Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation

doi:10.3969/j.issn.1000-2006.201812012

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2020, Vol. 44 ›› Issue (2): 117-124.doi: 10.3969/j.issn.1000-2006.201812012

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Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation

ZHOU Zeyu¹(), YANG Raohua², ZHANG Yuzhen¹, HUANG Xuanrui¹, ZHANG Zhidong¹, WANG Dongzhi¹^,^*(), LI Dayong²

1. College of Forestry Agricultural University of Hebei, Forest Resources Innovation and Protection Laboratory of Hebei, Baoding 071000, China
2. Mulan Weichang State-owned Forest Farm Administration Bureau of Hebei Province, Chengde 068450, China

Received:2018-12-06 Revised:2019-02-27 Online:2020-03-30 Published:2020-04-01
Contact: WANG Dongzhi E-mail:2291818678@qq.com;wangdz@126.com

Abstract

Abstract:

【Objective】 Based on different diameter distribution prediction models(Weibull distribution, Gamma distribution, Lognormal distribution), linear mixed-effects model including the main stand factors are constructed to help to reflect the response of diameter distribution to stand dynamics. 【Method】 Using the survey data of typical Larix principis-rupprechtii plantation, the model parameters were estimated by using the Maximum Likelihood Estimation (MLE), and the adaptability of the established model was evaluated via K-S (Kolmogorov-Smirnov)test, C-V (Cramer-von Mises) test, and A-D (Anderson-Darling) test. Based on the optimal model, a linear mixed-effects model of diameter distribution of Larix principis-rupprechtii plantation was constructed. 【Result】 The optimal model for the diameter distribution ofLarix principis-rupprechtii plantation was the 3-parameter Weibull distribution. Based on the optimal model, a linear mixed-effect model with inputs of stand dominant height, stand basal area and logarithmic density was constructed and the mixed-effect model had the best fitting result as the variance-covariance structure of random-effect and the error term variance-covariance structure was both Diagonal matrix UN(1). The R ² of linear mixed-effect model of Weibull distribution of parameter a, b, and c were estimated at 0.895, 0.888, and 0.801 respectively. The MSE were at 5.365, 1.724, 1.151 and RMSE were at 2.316, 1.313, 1.073. the fitting result was relatively accurate. 【Conclusion】 Linear mixed-effects model has the capability to accurately predict stand diameter distribution. The model can provide theoretical basis and technical parameters for accurately predicting the diameter distributions ofLarix principis-rupprechtii plantation.

Key words: Larix principis-rupprechtii, dynamic diameter distribution model, Maximum Likelihood Estimation(MLE), linear mixed-effect model

CLC Number:

S758.5⁺7

ZHOU Zeyu, YANG Raohua, ZHANG Yuzhen, HUANG Xuanrui, ZHANG Zhidong, WANG Dongzhi, LI Dayong. Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2020, 44(2): 117-124.

