天然落叶松林木冠幅模型与林分密度模型及其关系

doi:10.11707/j.1001-7488.LYKX20240250

摘要/Abstract

摘要：

目的: 研建林木冠幅模型、林分密度模型及其联立模型，探究林木冠幅模型与林分密度模型之间的关系，为进一步研究林分密度管理和指导森林经营提供科学依据。方法: 利用在全国范围内代表性采集的600株落叶松样木调查数据和第九次全国森林资源清查的1273个天然落叶松林样地调查数据，采用非线性回归和对数回归估计方法，分别建立了落叶松林木冠幅模型和林分密度模型；在分析二者之间内在相关性的基础上，采用含哑变量的多元非线性回归估计方法，建立了林木冠幅和林分密度联立模型，并确定了最大林分密度线。结果: 林木冠幅与胸径呈正相关，落叶松林木冠幅模型的确定系数R²在0.76以上，估计值的标准误SEE为1.03 m，平均预估误差MPE为2.16%；冠径比随胸径的增加而下降，从2 cm时的0.47快速下降至20 cm时的0.23，再缓慢下降至50 cm时的0.17。林分密度与平均胸径呈负相关，落叶松林分密度模型的R²达到0.88，SEE为147 株·hm^?2，MPE为2.58%；林分密度模型与林木冠幅模型的指数呈2倍负相关，根据联立模型得出的斜率参数为?1.384，可视为全国落叶松天然林自然稀疏线斜率的总体平均值。结论: 基于林分密度模型与林木冠幅模型之间的内在相关性，采用多元回归估计方法求解林分密度指数的斜率参数是一条可行的新途径。该方法对研究其他树种的林分密度指数及指导林分密度管理和森林科学经营也具有应用价值。

关键词: 林木冠幅, 林分密度, 最大密度线, 多元回归, 落叶松

Abstract:

Objective: This study aims to develop models for tree crown width(CW) and stand density(SD), as well as a combined model integrating both. By exploring the correlation between CW model and SD model, this research provides a scientific basis for further studies on stand density management and guidance for forest management practices. Method: Using the measurement data of 600 representative sample trees of larch collected throughout the whole country of China, and the data of 1273 permanent plots in natural larch forests from the 9^th national forest inventory, the CW model and the SD model of larch were established by using nonlinear regression and logarithmic regression estimation methods. Based on the analysis of the relationship between CW model and SD model, a multivariate nonlinear regression method with dummy variables was used to establish the simultaneous models, and the maximum stand density line was determined. Result: The results showed that CW was positively correlated with diameter at breast height (DBH); the determination coefficient R² of CW model for larch was higher than 0.76, the standard error of estimate (SEE) was 1.03 m, and the mean prediction error (MPE) was 2.16%. The ratio of CW-DBH decreased with the increase of DBH, from 0.53 at 2 cm to 0.23 at 20 cm and then slowly to 0.17 at 50 cm. The SD was negatively correlated with mean DBH; the R² of SD model for larch forests reached to 0.88, the SEE was 147 stems per hectare, and the MPE was 2.58%. There was a 2-fold negative correlation between the two power parameters of SD model and CW model, and the slope parameter from the simultaneous models is ?1.384, which can be regarded as the average value of the slopes of self-thinning lines of natural larch forests in China. Conclusion: It is a feasible new approach to use multivariate regression method for estimating the slope parameter of the stand density index (SDI) based on the correlation between SD model and CW model. This is of practical significance to study the SDI of other tree species and to guide the stand density management and forest scientific management.

Key words: tree crown width, stand density, maximum density line, multivariate regression, larch

中图分类号:

S758.5

曾伟生,杨学云,蒲莹. 天然落叶松林木冠幅模型与林分密度模型及其关系[J]. 林业科学, 2025, 61(2): 93-100.

