林分空间结构参数<i>N</i>元分布及其诠释 ——以小陇山锐齿栎天然混交林为例

张岗岗; 刘瑞红; 惠刚盈; 张弓乔; 赵中华; 胡艳波

doi:10.13332/j.1000-1522.20180228

林分空间结构参数N元分布及其诠释————以小陇山锐齿栎天然混交林为例

中国林业科学研究院林业研究所，国家林业局林木培育重点实验室，北京 100091

基金项目: “十三五”国家重点研发计划项目（2016YFD0600203）

详细信息

作者简介:
张岗岗。主要研究方向：森林经营理论与技术。Email：zg201394@163.com　地址：100091北京市海淀区香山路东小府1号中国林业科学研究院林业研究所

责任作者:
惠刚盈，研究员，博士生导师。主要研究方向：森林经营。Email：hui@caf.ac.cn　地址：同上

中图分类号: S758.5⁺3
计量
- 文章访问数: 2985
- HTML全文浏览量: 1161
- PDF下载量: 196
出版历程
- 收稿日期: 2018-07-11
- 修回日期: 2019-03-14
- 网络出版日期: 2019-04-01
- 发布日期: 2019-03-31

N-variate distribution and its annotation on forest spatial structural parameters: a case study of Quercus aliena var. acuteserrata natural mixed forest in Xiaolong Mountains, Gansu Province of northwestern China

Research Institute of Forestry, Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Chinese Academy of Forestry, Beijing 100091, China

摘要

摘要:
目的以甘肃省小陇山锐齿栎天然混交林为例，采用林分空间结构参数N元分布全面、系统地揭示林分空间结构特征，以实现森林结构信息的精确描述和直观表达，为森林结构精准调控和重建提供基础参考信息。
方法对70 m × 70 m标准地内的林木进行每木定位和调查，采用Winkelmass计算每株林木的混交度（M）、角尺度（W）、大小比数（U）和密集度（C），借助Excel透视表统计N元分布相对频率，并采用R 3.4.3、Origin 2015绘制N元分布图。
结果锐齿栎天然混交林整体及林分内大多数林木呈随机分布、混交良好、较为密集；林分整体中庸且各大小比数等级林木均接近20%；二元分布、三元分布和四元分布中该林分结构最突出特点表现为：不管结构参数如何组合，林分均表现出不同结构组合下大多数林木呈随机分布或混交良好。
结论结构参数N元分布借助分布频率表达优势从不同层次和角度全面系统地描述了林分结构特征信息，且不同分布之间优势互补，实现了林分结构从“点→线→面→体→超体”的精准详尽解译；双X横坐标或双Y纵坐标的3D图满足了多元分布结构信息直观展现需求；N元分布为森林结构精准调控和林分结构重建提供了先决信息。
- 结构参数 /
- 锐齿栎 /
- 二元分布 /
- 三元分布 /
- 四元分布
Abstract:
ObjectiveTo accurately describe and intuitively express forest structure information, and provide basic information for forest structure regulation and reconstruction, N-variate distributions were used to comprehensively and systematically characterize the spatial structure of the Quercus aliena var. acuteserrata natural mixed forest in Xiaolong Mountains, Gansu Province of northwestern China.
MethodEach tree in the 70 m × 70 m permanent sample plot was located and surveyed. The mingling (M), uniform angle index (W), neighborhood comparison (U) and crowding (C) of each tree were calculated by the Winkelmass software. The relative frequency of N-variate distributions was counted by the Excel Pivot Tables, and their corresponding multivariate diagrams were graphed by the R 3.4.3 and Origin 2015.
ResultIn the Quercus aliena var. acuteserrata natural mixed forest, the whole forest and most trees were randomly distributed, well mixed, relatively dense. The whole forest was moderately differentiated and each neighborhood comparison degree occupied near 20% trees. Among the bivariate distribution, trivariate distribution and quadrivariate distribution, the most prominent characteristics of the spatial structure was as follows: no matter how the structural parameters were combined, most trees were randomly distributed or well mixed under different structural combinations.
ConclusionThe N-variate distribution comprehensively and systematically describes the spatial structure characteristics from different levels and angles. Different distributions make their respective advantages complementary to each other and realize the stepwise interpretation process from point to hyperploid. 3D figures with double X horizontal coordinates or double Y vertical coordinates intuitively graph the structure information of the multivariate distribution. The N-variate distributions provide prior information for forest structure regulation and reconstruction.
- structural parameter /
- Quercus aliena var. acuteserrata /
- bivariate distribution /
- trivariate distribution /
- quadrivariate distribution