Figures/Tables 8

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References 45

[1]	孟宪宇. 测树学[M]. 北京: 中国林业出版社, 2006.
	MENG X Y. Tree survey [M], Beijing: Chinese Forestry Publishing House, 2006.
[2]	马炜, 孙玉军. 三种直径分布拟合模型在长白落叶松林分的实际应用[J]. 生物数学学报, 2012,27(3):548-554.
	MA W, SUN Y J. Modeling of stand diameter structure of Larix olgensis plantations [J]. J Biomath, 2012,27(3):548-554.
[3]	XU Y. Approximation of the median of the Gamma distribution[J]. Journal of Number Theory, 2017, 174:487-493. DOI: 10.1016/j.jnt.2016.11.019. doi: 10.1016/j.jnt.2016.11.019
[4]	PILISZEK A, WESOŁOWSKI J. Change of measure technique in characterizations of the Gamma and Kummer distributions[J]. J Math Anal Appl, 2018, 458(2):967-979.DOI: 10.1016/j.jmaa.2017.10.011. doi: 10.1016/j.jmaa.2017.10.011
[5]	ABBASI B, RABELO L, HOSSEINKOUCHACK M. Estimating parameters of the three-parameter Weibull distribution using a neural network[J]. Eur J Ind Eng, 2008, 2(4):428.DOI: 10.1504/ejie.2008.018438. doi: 10.1504/EJIE.2008.018438
[6]	POUDEL K P, CAO Q V. Evaluation of methods to predict weibull parameters for characterizing diameter distributions[J]. For Sci, 2013, 59(2):243-252.DOI: 10.5849/forsci.12-001.
[7]	CAO Q. Predicting parameters of a Weibull function for modeling diameter distribution[J]. Forest Science, 2004, 50(5):682-685.DOI: 10.1093/forestscience/50.5.682.
[8]	方精云, 菅诚. 利用Weibull分布函数预测林木的直径分布[J]. 北京林业大学学报, 1987(3):261-269.
	FANG J Y, JIAN C. Estimating diameter distribution with the Weibull distribution function[J]. J Beijing For Univ, 1987(3):261-269. DOI: 10.13332/j.1000-1522.1987.03.008.
[9]	国红, 雷渊才. 蒙古栎林分直径Weibull分布参数估计和预测方法比较[J]. 林业科学, 2016,52(10):64-71.
	GUO H, LEI Y C. Method comparison of weibull function for estimating and predicting diameter distribution of Quercus mongolica stands [J]. Sci Silvae Sin, 2016,52(10):64-71.DOI: 10.11707/j.1001-7488.20161008.
[10]	陈新美, 张会儒, 武纪成, 等. 柞树林直径分布模拟研究[J]. 林业资源管理, 2008(1):39-43.
	CHEN X M, ZHANG H R, WU J C, et al. Study on diameter distribution simulation of Quereus mongolica stands [J]. For Resour Manag, 2008(1):39-43.DOI: 10.3969/j.issn.1002-6622.2008.01.010.
[11]	符利勇, 刘应安, 张海东. 庞泉沟自然保护区主要树种直径正态分布拟合研究[J]. 林业资源管理, 2008(3):48-52.
	FU L Y, LIU Y G, ZHANG H D. Research on the fitting for the normal distribution of main tree species’ diameter in Pangquangou Nature Reserve[J]. For Resour Manag, 2008(3):48-52.DOI: 10.3969/j.issn.1002-6622.2008.03.012.
[12]	巢林, 洪滔, 林卓, 等. 中亚热带杉阔混交林直径分布研究[J]. 中南林业科技大学学报, 2014,34(9):31-37.
	CHAO L, HONG T, LIN Z, et al. Study on diameter distribution of Chinese fir and broad-leaved forest in mid-subtropical[J]. J Central South Univ For Technol, 2014,34(9):31-37.DOI: 10.3969/j.issn.1673-923X.2014.09.007.
[13]	王香春, 张秋良, 春兰, 等. 大青山落叶松人工林直径分布规律的研究[J]. 山东农业大学学报(自然科学版), 2011,42(3):349-355.
	WANG X C, ZHANG Q L, CHUN L, et al. Study on the Larix principis-rupprechtii mayr plantations diameter distribution in Daqing Mountain [J]. Journal of Shandong Agricultural University (Natural Science Edition), 2011,42(3):349-355. DOI: 10.3969/j.issn.1000-2324.2011.03.005.
[14]	郝敬锋, 刘红玉, 李玉凤, 等. 基于转移矩阵模型的江苏海滨湿地资源时空演变特征及驱动机制分析[J]. 自然资源学报, 2010,25(11):1918-1929.
	HAO J F, LIU H Y, LI Y F, et al. Spatio-temporal variation and driving forces of the coastal wetland resources based on the transition matrix in Jiangsu Province[J]. J Nat Resour, 2010,25(11):1918-1929.DOI: 10.11849/zrzyxb.2010.11.011.
[15]	符利勇, 张会儒, 李春明, 等. 非线性混合效应模型参数估计方法分析[J]. 林业科学, 2013,49(1):114-119.
	FU L Y, ZHANG H R, LI C M, et al. Analysis of nonlinear mixed effects model parameter estimation methods[J]. Sci Silvae Sin, 2013,49(1):114-119.DOI: 10.11707/j.1001-7488.20130117.
[16]	赖巧玲, 胥辉, 杨为民. 非参数估计在构造树高曲线中的应用[J]. 北京林业大学学报, 2006,28(4):77-81.
