An application of mixed-effects model to evaluate the effects of initial spacing on radial variation in wood density in Japanese larch (Larix kaempferi)

The effects of initial tree spacing on wood density at breast height were examined for 22-year-old Japanese larch (Larix kaempferi). The experiment involved the use of three plots with different initial tree spacing densities (300, 500, and 1000 trees/ha). For five trees selected from each plot, the total tree height, diameter at breast height, height to the base of the live crown, and crown diameter were measured. Ring width and wood density for individual growth rings were determined by X-ray densitometry. A mixed-effects model was applied for fitting the radial variation in wood density in relation to initial spacing. Models having various mean and covariance structures were tested in devising an appropriate wood density model. The model, consisting of the mean structure with quadratic age effects and heterogeneous first-order autoregressive covariance, was able to describe the radial variation in wood density. Closer spacing of trees (1000 trees/ha) resulted in a faster increase in wood density from the pith outward than for more widely spaced trees, indicating that initial tree spacing may influence the age of transition from juvenile to mature wood.     

A method for reconstructing the development of the sapwood area of balsam fir

Leaf area is commonly estimated as a function of sapwood area. However, because sapwood changes to heartwood over time, it has not previously been possible to reconstruct either the sapwood area or the leaf area of older trees into the past. In this study, we report a method for reconstructing the development of the sapwood area of dominant and codominant balsam fir (Abies balsamea (L.) Mill.). The technique is based on establishing a species-specific relationship between the number of annual growth rings in the sapwood area and tree age. Because the number of annual growth rings in the sapwood of balsam fir at a given age was found to be independent of site quality and stand density, the number of rings in sapwood (NRS) can be predicted from the age of a tree thus: NRS = 14.818 (1 - e(-0.031 age)), unweighted R(2) = 0.80, and NRS = 2.490 (1 - e(-0.038 age)), unweighted R(2) = 0.64, for measurements at breast height and at the base of the live crown, respectively. These nonlinear asymptotic regression models based only on age, were not improved by adding other tree variables such as diameter at breast height, diameter at the base of the live crown, total tree height or percent live crown.     

广西大青山柚木人工林生长过程研究

[目的]研究柚木人工林生长过程及其与气象因子的相关性,为柚木抚育经营提供理论依据。[方法]以优良、中等和差3种生长类型的30余年生柚木人工林为对象,基于样地调查,选取优势木、平均木、被压木进行树干解析,对比分析其生长过程,应用灰色关联分析法揭示气象因子对柚木生长的影响。[结果]表明:3种生长类型林分柚木胸径、树高和材积生长过程基本一致,各分级木的生长过程亦相似,其胸径平均和连年生长量随年龄的增大呈先增加后逐渐降低的趋势,树高生长整体上呈下降趋势,材积生长则呈递增趋势。各优良林分的林木及各类型林分的优势木,其胸径、材积平均和连年生长量较大,速生期持续时间长,生长衰减慢,而其树高生长量的优势相对不明显;30余年生时柚木尚未达数量成熟龄。各类型林分间柚木生长与气象因子关系的差异仅体现在胸径,优良林分胸径连年生长量主要受极端低温影响,而中等和差林分则与年均降水量相关性最大;各分级木间柚木生长与气象因子的关系无明显差异;影响树高和材积连年生长量的最主要气象因子分别为年均降水量和年均气温。[结论]柚木各生长类型及分级木的生长过程整体趋势基本一致,其差异主要体现在生长量大小和快速生长期长短。约30年生柚木人工林仍未达到数量成熟,后期抚育经营对于其优质大径材高效培育仍不可忽视。     

Study on height growth model ofPinus koraiensis

Growth model is an efficient way to study growing process of some factors of plants quantitatively. Height growth of Korean pine (Pinus koraiensis) was studied by using Hyperbola equation, Logistic equation, Richards equation with three parameters, and Richards equation with four parameters in this paper. The results showed that Richards equation with four parameters was the most suitable and could be turned into other theoretical equations when some parameters were given different value. The maximum height of trees could be given in advance when using Richards equation with four parameters, and it was even more corresponding to reality. In addition, a height growth model with real height of fixed age as a parameter was discussed in this paper. This kind of growth model could be used to calculate height growth of a given tree effectively. Foundation item: This paper was supported by Great Item National Natural Science Foundation of China (39899370) and National Natural Science Foundation of China (NSFC39970123), and Changbai Mountain Open Research Station. Biography: DENG Hong-bing (1971-), male, Ph. Doctor, assistant research fellow in Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110015, Post-doctor in Institute of Hydrobiology, Chinese Academy of Sciences. P. R. China. Responsible editor: Song Funan     