HTML全文

图 1 林木分布

不同实心圆●●●●●●●分别代表锐齿栎、山榆、华山松、辽东栎、太白槭、山核桃和其他树种，其大小代表林木胸径大小；空心圆代表冠幅大小。Different solid circles ●●●●●●● respectively represent Quercus aliena var. acuteserrata, Ulmus davidiana, Pinus armandii, Quercus wutaishanica, Acer caesium, Carya cathayensis and other species, and their size represents the DBH size. Different hollow circles represent the canopy size.

Figure 1. Tree distribution

下载: 全尺寸图片幻灯片

图 2 结构参数具体取值和生物学意义

Figure 2. Specific meanings of the W, M, U and C

下载: 全尺寸图片幻灯片

图 3 一元分布

Figure 3. Univariate distribution

下载: 全尺寸图片幻灯片

图 4 二元分布

Figure 4. Bivariate distribution

下载: 全尺寸图片幻灯片

图 5 三元分布

Figure 5. Trivariate distribution

下载: 全尺寸图片幻灯片

图 6 四元分布

Figure 6. Quadrivariate distribution

下载: 全尺寸图片幻灯片

表 1 主要树种概况

Table 1 General situation of main tree species

树种　 Tree species	蓄积/(m³·hm^{− 2}) Volume/(m³·ha^{− 1})	断面积/(m²·hm^{− 2}) Basal area/(m²·ha^{− 1})	平均胸径 Mean DBH/cm	平均树高 Mean tree height/m	密度/(tree·hm^{− 2}) Density/(tree·ha^{− 1})
锐齿栎 Quercus aliena var. acuteserrata	120.10	13.39	28.61	18.92	208
山榆 Ulmus davidiana	37.23	4.34	26.36	18.78	80
华山松 Pinus armandii	14.45	1.82	15.70	12.02	94
辽东栎 Quercus wutaishanica	11.67	1.36	30.70	18.04	18
太白槭 Acer caesium	6.40	1.02	9.96	11.13	131
山核桃 Carya cathayensis	5.72	0.68	37.69	17.53	6
其他树种 Other species	27.95	4.30	12.28	9.30	363
总计 Total	223.52	26.91	19.51	13.15	900