	LAI Q L, XU H, YANG W M. Application of nonparametric estimation method in establishing height-diameter curves of trees[J]. J Beijing For Univ, 2006,28(4):77-81.DOI: 10.3321/j.issn:1000-1522.2006.04.015.
[17]	BUCH-LARSEN T, NIELSEN J P, GUILLÉN M, et al. Kernel density estimation for heavy-tailed distributions using the champernowne transformation[J]. Statistics, 2005, 39(6):503-516.DOI: 10.1080/02331880500439782. doi: 10.1080/02331880500439782
[18]	DIAMANTOPOULOU M J, ÖZÇELIK R, CRECENTE-CAMPO F, et al. Estimation of Weibull function parameters for modelling tree diameter distribution using least squares and artificial neural networks methods[J]. Biosyst Eng, 2015, 133:33-45.DOI: 10.1016/j.biosystemseng.2015.02.013. doi: 10.1016/j.biosystemseng.2015.02.013
[19]	BULLOCK B P, BURKHART H E. Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function[J]. New Forest, 2005, 29(3):233-244.DOI: 10.1007/s11056-005-5651-5. doi: 10.1007/s11056-005-5651-5
[20]	BORDERS B E, WANG M L, ZHAO D H. Problems of scaling plantation plot diameter distributions to stand level[J]. Forest Science, 2008, 54(3):349-355.DOI: 10.1093/forestscience/54.3.349.
[21]	EVANS D L, DREW J H, LEEMIS L M. The distribution of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters[J]. Communications in Statistics Simulation and Computation, 2008, 37(7):1396-1421. DOI: 10.1080/03610910801983160. doi: 10.1080/03610910801983160
[22]	张会儒, 李春明, 武纪成. 金沟岭天然和半天然混交林林分空间结构比较[J]. 科技导报, 2009,27(19):79-84.
	ZHANG H R, LI C M, WU J C. Comparison of spatial structure for natural and semi-natural mixed forests in jingouling forestry farm,Jilin Province of China[J]. Sci Technol Rev, 2009,27(19):79-84.DOI: 10.3321/j.issn:1000-7857.2009.19.019.
[23]	段爱国, 张建国, 童书振, 等. 杉木人工林林分直径结构动态变化及其密度效应的研究[J]. 林业科学研究, 2004,17(2):178-184.
	DUAN A G, ZHANG J G, TONG S Z, et al. Studies on dynamics of diameter structure of Chinese fir plantations and affection of density on it[J]. For Res, 2004,17(2):178-184.DOI: 10.3321/j.issn:1001-1498.2004.02.007.
[24]	李俊, 佘济云, 胡焕香, 等. 昌化江流域天然林直径结构研究[J]. 中南林业科技大学学报, 2012,32(3):37-43.
	LI J, SHE J Y, HU H X, et al. Research on diameter structure of natural forest in Changhua River Basin[J]. J Central South Univ For Technol, 2012,32(3):37-43.DOI: 10.3969/j.issn.1673-923X.2012.03.007.
[25]	NELSON T C. Diameter distribution and growth of Loblolly pine[J]. Forest Science, 10(1):105-114. DOI: 10.1093/forestscience/10.1.105.
[26]	PODLASKI R. Forest modelling: the Gamma shape mixture model and simulation of tree diameter distributions[J]. Annals of Forest Science, 2017, 74(2):29. DOI 10.1007/s13595-017-0629-y. doi: 10.1007/s13595-017-0629-y
[27]	周国模, 刘恩斌, 刘安兴, 等. Weibull分布参数辨识改进及对浙江毛竹林胸径年龄分布的测度[J]. 生态学报, 2006,26(9):2918-2926.
	ZHOU G M, LIU E B, LIU A X, et al. The algorithm update of Weibull distribution parametric identification and its application on measuring the distribution of diameter and age of Moso bamboo forests in Zhejiang Province,China[J]. Acta Ecol Sin, 2006,26(9):2918-2926.DOI: 10.3321/j.issn:1000-0933.2006.09.018.
[28]	葛宏立, 周国模, 刘恩斌, 等. 浙江省毛竹直径与年龄的二元Weibull分布模型[J]. 林业科学, 2008,44(12):15-20.
	GE H L, ZHOU G M, LIU E B, et al. Diameter-age bivariate Weibull distribution model for moso bamboo forests in Zhejiang Province[J]. Sci Silvae Sin, 2008,44(12):15-20.DOI: 10.3321/j.issn:1001-7488.2008.12.003.
[29]	王蒙, 李凤日. 基于抚育间伐效应的落叶松人工林直径分布动态模拟[J]. 应用生态学报, 2016,27(8):2429-2437.
	WANG M, LI F R. Modeling the diameter distribution of Larix olgensis plantation based on thinning effects [J]. China J Appl Ecol, 2016,27(8):2429-2437.DOI: 10.13287/j.1001-9332.201608.026.
[30]	庄崇洋, 黄清麟, 马志波, 等. 典型中亚热带天然阔叶林各林层直径分布及其变化规律[J]. 林业科学, 2017,53(4):18-27.
	ZHUANG C Y, HUANG Q L, MA Z B, et al. Diameter distribution in each storey and law of typical natural broad-leaved forest in mid-subtropical zone[J]. Sci Silvae Sin, 2017,53(4):18-27.DOI: 10.11707/j.1001-7488.20170403.