Prediction of annual tree growth and survival for thinned and unthinned even-aged maritime pine stands in Portugal from data with different time measurement intervals

An annual individual tree survival and growth model was developed for pure even-aged stands of maritime pine in Portugal, using a large data set containing irregularly time-spaced measurements and considering thinning effects. The model is distance-independent and is based on a function for diameter growth, a function for height growth and a survival function. Two approaches are compared for modeling annual tree growth. The first approach directly estimates a future diameter or height using well-known growth functions formulated in difference form. The second approach estimates diameter or height using a function in differential form estimating the increment over a year period. In both approaches, the function parameters were related to tree and stand variables reflecting the competition status of the tree as well as of a thinning response factor. Variable growth and survival rates were assumed in the modeling approaches. An iterative method was used to continuously update tree and stand attributes using a cut-off to convert the survival probability for a living or a dead tree. The individual tree diameter growth model and the survival probability model were fitted simultaneously using seemingly unrelated regression (SUR). Parameters of the height function were obtained separately as the number of observations for height was much lower than the number of observations for diameter, which may affect the statistical inference and the estimation of contemporaneous cross-equation error correlation inherent to the system of equations. PRESS residuals were used to evaluate the predictive performance of the diameter and the height growth functions. Additional statistics based in the log likelihood function and also in the survival probability were computed to evaluate the survival function. The second modeling approach, which integrates components of growth expansion and decline, performed slightly better than the first approach. A variable accounting for the thinning response that was tested proved to be significant for predicting diameter growth, even if the model already included competition-related explanatory variables, namely the basal area of trees larger than the subject tree. However, this thinning response factor was not significant for predicting height growth.     

Difference in cutting age for highest profit by methods for calculating CO<Subscript>2</Subscript> emission trading and the price of CO<Subscript>2</Subscript>

 The amounts of CO₂ that are absorbed and emitted by forest in a model stand area were determined using two calculation methods, namely the flow approach and the stock approach for emission trading, to understand the relationships between the cutting age for the highest profit rate (CAHPR; optimum tree ages to be cut so as to maximize the profit) and (1) the prices of CO₂ and (2) the balance between CO₂ emission and absorption. The resultant CAHPR differed between these two CO₂ accounting methods, which give different tree ages for maximum log volume yield. A rise in CO₂ price caused the CAHPR to approach the tree age of maximum log volume in the flow approach method, and to deviate from the tree age of maximum log volume in the stock approach method. Even at the same CO₂ price, the CAHPR differed between the CO₂ accounting methods. At low CO₂ prices, the CAHPR did not affect situations where the difference of average profit is large by cutting age. On the other hand, the CAHPR was greatly affected at low CO₂ prices when the mean log volume growth changed with tree age. These trends were found to be universal. Received: September 18, 2001 / Accepted: October 25, 2002 Acknowledgments This study is one of the fifth science study subsidy projects of the Japan Forest Technology Association. Correspondence to:K. Sakata     

异常气候环境变化与树木年轮

介绍了国外应用统计学方法分析树木年轮,获得精度高、稳定性强的气候环境变化信息的方法;概述了环境污染、大气CO₂浓度增加与树木年轮关系的研究现状,以及异常气候环境变化对树木年轮影响的最新研究进展。     

Picea abies sapwood width: Variations within and between trees

Abstract

This study focused on the amount of sapwood and its variation by means of computed tomographic (CT) imaging. Twenty-four trees were selected from four Norway spruce [Picea abies (L.) Karst.] stands in north-eastern France, varying in age, density and fertility. In each stand, sampled trees represented the dominant, co-dominant and suppressed strata. The heartwood/sapwood boundary was detected from the CT images, and the heartwood and sapwood amount and their variations were then evaluated. At the within-tree level sapwood width was relatively constant along the tree stem above the butt swelling and below the living crown. The between-tree sapwood width variations were partially explained by the total cross-sectional area of living branches. This result opens up the possibility of investigating within-tree allometric relationships. Sapwood width was found to be highly correlated with tree slendemess (tree height/breast height diameter) and with the relative height of the crown. This suggests that sapwood width could be readily predicted from conventional forest inventory measurements. The number of sapwood rings within the stem was largely dependent on cambial age, and could be determined dynamically using the concept of mean lifetime of sapwood rings.     