下载: 导出CSV

表 2 结构参数N元分布比较

Table 2 Comparison of different N-variate distributions

类别 Type	零元分布（均值） Zero variate distribution (average value)	一元分布 Univariate distribution	二元分布 Bivariate distribution	三元分布 Trivariate distribution	四元分布 Quadrivariate distribution
几何形状 Geometrical shape	点 Point	线 Line	面 Plane	体 Cube	超体 Supercube
结构组合 Structural combination	$\scriptstyle C_1^1$ = 1	$\scriptstyle C_5^1$ = 5	$\scriptstyle C_5^1 C_5^1$ = 25	$\scriptstyle C_5^1 C_5^1 C_5^1$ = 125	$\scriptstyle C_5^1 C_5^1 C_5^1 C_5^1$ = 625
结构信息量 Quantity of structural information	$\scriptstyle C_4^1 C_1^1$ = 4	$\scriptstyle C_4^1 C_5^1$ = 20	$\scriptstyle C_4^2 C_5^1 C_5^1$ = 150	$\scriptstyle C_4^3 C_5^1 C_5^1 C_5^1$ = 500	$\scriptstyle C_4^4 C_5^1 C_5^1 C_5^1 C_5^1$ = 625
特点 Characteristics	描述林分整体结构的平均状态；易于理解且计算简便；非常适于林分总体特征判断。 Describing the average state of the overall forest structure; being easy to understand and calculate makes it very suitable to evaluate the overall characteristics of stand.	刻画林分单方面结构特征；计算简易，图表展现非常直观；结果易于解释和应用；适于需要详细了解单方面结构信息的林分。 Describing the unilateral characteristics of stand structure; its calculation is simple and graphing is intuitional, and its results could be easily explained and applied. It is very powerful for detailedly interpreting unilateral structural information.	同时表征林分结构2方面结构特征；可推导出对应的两个一元分布及其平均值；图表展现多样，比较直观；适于详细同步分析林分某两方面结构信息，可操作性较强。 Simultaneously characterize two aspects of stand structure; the corresponding two univariate distributions and their mean values could be derived. The results graphing are diverse and intuitive. It is suitable for simultaneously analyzing two aspects of structural information in detail.	同时反映林分结构某3方面特征；可推导出3个二元分布、一元分布及其平均值；图表展现比较直观，信息量较大；适于详细同步分析林分结构的3个方面，针对性、实用性和可操作性较强。 Simultaneously characterize three aspects of stand structure; three bivariate distributions, univariate distributions and their mean values can be derived. The result charts are intuitive and contain more information. It is suitable for detailedly interpreting three aspects of heterogeneous structural information, being highly specific, practical and feasible.	全面量化林分结构4方面特征，是最详细完整的结构解译；可推导出6个二元分布，4个三元分布、一元分布及其平均值；图表内容详实，信息量最丰富；非常适于复杂林分的结构分析，尤其是适合林分结构全方位精准调整和重建。 Comprehensively analyze four aspects of stand structure, being the most detailed and complete structural interpretation; six bivariate distributions, four trivariate distributions, univariate distributions and their mean values can be derived. The charts and graphs are detailed and informative. It is very suitable for the structural analysis of complex stands, especially for the adjustment and reconstruction of stand structures in all aspects.
应用示例 Application examples	文献[8, 19-21] References [8, 19-21]	文献[8, 19-21] References [8, 19-21]	文献[12-13] References [12-13]	文献[17] Reference [17]	本文 This article
共同点 Common points	基于最近相邻木空间关系从林木大小、分布格局、是否异种和密集4个方面量化林分结构；借助U、W、M和C4个结构参数的N元分布对林分结构“分而析之”，也即从不同角度、不同层次和深度精准解析林分结构，利于林分结构潜在问题的精准判定、精确量化、精细调整和采伐木的高效选择。 Based on the spatial relationships among the nearest neighboring trees, the stand structure is quantified from four aspects: tree size, horizontal pattern, species diversity and crowding degree. N-variate distributions of the four structural parameters (U, W, M and C) can precisely characterize forest structure from different angles, levels and depths, which is conducive to the accurate determination, precise quantification, and fine adjustment of the potential problems of stand structure and the effective selection of cutting wood.
联系和区别 Connection and distinction	N元分布是N-一元分布的逐步细化；基于垂直投影降维和边际分布函数可对四元分布→三元分布→二元分布→一元分布→零元分布（均值）“合而求之”，但该递推过程不可逆；不同分布之间优势互补，联合效应类似“1 + 1 > 2”。 N-variate distribution is the stepwise refinement of N-1-variate distribution. Based on the vertical projection dimensionality reduction and marginal probability distribution function, it is possible to realize the stepwise recurrence from the quadrivariate distribution to zero variate distribution (mean value), but the recursive process is not reversible. Different N-variate distributions are complementary to each other, and their combined use has better effects, similar to “1 + 1 > 2”.