Weisheng Zeng,Xueyun Yang,Ying Pu. Tree Crown Width Model, Stand Density Model and Their Relationships for Natural Larch[J]. Scientia Silvae Sinicae, 2025, 61(2): 93-100.

图/表 4

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参考文献 0

	董　晨, 吴保国, 韩焱云, 等. 基于修正函数的杉木人工林单木冠幅预测模型. 东北林业大学学报, 2015, 43 (5): 49- 53. doi: 10.3969/j.issn.1000-5382.2015.05.010
	Dong C, Wu B G, Han Y Y, et al. An individual crown-width model for Chinese fir plantation based on modified function. Journal of Northeast Forestry University, 2015, 43 (5): 49- 53. doi: 10.3969/j.issn.1000-5382.2015.05.010
	符亚健, 吕飞舟, 朱光玉, 等. 华北落叶松天然次生林单木冠幅模型构建. 林业资源管理, 2016, (5): 65- 70.
	Fu Y J, Lü F Z, Zhu G Y, et al. Construction of crown width model for single tree of natural Larix principis-rupprechtii forest. Forest Resources Management, 2016, (5): 65- 70.
	和璐璐, 张　萱, 章毓文, 等. 辽东山区不同坡向长白落叶松人工林树冠特征与林木生长关系. 植物生态学报, 2023, 47 (11): 1523- 1539. doi: 10.17521/cjpe.2022.0390
	He L L, Zhang X, Zhang Y W, et al. Crown characteristics and its relationship with tree growth on different slope aspects for Larix olgensis var. changbaiensis plantation in eastern Liaoning mountainous area, China. Chinese Journal of Plant Ecology, 2023, 47 (11): 1523- 1539. doi: 10.17521/cjpe.2022.0390
	马爱云, 李凤日, 董利虎. 应用混合效应法建立的杂种落叶松人工林单木冠幅预测模型. 东北林业大学学报, 2021, 49 (3): 9- 14,38. doi: 10.3969/j.issn.1000-5382.2021.03.002
	Ma A Y, Li F R, Dong L H. Individual crown diameter prediction for hybrid larch based on mixed effects models. Journal of Northeast Forestry University, 2021, 49 (3): 9- 14,38. doi: 10.3969/j.issn.1000-5382.2021.03.002
	国家林业和草原局. 2019. 中国森林资源报告(2014—2018). 北京: 中国林业出版社.
	National Forestry and Grassland Administration. 2019. Report on forest resources in China (2014—2018). Beijing: China Forestry Publishing House. ［in Chinese］
	邱思玉, 孙玉军. 长白落叶松人工林单木冠幅模型. 东北林业大学学报, 2021, 49 (2): 49- 53.
	Qiu S Y, Sun Y J. Individual tree crown width prediction models for Larix olgensis plantation. Journal of Northeast Forestry University, 2021, 49 (2): 49- 53.
	唐守正, 郎奎建, 李海奎. 2009. 统计和生物数学模型计算: ForStat教程. 北京: 科学出版社.
	Tang S Z, Lang K J, Li H K. 2009. Statistical and biomathematics model calculation: ForStat course. Beijing: Science Press. ［in Chinese］
	田　猛, 曾伟生, 孟京辉, 等. 福建杉木人工林密度控制图研制及应用. 西北林学院学报, 2015, 30 (3): 157- 163. doi: 10.3969/j.issn.1001-7461.2015.03.27
	Tian M, Zeng W S, Meng J H, et al. Development and application of density management diagram for Cunninghamia lanceolata plantation in Fujian. Journal of Northwest Forestry University, 2015, 30 (3): 157- 163. doi: 10.3969/j.issn.1001-7461.2015.03.27
	杨　阳, 彭浩贤, 潘　萍, 等. 基于混合效应的飞播马尾松林单木冠幅预测模型. 江西农业大学学报, 2020, 42 (5): 990- 1001.
	Yang Y, Peng H X, Pan P, et al. Individual crown diameter prediction models for aerially seeded Pinus massoniana based on mixed effects models. Acta Agriculturae Universitatis Jiangxiensis, 2020, 42 (5): 990- 1001.
	曾伟生, 唐守正. 非线性模型对数回归的偏差校正及与加权回归的对比分析. 林业科学研究, 2011, 24 (2): 137- 143.
	Zeng W S, Tang S Z. Bias correction in logarithmic regression and comparison with weighted regression for non-linear models. Forest Research, 2011, 24 (2): 137- 143.
	曾伟生, 唐守正. 一个新的通用性相对生长生物量模型. 林业科学, 2012, 48 (1): 48- 52. doi: 10.11707/j.1001-7488.20120109
	Zeng W S, Tang S Z. A new general biomass allometric model. Scientia Silvae Sinicae, 2012, 48 (1): 48- 52. doi: 10.11707/j.1001-7488.20120109
	张晓芳, 郭旭展, 洪　亮, 等. 冬奥核心区华北落叶松和白桦单木冠幅预测模型——组级贝叶斯模型、加性模型和混合效应模型比较. 林业科学, 2022, 58 (10): 89- 100.
	Zhang X F, Guo X Z, Hong L, et al. Comparison of single tree crown prediction models of Larix principis-rupprechtii and Betula platyphylla in the core area of the Winter Olympics in China. Scientia Silvae Sinicae, 2022, 58 (10): 89- 100.
	Andrews C, Weiskittel A, D’Amato A W, et al. Variation in the maximum stand density index and its linkage to climate in mixed species forests of the North American Acadian Region. Forest Ecology and Management, 2018, 417, 90- 102. doi: 10.1016/j.foreco.2018.02.038