[31]	陈英, 杨华, 赵浩彦, 等. 北京地区侧柏人工林林木直径分布模型研究[J]. 中南林业科技大学学报, 2012,32(9):59-64.
	CHEN Y, YANG H, ZHAO H Y, et al. Study on tree diameter distribution model of Platycluadus orientalis plantation in Beijing [J]. J Central South Univ For Technol, 2012,32(9):59-64.DOI: 10.14067/j.cnki.1673-923x.2012.09.020.
[32]	赵丹丹, 李凤日, 董利虎. 落叶松人工林直径分布动态预估模型1)[J]. 东北林业大学学报, 2015,43(5):42-48.
	ZHAO D D, LI F R, DONG L H. Predicting models of diameter distribution dynamic for larch plantation[J]. J Northeast For Univ, 2015,43(5):42-48.DOI: 10.3969/j.issn.1000-5382.2015.05.009.
[33]	NEWTON P F, LEI Y, ZHANG S Y. Stand-level diameter distribution yield model for black spruce plantations[J]. Forest Ecology and Management, 2005, 209(3):181-192.DOI: 10.1016/j.foreco.2005.01.020. doi: 10.1016/j.foreco.2005.01.020
[34]	雷娜庆, 铁牛, 刘洋, 等. 兴安落叶松天然林林分直径分布和树高分布[J]. 东北林业大学学报, 2017,45(1):90-93.
	LEI N Q, TIE N, LIU Y, et al. Structure of diameter and height for naturally growing Larix gmelinii forest [J]. J Northeast For Univ, 2017,45(1):90-93.DOI: 10.13759/j.cnki.dlxb.2017.01.019.
[35]	张海平, 李凤日, 董利虎, 等. 基于气象因子的白桦天然林单木直径生长模型[J]. 应用生态学报, 2017,28(6):1851-1859.
	ZHANG H P, LI F R, DONG L H, et al. Individual tree diameter increment model for natural Betula platyphylla forests based on meteorological factors [J]. China J Appl Ecol, 2017,28(6):1851-1859.DOI: 10.13287/j.1001-9332.201706.009.
[36]	陈东升, 李凤日, 孙晓梅, 等. 基于线性混合模型的落叶松人工林节子大小预测模型[J]. 林业科学, 2011,47(11):121-128.
	CHEN D S, LI F R, SUN X M, et al. Models to predict knot size for larch plantation using linear mixed model[J]. Sci Silvae Sin, 2011,47(11):121-128.
[37]	许崇华, 崔珺, 黄兴召, 等. 基于线性混合效应模型的杉木树高-胸径模型[J]. 西北农林科技大学学报(自然科学版), 2017,45(6):53-60.
	XU C H, CUI J, HUANG X Z, et al. Height-diameter model for Chinese fir based on linear mixed model[J]. J Northwest A & F Univ (Nat Sci Ed), 2017,45(6):53-60.DOI: 10.13207/j.cnki.jnwafu.2017.06.008.
[38]	王冬至, 张冬燕, 张志东, 等. 基于非线性混合模型的针阔混交林树高与胸径关系[J]. 林业科学, 2016,52(1):30-36.
	WANG D Z, ZHANG D Y, ZHANG Z D, et al. Height-diameter relationship for conifer mixed forest based on nonlinear mixed-effects model[J]. Sci Silvae Sin, 2016,52(1):30-36.DOI: 10.11707/j.1001-7488.20160104.
[39]	VON GADOW K. Fitting distributions in Pinus patula stands[J]. S Afr N For J, 1983, 126(1):20-29.DOI: 10.1080/00382167.1983.9628894.
[40]	李春明. 混合效应模型在森林生长模拟研究中的应用[D]. 北京:中国林业科学研究院, 2010.
	LI C M. Application of mixed effects models in forest growth models[D]. Beijing: Chinese Academy of Forestry, 2010.
[41]	李春明. 基于两层次线性混合效应模型的杉木林单木胸径生长量模型[J]. 林业科学, 2012,48(3):66-73.
	LI C M. Individual tree diameter increment model for Chinese fir plantation based on two-level linear mixed effects models[J]. Sci Silvae Sin, 2012,48(3):66-73.DOI: 10.11707/j.1001-7488.20120311.
[42]	许昊, 孙玉军, 王新杰, 等. 利用线性混合效应模型模拟杉木人工林枝条生物量[J]. 应用生态学报, 2015,26(10):2969-2977.
	XU H, SUN Y J, WANG X J, et al. Simulation of the branch biomass for Chinese fir plantation using the linear mixed effects model[J]. Chin J Appl Ecol, 2015,26(10):2969-2977.DOI: 10.13287/j.1001-9332.20150921.026.
[43]	PINHEIRO J C, BATES D M, LINDSTROM M J. Model building for nonlinear mixed effects models[R]. Madision: Department of Statistics University of Wisconsin, 1994.
[44]	CALAMA R, MONTERO G. Interregional nonlinear height diameter model with random coefficients for stone pine in Spain[J]. Can J For Res, 2004, 34(1):150-163.DOI: 10.1139/x03-199. doi: 10.1139/x03-199
[45]	董灵波, 刘兆刚, 李凤日, 等. 基于线性混合模型的红松人工林一级枝条大小预测模拟[J]. 应用生态学报, 2013,24(9):2447-2456.
	DONG L B, LIU Z G, LI F R, et al. Primary branch size of Pinus koraiensis plantation:a prediction based on linear mixed effect model [J]. Chin J Appl Ecol, 2013,24(9):2447-2456.DOI: 10.13287/j.1001-9332.2013.0490.