Predicting Knot Diameter of Pinus sylvestris in Sweden

Average diameter of the thickest knot of each whorl within a specific stem section of Scots pine (TK) was studied using functions based on growth ring widths, diameter of dry branches, site index, stand age, and latitude. Data from the Pine Stem Bank - a database of external and internal properties where knots were detected by computerized tomography (CT) scanning - were used. A high value of the corrected coefficient of determination, R²(adj)=0.63, was found between TK and two independent variables, average width of growth rings 11 - 20 at stump height and latitude. It is argued that TK is a good parameter for describing timber quality, and that it now is predictable on standing trees as well as on existing data from the National Forest Inventory (NFI). An attempt was made to quantify the change in the TK - value by site index, tree class, age class, and region by applying functions to NFI data from 1988 - 92. In a second analysis, also based on NFI data, the TK - value had increased by 17% from 1966 to 1988 - 92. The authors believe that this is mainly a result of the silvicultural systems used and that it is possible to reverse the negative trend by changing silvicultural methods.     

基于空间结构的杉木树冠生长可视化模拟

[目的]定量研究杉木林分中不同空间结构对林木冠形生长变化的影响,实现基于空间结构的杉木树冠生长可视化模拟。[方法]以湖南省攸县黄丰桥国有林场为试验区,在林分中选择并划分空间结构单元,进行冠形和空间结构数据调查,将林木东南西北4个方向的活枝下高、冠高、冠幅作为林木冠形描述因子,将周围木影响距离、相对树高定义为水平空间结构参数Ph和垂直空间结构参数Pv,使用多元逐步回归的分析方法,分析冠形描述因子与年龄、水平、垂直空间结构参数的关系,建立不同空间结构下杉木冠形的生长变化模型。基于B样条曲线模拟杉木冠形,构建不同生长阶段的三维杉木模型,结合三维动态渲染技术,实现杉木树冠生长的可视化模拟。[结果]通过对年龄和水平、垂直空间结构参数的逐步回归分析,结果表明:林木活枝下高、冠高和年龄、垂直空间结构参数呈现显著相关关系,模型决定系数R~2分别为0.754和0.813;林木各向冠幅和年龄、水平空间结构参数呈现极显著相关关系,模型决定系数R~2为0.623。基于杉木树冠生长模型和三维动态渲染技术,实现了树冠在东南西北不同方向的生长可视化。[结论]通过划分空间结构单元的方法选择研究目标并进行数据调查,使用逐步回归的方法,分析杉木冠形数据和年龄与空间结构数据的关系,建立树冠各方向活枝下高、冠高、冠幅的生长模型,结合三维动态渲染技术,使用MOGRE三维渲染引擎作为工具,实现了基于空间结构的杉木树冠生长可视化模拟。     

Tropical Tree Growth and Longevity: Validation of Growth Simulation,a Bootstrapping Model

ABSTRACT

Growth Simulation, an analytical modeling technique, has been increasingly used in ecological studies and practical forestry applications where dendrochronology is not applicable. The technique uses randomly sampled diameter increments from tagged trees over a known time interval to assemble a statistical sample of lifetime growth trajectories. We carried out a validation of Growth Simulation using a temperate species in order to compare indirect model outputs with direct tree ring analysis. Rings were measured on sample disks cut from 55 pine branches ranging in age from 8–36 years. Assessments included lifetime growth rates, growth rate with respect to diameter and age, periodic annual increment (PAI), cross-referencing of rings by date, and autocorrelation of growth over successive periods. Tree ring analysis and Growth Simulation showed close correspondence for all parameters tested (maximum, median, and minimum growth rates; longevity estimates). Growth Simulation is found to be a robust and informative technique for studies of tropical tree growth, and is especially useful where analysis of tree rings is not feasible or when bootstrapping analysis of ring data is of interest.     