	Chivhenge E, Ray D G, Weiskittel A R, et al. Evaluating the development and application of stand density index for the management of complex and adaptive forests. Current Forestry Reports, 2024, 10 (2): 133- 152. doi: 10.1007/s40725-024-00212-w
	Condés S, Sterba H. Derivation of compatible crown width equations for some important tree species of Spain. Forest Ecology and Management, 2005, 217 (2/3): 203- 218.
	Coombes A, Martin J, Slater D. Defining the allometry of stem and crown diameter of urban trees. Urban Forestry & Urban Greening, 2019, 44, 126421.
	Drew T J, Flewelling J W. Stand density management: an alternative approach and its application to douglas-fir plantations. Forest Science, 1979, 25 (3): 518- 532.
	Ge F X, Zeng W S, Ma W, et al. Does the slope of the self-thinning line remain a constant value across different site qualities? —an implication for plantation density management. Forests, 2017, 8 (10): 355. doi: 10.3390/f8100355
	Gill S J, Biging G S, Murphy E C. Modeling conifer tree crown radius and estimating canopy cover. Forest Ecology and Management, 2000, 126 (3): 405- 416. doi: 10.1016/S0378-1127(99)00113-9
	Hemery G E, Savill P S, Pryor S N. Applications of the crown diameter–stem diameter relationship for different species of broadleaved trees. Forest Ecology and Management, 2005, 215 (1/2/3): 285- 294.
	Pretzsch H, Biber P, Uhl E, et al. Crown size and growing space requirement of common tree species in urban centres, parks, and forests. Urban Forestry & Urban Greening, 2015, 14 (3): 466- 479.
	Qin Y P, Wu B Y, Lei X D, et al. Prediction of tree crown width in natural mixed forests using deep learning algorithm. Forest Ecosystems, 2023, 10, 100109. doi: 10.1016/j.fecs.2023.100109
	Reineke L H. Perfecting a stand-density index for even-aged forests. Journal of Agricultural Research, 1933, 46, 627- 638.
	Sharma R P, Vacek Z, Vacek S. Individual tree crown width models for Norway spruce and European beech in Czech Republic. Forest Ecology and Management, 2016, 366, 208- 220. doi: 10.1016/j.foreco.2016.01.040
	VanderSchaaf C L, Burkhart H E. Comparison of methods to estimate reineke’s maximum size-density relationship species boundary line slope. Forest Science, 2007, 53 (3): 435- 442. doi: 10.1093/forestscience/53.3.435
	West G B, Brown J H, Enquist B J. A general model for the structure and allometry of plant vascular systems. Nature, 1999, 400, 664- 667. doi: 10.1038/23251
	Woodall C W, Miles P D, Vissage J S. Determining maximum stand density index in mixed species stands for strategic-scale stocking assessments. Forest Ecology and Management, 2005, 216 (1/2/3): 367- 377.
	Xue W Y, Zhang W W, Chen Y M. Climate mediates the effects of forest gaps on tree crown allometry. Forest Ecology and Management, 2022, 525, 120563. doi: 10.1016/j.foreco.2022.120563
	Yoda K, Kira T, Ogawa H, et al. Self-thinning in overcrowded pure stands under cultivated and natural conditions (intraspecifc competition among higher plants XI). Journal of Biology Osaka City University, 1963, 14, 107- 129.
	Zeng W S. Using nonlinear mixed model and dummy variable model approaches to develop origin-based individual tree biomass equations. Trees, 2015, 29 (1): 275- 283. doi: 10.1007/s00468-014-1112-0
	Zhang L J, Bi H Q, Gove J H, et al. A comparison of alternative methods for estimating the self-thinning boundary line. Canadian Journal of Forest Research, 2005, 35 (6): 1507- 1514. doi: 10.1139/x05-070
	Zhang J, Gou Z H, Zhang F, et al. A study of tree crown characteristics and their cooling effects in a subtropical city of Australia. Ecological Engineering, 2020, 158, 106027. doi: 10.1016/j.ecoleng.2020.106027
	Zhang X Q, Zhang J G, Duan A G. A hierarchical Bayesian model to predict self-thinning line for Chinese fir in southern China. PLoS One, 2015, 10 (10): e0139788. doi: 10.1371/journal.pone.0139788