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数据类型 data type	变量 variable	平均胸径/ cm DBH	林分平均高/m height	林分密度/ (株· hm^-2) stand density	年龄/a age	林分断面积/ (m²·hm^-2) stand basal area	优势高/m dominant height	海拔/m elevation	坡度/ (°) slope
建模数据 modeling data	最小值min.	6.70	5.0	267	10	6.42	6.4	953	1
	最大值max.	31.30	21.9	3 014	53	41.98	23.5	1 429	37
	均值mean	19.39	14.9	769	35	20.58	16.2	1 184	17
	标准差SD	4.29	3.1	499	7	9.28	3.1	258	8
检验数据 validation data	最小值min.	7.80	5.0	258	11	8.79	6.4	930	2
	最大值max.	31.30	20.7	2 980	45	35.23	21.9	1 423	40
	均值mean	21.44	15.9	772	36	20.49	17.1	1 162	18
	标准差SD	4.10	2.9	501	7	5.51	2.9	260	8

模型 model	通过率/% pass rate	未通过率/% unpass rate
3-Gamma	58.7	41.3
3-Weibull	100.0	0.0
3-Lognormal	52.6	47.4

参数 parameter	Weibull分布 Weibull distribution					拟合优度 fitting goodness
参数 parameter	最大值max.	最小值min.	均值mean	标准差SD	D		W²		A²
a	23.02	0.69	10.43	4.63		0.072 (P<0.01)		0.266 (P<0.001)		1.756 (P<0.001)
b	20.75	3.01	8.98	4.27
c	9.81	1.00	3.03	1.47