楸树无性系早期生长变异和优选

[目的]为评价和选育优良楸树(Catalpa bungei C. A. Mey)无性系。[方法]本研究利用32个楸树无性系7年的生长测定数据,以分析其生长规律及早期生长过程。对各无性系的单株材积生长进行Logistic拟合回归分析。在此基础上,分析不同指标间的相关性并对32个无性系进行聚类分析。[结果]楸树无性系在不同年份(1 a除外)胸径、树高、单株材积差异极显著,说明楸树无性系间变异丰富。楸树单株材积变异系数最大(7.84%～35.56%),胸径次之(11.89%～17.29%),树高最低(6.91%～10.87%),无性系单株材积改良潜力较大。同时生长后期单株材积(0.75)和胸径(0.82)保持较高的重复力,意味楸树单株材积受遗传控制较强。利用无性系单株材积生长平均值,拟合了楸树无性系单株材积生长曲线的Logistic模型,估算的生长参数在无性系间具有较大差异。楸树无性系7年生单株材积平均年生长量呈"S"型曲线生长趋势,而连年生长量先上升后下降,在第5年达到高峰,截止到本次调查时还未达到数量成熟。相关性分析显示:楸树无性系单株材积生长量与最大生长速率(MGR)、线性生长速率(LGR)、线性生长量(LGI)极显著正相关。聚类分析结果表明:供试的32个楸树无性系分为4大类,其中第I类的楸树单株材积生长总量较大,且具有较强的后期生长潜力。[结论]不同楸树无性系的遗传变异丰富, 1-1、22-07、19-01、16-05、16-01、16-07等6个无性系生长潜力较高,可作为楸树的优良无性系进行推广。     

Geographic variation and genetic performance of Picea koraiensis in growth and wood characteristics

Eight provenances of 19-year-oldPicea koraiensis Nakai from the provenance trials of Maoershan (45°20′N, 127°30′E), Liangshui (47°10′N, 128°53′E) and Jiagedaqi (50°24′N, 124°07′E) in Northeast China were investigated to analyze the genetic variation in growth characteristics (tree height and diameter) and wood characteristics (tracheid length, tracheid diameter, tracheid wall thickness, annual ring width as well as wood density). Great variation in height growth and breast height diameter growth was observed among the provenances, and along with the increase of tree age, these provenances presented different geographic adaptability. The growth characteristics ofPicea koraiensis stand at age of 10 in Maoershan and Liangshui provenance trials had a positive correlation with longitude, and with increase of tree age to 15 and 19, the tree growth of the provenances displayed a significant positive correlation with latitude as well as altitude. For wood characteristics, great variation was also found among the provenances. There exists a close relation between growth characteristics and wood properties of the provenance. The height and breast height diameter growth of the provenance had a positive correlation with tracheid diameter and annual ring width, and a negative correlation with tracheid wall thickness and wood density. Genetic performance of the provenance in all above characteristics was also investigated in order to provide more useful information for comprehensive selection of this species for pulpwood and plywood production. Foundation item: The paper was supported by National Key Project of The State Forestry Administration. (96-011-01-06) Biography: WANG Qiu-yu (1957-), female, professor in College of Life Sciences, Northeast Forestry University, Harbin 150040, P. R. China. Responsible editor: Song Funan     

北美鹅掌楸人工林生长规律及早期选择可行性探究

[目的]北美鹅掌楸为优良的珍贵用材树种,研究其生长发育规律及生长性状早晚期相关对于北美鹅掌楸人工林高效培育有重要的指导意义。[方法]本文利用树干解析的方法对江苏句容24年生的北美鹅掌楸人工林生长规律研究,并在此基础上进行胸径、树高和材积性状的年年相关分析以及早期选择效率评价。[结果]研究结果表明:北美鹅掌楸胸径、树高从6 a进入快速生长期,持续到17 a,而材积则在1 10 a增长缓慢,12 a后进入速生期,生长速率在20 a达到最大,22 a后逐渐降低,林分接近数量成熟。生长性状的年年相关及早期选择效率分析结果表明:胸径、树高在6 a与18 a显著相关,材积在6 a与16 a达到显著相关,且此时选择效率最高;若以24 a为伐期年龄早晚相关分析,胸径、材积在16 a与24 a生长量达到显著相关水平,而树高则为14 a。[结论]北美鹅掌楸胸径、树高早期增速较快,进入中壮龄阶段竞争加剧,个体间分化增大。随着林分年龄的增长,研究获得的早期选择年龄也相应地延迟。从加速育种角度,在6 a进行早期选择较为合理,而在培育大径材北美鹅掌楸方面可以16 a之后再进行疏伐选择。     