下载: 导出CSV

参考文献(51)

[1]	Franklin J F, Spies T A, Van Pelt R, et al. Disturbances and structural development of natural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example[J]. Forest Ecology and Management, 2002, 155(1−3): 399−423. doi: 10.1016/S0378-1127(01)00575-8
[2]	Spies T A. Forest structure: a key to the ecosystem[J]. Northwest Science, 1998, 72(2): 34−39.
[3]	Pommerening A. Evaluating structural indices by reversing forest structural analysis[J]. Forest Ecology and Management, 2006, 224(3): 266−277. doi: 10.1016/j.foreco.2005.12.039
[4]	Gadow K V, Zhang C Y, Wehenkel C, et al. Forest structure and diversity[M]//Pukkala T, Gadow K V. Continuous cover forestry. Dordrecht: Springer, 2012: 29−83.
[5]	惠刚盈, Gadow K V, 赵中华, 等. 结构化森林经营原理[M]. 北京: 中国林业出版社, 2016. Hui G Y, Gadow K V, Zhao Z H, et al. Principles of structure-based forest management[M]. Beijing: China Forestry Publishing House, 2016.
[6]	汤孟平. 森林空间结构分析与优化经营模型研究[D]. 北京: 北京林业大学, 2003. Tang M P. Study on forest spatial structure analysis and optimal management model[D]. Beijing: Beijing Forestry University, 2003.
[7]	惠刚盈. 基于相邻木关系的林分空间结构参数应用研究[J]. 北京林业大学学报, 2013, 35(4):1−8. Hui G Y. Studies on the application of stand spatial structure parameters based on the relationship of neighborhood trees[J]. Journal of Beijing Forestry University, 2013, 35(4): 1−8.
[8]	胡艳波, 惠刚盈. 基于相邻木关系的林木密集程度表达方式研究[J]. 北京林业大学学报, 2015, 37(9):1−8. Hu Y B, Hui G Y. How to describe the crowding degree of trees based on the relationship of neighboring trees[J]. Journal of Beijing Forestry University, 2015, 37(9): 1−8.
[9]	李远发. 林分空间结构参数二元分布的研究[D]. 北京: 中国林业科学研究院, 2013. Li Y F. The bivariate distribution of forest stand spatial structural parameters[D]. Beijing: Chinese Academy of Forestry, 2013.
[10]	Gadow K V, Hui G Y. Characterizing forest spatial structure and diversity[C]//Proceedings of the SUFOR International “Sustainable Forestry in Temperate Regions”. Lund: University of Lund, 2001: 20−30.
[11]	胡艳波, 惠刚盈, 戚继忠, 等. 吉林蛟河天然红松阔叶林的空间结构分析[J]. 林业科学研究, 2003, 16(5):523−530. doi: 10.3321/j.issn:1001-1498.2003.05.002 Hu Y B, Hui G Y, Qi J Z, et al. Analysis of the spatial structure of natural Korean pine broadleaved forest[J]. Forest Research, 2003, 16(5): 523−530. doi: 10.3321/j.issn:1001-1498.2003.05.002
[12]	Li Y F, Hui G Y, Zhao Z H, et al. The bivariate distribution characteristics of spatial structure in natural Korean pine broad-leaved forest[J]. Journal of Vegetation Science, 2012, 23(6): 1180−1190. doi: 10.1111/jvs.2012.23.issue-6
[13]	Li Y F, Hui G Y, Zhao Z H, et al. Spatial structural characteristics of three hardwood species in Korean pine broad-leaved forest: validating the bivariate distribution of structural parameters from the point of tree population[J]. Forest Ecology and Management, 2014, 314: 17−25. doi: 10.1016/j.foreco.2013.11.012
