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

Lai Zhou,Saeed Sajjad,Kok Kian Yong,Yaxin Zhang,Keyi Chen,Yujun Sun,Bo Zhang

doi:10.3390/f11020183

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.

Highlights

The relationship between diameter at breast height (DBH) and tree height (H) is an important factor in forest research and is often used to estimate forest resources and wood production [1,2,3].Forests 2020, 11, 183; doi:10.3390/f11020183 www.mdpi.com/journal/forestsIn the study of forest ecology and forest management, the height-diameter (H-D) relationship is one of the most important elements in estimating the stand volume and biomass, and is used as a reliable indicator of forest growth and sustainable forest management [4,5,6]
The difference in the DBH between the competition levels ranged from 11.33% to 23.31% with the increase in competitive pressure (D0 to D1 level), while the difference in tree height ranged from 5.78% to 17.65%
Quantile regression are obvious: the fitted of the model follows of the the limitations of quantile regression arecurve obvious: the fitted curvethe of distribution the model follows observed data and the basic shapes dictated by the quantile regressions

Summary

Introduction

The relationship between diameter at breast height (DBH) and tree height (H) is an important factor in forest research and is often used to estimate forest resources and wood production [1,2,3]. In the study of forest ecology and forest management, the height-diameter (H-D) relationship is one of the most important elements in estimating the stand volume and biomass, and is used as a reliable indicator of forest growth and sustainable forest management [4,5,6]. Parresol [9] described the relationship between the height and diameter of a stem as important components in yield estimation, stand description and damage appraisal. The H-D model has been widely used as an important method for obtaining tree heights and evaluating forest productivity in even or uneven-aged forests [10,11]. The H-D model varies between stands and species; depending on the variables used, the models were classified into two types: the locally applied model and the generalized use model [13,14]

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