造林密度对米老排人工林初期生长的影响

[目的]探讨不同造林密度对米老排人工林生长的影响规律,为米老排人工林定向培育过程中的密度控制提供参考。[方法]以广东省云浮市造林后6年生米老排人工林为研究对象,对不同造林密度(625、833、1 111、1 667、2 500株·hm~(-2))林分平均树高、优势木高、胸径、保留率和枝下高等生长指标进行连续4年调查。[结果]表明:随着造林密度的增大,米老排林分平均胸径、胸径连年生长量、保留率、单株材积和材积连年生长量均显著减小,而枝下高、林分蓄积量和蓄积连年生长量显著增加。在一定密度范围内,造林密度对林分高生长的影响比较小。造林后第6年,密度1 667株·hm~(-2)林分的平均树高最大(11.4 m),优势木高以密度1 111株·hm~(-2)林分的最大(13.3m),树高连年生长量以密度625株·hm~(-2)林分的最大(1.5 m·a~(-1));密度625株·hm~(-2)林分的平均胸径、胸径连年生长量、单株材积和材积连年生长量均最大,分别为14.3 cm、2.5 cm·a~(-1)、0.097 3 m~3和0.038 2 m~3·a~(-1),比密度2 500株·hm~(-2)林分的分别增加27.7%、81.0%、49.0%和82.4%;密度2 500株·hm~(-2)林分的枝下高、蓄积量和蓄积连年生长量均最大,分别为6.0 m、149.4 m~3·hm~(-2)和44.8 m~3·hm~(-2)·a~(-1),分别是密度625株·hm~(-2)林分的2.61、2.52、1.95倍。[结论]分析了造林密度对米老排初期生长的影响,对米老排人工林的培育具有理论指导意义。     

基于树高和树冠因子的立木材积模型研究

[目的]由于激光雷达技术已经能准确测定立木树高及相关树冠因子,应用该技术建立基于树高和树冠因子的立木材积模型,为激光技术在森林蓄积估计中提供技术支撑.[方法]利用云杉、冷杉、栎树、桦树4个树种组的3 010株实测样木数据,分析了立木材积与胸径、树高、树冠因子之间的相关关系;并通过对数回归方法构建了基于树高和树冠因子的立木材积模型,用确定系数R²和平均预估误差MPE等6项指标对模型进行评价.[结果]表明,立木材积与单一因子之间的相关,以胸径最为紧密,其次是树高,再次是冠长和冠幅.基于树高和树冠因子的立木材积模型中,以树高和冠幅作为解释变量的二元模型效果较好,再增加冠长因子的三元模型改进不大.云杉、冷杉、栎树、桦树4个树种组基于树高冠幅的立木材积模型,其R²分别为0.81、0.80、0.76和0.77,MPE分别为4.7%、5.3%、5.4%和5.3%,模型预估精度均能达到95%左右.[结论]本文对材积与林木因子之间相关关系的定量分析,建立了云杉、冷杉、栎树、桦树4个树种的立木材积模型,模型预估精度高.为激光雷达技术定量估测森林参数提供了依据.     

Sensitivity of ring growth and carbon allocation to climatic variation vary within ponderosa pine trees

Most dendrochronological studies focus on cores sampled from standard positions (main stem, breast height), yet vertical gradients in hydraulic constraints and priorities for carbon allocation may contribute to different growth sensitivities with position. Using cores taken from five positions (coarse roots, breast height, base of live crown, mid-crown branch and treetop), we investigated how radial growth sensitivity to climate over the period of 1895-2008 varies by position within 36 large ponderosa pines (Pinus ponderosa Dougl.) in northern Arizona. The climate parameters investigated were Palmer Drought Severity Index, water year and monsoon precipitation, maximum annual temperature, minimum annual temperature and average annual temperature. For each study tree, we generated Pearson correlation coefficients between ring width indices from each position and six climate parameters. We also investigated whether the number of missing rings differed among positions and bole heights. We found that tree density did not significantly influence climatic sensitivity to any of the climate parameters investigated at any of the sample positions. Results from three types of analyses suggest that climatic sensitivity of tree growth varied with position height: (i) correlations of radial growth and climate variables consistently increased with height; (ii) model strength based on Akaike's information criterion increased with height, where treetop growth consistently had the highest sensitivity and coarse roots the lowest sensitivity to each climatic parameter; and (iii) the correlation between bole ring width indices decreased with distance between positions. We speculate that increased sensitivity to climate at higher positions is related to hydraulic limitation because higher positions experience greater xylem tensions due to gravitational effects that render these positions more sensitive to climatic stresses. The low sensitivity of root growth to all climatic variables measured suggests that tree carbon allocation to coarse roots is independent of annual climate variability. The greater number of missing rings in branches highlights the fact that canopy development is a low priority for carbon allocation during poor growing conditions.     