数据类型 Data type	样本量 Sample size	变量 Variable	最小值 Min	最大值 Max	平均值 Mean	标准差 SD	变动系数 CV（%）
样木数据 Tree data	600	冠幅Crown width C_W/m	0.45	10.62	3.82	2.12	55.5
样木数据 Tree data	600	胸径 Diameter D/cm	1.5	50.7	16.4	11.7	71.8
样地数据 Plot data	1273	每公顷株数 Stems per hectare N/hm^?2	50	3267	996	566	56.8
样地数据 Plot data	1273	平均胸径 Mean diameter D_M/cm	9.5	47.4	17.1	6.9	40.3

模型 Models	模型参数Parameters		评价指标 Evaluation indices
模型 Models	a/α	b/β	R²	SEE	TRE（%）	ASE（%）	MPE（%）	MPSE（%）
（1）	0.6934	0.6337	0.769	1.02	0.25	1.38	2.14	22.32
（2a）	53901	?1.4797	0.871	152	2.32	4.76	2.66	22.71
（2b）	56709	?1.4797	0.860	158	?2.74	?0.42	2.78	21.57
（2c）	41565	?1.3798	0.880	146	?0.09	?0.15	2.57	20.86

模型 Models	模型参数Parameters		评价指标 Evaluation indices
模型 Models	a/α	b/β	R²	SEE	TRE（%）	ASE（%）	MPE（%）	MPSE（%）
（6a1）	0.5712	0.6946	0.764	1.03	1.95	6.24	2.16	23.89
（6b1）	0.5758	0.6921	0.765	1.03	1.88	6.02	2.16	23.79
（6a2）	42950	?1.389	0.879	147	?0.68	?0.52	2.59	20.86
（6b2）	42250	?1.384	0.880	147	?0.48	?0.43	2.58	20.84

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