[14]	Li Y F, Hui G Y, Yu S F, et al. Nearest neighbour relationships in Pinus yunnanensis var. tenuifolia forests along the Nanpan River, China[J]. iForest-Biogeosciences and Forestry, 2017, 10(4): 746−753. doi: 10.3832/ifor2405-010
[15]	Chai Z Z, Sun C L, Wang D X, et al. Spatial structure and dynamics of predominant populations in a virgin old-growth oak forest in the Qinling Mountains, China[J]. Scandinavian Journal of Forest Research, 2017, 32(1): 19−29. doi: 10.1080/02827581.2016.1183703
[16]	Zhang R B, Ding G J, Luo X M, et al. Bivariate distribution characteristics of spatial structure in five different Pinus massoniana forests[J]. Dendrobiology, 2017, 78: 75−84. doi: 10.12657/denbio.078.008
[17]	白超. 空间结构参数及其在锐齿栎天然林结构动态分析中的应用[D]. 北京: 中国林业科学研究院, 2016. Bai C. Spatial structure parameters and the application on studying structure dynamics of natural Quercus aliena var. acuteserrata forest [D]. Beijing: Chinese Academy of Forestry, 2016.
[18]	鲁东民, 王忠明, 付贺龙. 基于网络地理信息系统的林业资源统计数据可视化系统设计[J]. 世界林业研究, 2017, 30(3):46−51. Lu D M, Wang Z M, Fu H L. Design of forestry resources statistical data visualization system based on WebGIS[J]. World Forestry Research, 2017, 30(3): 46−51.
[19]	惠刚盈, Klaus von Gadow, Matthias Albert. 角尺度: 一个描述林木个体分布格局的结构参数[J]. 林业科学, 1999, 35(1):37−42. doi: 10.3321/j.issn:1001-7488.1999.01.006 Hui G Y, Gadow K V, Albert M. The neighbourhood pattern: a new structure parameter for describing distribution of forest tree position[J]. Scientia Silvae Sinicae, 1999, 35(1): 37−42. doi: 10.3321/j.issn:1001-7488.1999.01.006
[20]	惠刚盈, Gadow K V, Matthias Albert. 一个新的林分空间结构参数:大小比数[J]. 林业科学研究, 1999, 12(1):1−6. doi: 10.3321/j.issn:1001-1498.1999.01.001 Hui G Y, Gadow K V, Albert M. A new parameter for stand spatial structure: neighbourhood comparison[J]. Forest Research, 1999, 12(1): 1−6. doi: 10.3321/j.issn:1001-1498.1999.01.001
[21]	惠刚盈, 胡艳波. 混交林树种空间隔离程度表达方式的研究[J]. 林业科学研究, 2001, 14(1):23−27. doi: 10.3321/j.issn:1001-1498.2001.01.004 Hui G Y, Hu Y B. Measuring species spatial isolation in mixed forests[J]. Forest Research, 2001, 14(1): 23−27. doi: 10.3321/j.issn:1001-1498.2001.01.004
[22]	赵中华, 刘文桢, 石小龙, 等. 小陇山锐齿栎天然林结构动态分析[J]. 林业科学研究, 2015, 28(6):759−766. doi: 10.3969/j.issn.1001-1498.2015.06.001 Zhao Z H, Liu W Z, Shi X L, et al. Structure dynamic of Quercus aliena var. acuteserrata natural forest on Xiaolongshan[J]. Forest Research, 2015, 28(6): 759−766. doi: 10.3969/j.issn.1001-1498.2015.06.001
[23]	吕寻, 杨双宝, 刘文桢, 等. 小陇山锐齿栎原始群落林木径阶空间结构特征[J]. 北京林业大学学报, 2015, 37(5):11−18. Lü X, Yang S B, Liu W Z, et al. Analysis of spatial structure characteristics based on diameter class of trees in primeval Quercus aliena var. acuteserrata community in the forest area of Xiaolong Mountain, Gansu Province[J]. Journal of Beijing Forestry University, 2015, 37(5): 11−18.