Application of theoretical growth functions for Mongolian oak (Qurcus mongolica)

Four alternative functions are used for fitting tree height and diameter growth models for mongolian oak. (Quercus mongolica Fisch. et Turcz.). The data set includes 1250 random trees and 755 dominant trees coming from 510 temporary plots. The resultsshow that the Richards function is the best model for predicting height. diameter at breast height (DBH) and dominant height from age. The average growth curve of dominant height is used as a guide curve for the construction of a site index table which is partially validated using an independent data set. The Mitscherlich function is the best model for estimating height and dominant height from DBH. (Responsible Editor: Chai Ruihai)     

Variation in density of Picea sitchensis in relation to within-tree trends in tracheid diameter and wall thickness

The influences of cambial age and ring width on density of Sitkaspruce (Picea sitchensis (Bong.) Carr) were analysed in relationto within-tree trends in tracheid diameter and cell wall thickness.Discs were sampled at breast height from a total of 24 trees,from seven stands at three contrasting sites in Wales, and atbreast height, 30 per cent and 60 per cent total tree heightfrom one of the stands. Across the juvenile wood, ring density decreased with ring numberfrom the pith while radial tracheid diameter increased. Theseoverall trends were considered to be inherent to tree growth,presumably associated with cambial ageing, since they occurredin all trees on all sites. In juvenile wood, density also variedwith site growth rate (as indicated by ring width) at similarcambial age, wider rings being associated with more rapidrateof change in tracheid diameter with ring number and with decreasein tracheid wall thickness. Consequently, on a site having treeswith high growth rate density decreased more rapidly acrossthe juvenile wood, down to a lower minimum value, than on siteswith a slower growth rate. In mature wood, the decrease in densitywith increase in ring width was associated with differencesin both tracheid diameter and wall thickness. Density was slightly(though not significantly) higher at breast height than in comparablerings at 30 per cent total height, associated with significantlythicker tracheid walls at breast height. Changes in radial tracheid diameter (with ring number, or withring width) were associated with greater differences in theearlywood than towards the latewood end of each growth ring,while variations in wall thickness with ring width were associatedwith rate of increase in wall thickness towards the latewoodend. This may account for some previously conflicting reportson influence of silvicultural management on density, for densityis likely to vary with influence of environment on the seasonalcycle of cambial activity. The extent of the juvenile wood as delimited by the inner coreof wide growth rings does not necessarily correspond to theregion of varying tracheid dimensions in Sitka spruce.     

Long-term growth analyses of Japanese cedar trees in a plantation: neighborhood competition and persistence of initial growth deviations

The individual growth of tree diameter at breast height (dbh) is analyzed in an even-aged plantation of Cryptomeria japonica from stand age of 45 to 94 years, to examine how the growth of individual trees has been affected by the changes in spacing resulting from thinning operations. At any age, a significant proportion (0.37–0.46) of the variation in dbh growth during a 5–11-year period was explained by dbh at the beginning of the period, probably due to greater leaf mass of larger trees. Next, either one-sided or two-sided competition was added to the model, by calculating the basal area (BA) of neighboring trees around each tree within a given radius or BA for trees having larger dbh than the focal tree within the radius. After preliminary analyses, a radius of 8 m was selected as the critical range for tree competition. Although both types of competition explained a significant proportion (0.09–0.43) of growth variation, one-sided competition was not significant at ages greater than 54 years. Based on the model at 45 years of age, the initial deviation of growth rate for each tree from the predicted rate was calculated and added to the models as a third variable. This raised the coefficient of determination up to 0.50–0.74. These findings have practical significance for forest plantation management, particularly for controlling the growth of standing trees via thinning, to produce high-quality timber in the future.