional stand variables [8]. A generalized height equation evaluates the contribution of stand attributes, such as the stand density per hectare, the basal area per hectare, the quadratic mean diameter, and others in height-diameter models [9,10]. The inclusion of stand variables improves the predictive capacity of the selected height-diameter equation, but this technique requires additional sampling effort and reduces its practical application.…”