变量 variable	1	2	3	4	5	6
D_g	0.487 2	-0.172 1	0.267 9	-0.197 5	-0.495 4	0.613 9
D_d	0.459 1	-0.175 9	0.262 4	0.786 6	0.257 3	-0.067 5
H_d	0.483 0	0.054 2	0.036 7	-0.511 5	0.707 3	0.022 0
A	0.423 8	0.120 6	-0.873 9	0.123 6	-0.163 5	-0.013 3
G	0.344 5	0.572 7	0.305 9	-0.107 6	-0.355 1	-0.567 5
log s	-0.142 6	0.770 7	0.026 5	0.232 0	0.187 9	0.543 9

主成分 principle component	特征值 eigenvalue	方差贡献率 variance contribution	累积贡献率 cumulative contribution
1	3.638 3	0.606 4	0.606 4
2	1.511 9	0.252 0	0.858 4
3	0.414 5	0.069 1	0.927 5
4	0.237 1	0.039 5	0.967 0
5	0.168 1	0.028 0	0.995 0
6	0.030 1	0.005 0	1.000 0

Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation

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参数类别 parameter category	随机效应 random-effect	AIC	BIC	-2Log- Like	LRT	P
位置参数 location parameter	截距 intercept	566.9	583.8	554.9	0.05	0.950
	H_d、log s	544.2	566.7	528.2	7.86	0.005
	H_d	593.7	585.2	572.7	2.62	0.450
	log s	583.7	591.6	582.7	1.58	0.640
尺度参数 scale- parameter	截距 intercept	429.9	446.8	417.9	0.01	0.998
	H_d、log s	443.6	426.8	414.8	3.17	0.075
	H_d	529.8	545.6	517.8	1.05	0.560
	log s	527.8	541.1	517.8	1.21	0.510
形状参数 shape parameter	截距 intercept	431.3	451.0	417.3	0.02	0.920
	H_d、log s	425.6	436.8	417.6	4.73	0.193
	H_d	429.8	445.6	417.8	3.54	0.420
	log s	427.8	441.1	417.8	3.62	0.380

参数 parameter	位置参数 location parameter				尺度参数 scale parameter				形状参数 shape parameter
参数 parameter	估计值 estimation	标准差 SD	t	P	估计值 estimation	标准差 SD	t	P	估计值 estimation	标准差 SD	t	P
截距interept	-4.723	1.554	-3.04	0.081	-10.456	1.822	-5.73	0.010	1.733	2.390	3.23	0.012
H_d	1.029	0.081	12.77	<0.001	0.812	0.051	15.86	<0.001	0.023	0.057	9.74	<0.001
G	0.072	0.028	2.53	0.020	0.002	0.016	6.96	0.052	0.026	0.021	4.28	0.032
log s	-0.089	0.162	-3.66	0.041	0.734	0.239	-3.06	0.081	0.048	0.329	-2.61	0.018
$σ u 1 2$	0.032	0.069	3.26	0.007	0.001	0.524	6.28	0.025	0.001	0.007	2.00	0.023
$σ u 2 2$	0.150	0.393	4.08	0.049	0.031	0.338	3.87	0.047	0.058	0.284	5.23	0.008
e_ij	0.017 28	0.020	2.98	0.090	0.287	0.614	1.52	0.073	1.799	1.569	3.51	0.101
R²	0.895	0.888	0.801
σ_MSE	5.365				1.724				1.151
σ_RMSE	2.316				1.313				1.073

[1]	WANG Yunni, CAO Gongxiang, XU Lihong, CHEN Shengnan. Evapotranspiration characteristics of Larix principis-rupprechtii plantation and its impact factors in the Daqing Mountains of Inner Mongolia [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2023, 47(4): 148-156.
[2]	NIE Luyi, DONG Lihu, LI Fengri, MIAO Zheng, XIE Longfei. Construction of taper equation for Larix olgensis based on two-level nonlinear mixed effects model [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2022, 46(3): 194-202.
[3]	LIU Zixuan, JIA Cun, QIN Zhiqiang, LI Yongning. Effects of light conditions on the growth of understory Picea meyeri sapling in Larix principis-rupprechtii forest [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2020, 44(6): 111-117.