Utilizing quantile regressions to predict vertical distribution of branch size in Larix olgensis Henry: Capturing the differentiated responses of varying branch sizes to stand and tree factors

Abstract

Branch size is a crucial characteristic, closely linked to both tree growth and wood quality. A review of existing branch size models reveals various approaches, but the ability to estimate branch diameter and length within the same whorl remains underexplored. In this study, a total of 77 trees were sampled from Northeast China to model the vertical distribution of branch diameter and length within each whorl along the crown. Several commonly used functions were taken as the alternative model forms, and the quantile regression method was employed and compared with the classical two-step modeling approach. The analysis incorporated stand, tree, and competition factors, with a particular focus on how these factors influence branches of varying sizes. The modified Weibull function was chosen as the optimal model, due to its excellent performance across all quantiles. Eight quantile regression curves (ranging from 0.20 to 0.85) were combined to predict branch diameter, while seven curves (ranging from 0.20 to 0.80) were used for branch length. The results showed that the quantile regression method outperformed the classical approach at model fitting and validation, likely due to its ability to estimate different rates of change across the entire branch size distribution. Lager branches in each whorl were more sensitive to changes in $\text{DBH}$, crown length ($\text{CL}$), crown ratio ($\text{CR}$) and dominant tree height ($H_{\text{dom}}$), while slenderness ($\text{HDR}$) more effectively influenced small and medium-sized branches. The effect of stand basal area ($\text{BAS}$) was relatively consistent across different branch sizes. The findings indicate that quantile regression is a good way not only a more accurate method for predicting branch size but also a valuable tool for understanding how branch growth responds to stand and tree factors. The models developed in this study are prepared to be further integrated into tree growth and yield simulation system, contributing to the assessment and promotion of wood quality.