[24]	郭小龙, 刘文桢, 张宋智, 等. 小陇山林区锐齿栎原始林群落的空间结构特征[J]. 西北农林科技大学学报(自然科学版), 2014, 42(11):106−112. Guo X L, Liu W Z, Zhang S Z, et al. Spatial structure characteristics of Quercus aliena var. acuteserrata primeval forest in Xiaolongshan Forest Area[J]. Journal of Northwest A&F University (Natural Science Edition), 2014, 42(11): 106−112.
[25]	巫志龙, 周成军, 周新年, 等. 杉阔混交人工林林分空间结构分析[J]. 林业科学研究, 2013, 26(5):609−615. Wu Z L, Zhou C J, Zhou X N, et al. Analysis of stand spatial structure of Cunninghamia lanceolata-broadleaved mixed plantation[J]. Forest Research, 2013, 26(5): 609−615.
[26]	曹小玉, 李际平, 封尧, 等. 杉木生态公益林林分空间结构分析及评价[J]. 林业科学, 2015, 51(7):37−48. Cao X Y, Li J P, Feng Y, et al. Analysis and evaluation of the stand spatial structure of Cunninghamia lanceolata ecological forest[J]. Scientia Silvae Sinicae, 2015, 51(7): 37−48.
[27]	刘灵, 胡艳波, 王千雪, 等. 沙地樟子松天然纯林的结构特征[J]. 林业科学研究, 2016, 29(5):623−629. doi: 10.3969/j.issn.1001-1498.2016.05.001 Liu L, Hu Y B, Wang Q X, et al. Structure characters of Pinus sylvestris var. mongolica natural forest on sandy land[J]. Forest Research, 2016, 29(5): 623−629. doi: 10.3969/j.issn.1001-1498.2016.05.001
[28]	张岗岗, 王得祥, 柴宗政, 等. 小陇山2种典型天然林空间结构参数分布特征[J]. 林业科学研究, 2015, 28(4):531−537. doi: 10.3969/j.issn.1001-1498.2015.04.012 Zhang G G, Wang D X, Chai Z Z, et al. Distribution characteristics of two typical natural forest spatial structure parameters in Xiaolongshan[J]. Forest Research, 2015, 28(4): 531−537. doi: 10.3969/j.issn.1001-1498.2015.04.012
[29]	王占刚, 庄大方, 邱冬生, 等. 林业数据挖掘与可视化的应用分析[J]. 地球信息科学学报, 2007, 9(4):19−22. doi: 10.3969/j.issn.1560-8999.2007.04.004 Wang Z G, Zhuang D F, Qiu D S, et al. Application analysis of data mining and visualization in forestry[J]. Geo-information Science, 2007, 9(4): 19−22. doi: 10.3969/j.issn.1560-8999.2007.04.004
[30]	Ni R Q, Baiketuerhan Y, Zhang C Y, et al. Analysing structural diversity in two temperate forests in northeastern China[J]. Forest Ecology and Management, 2014, 316: 139−147. doi: 10.1016/j.foreco.2013.10.012
[31]	Pommerening A. Approaches to quantifying forest structures[J]. Forestry, 2002, 75(3): 305−324. doi: 10.1093/forestry/75.3.305
[32]	Szmyt J. Spatial structure of managed beech-dominated forest: applicability of nearest neighbors indices[J]. Dendrobiology, 2012, 68: 69−76.
[33]	Zhang L J, Hui G Y, Hu Y B, et al. Spatial structural characteristics of forests dominated by Pinus tabulaeformis Carr. [J/OL]. PLoS ONE, 2018, 13(4): e0194710 [2018−03−10]. https://doi.org/10.1371/journal.pone.0194710.
[34]	Kint V, Van Meirvenne M, Nachtergale L, et al. Spatial methods for quantifying forest stand structure development: a comparison between nearest-neighbor indices and variogram analysis[J]. Forest Science, 2003, 49(1): 36−49.
[35]	Aguirre O, Hui G Y, Gadow K V, et al. An analysis of spatial forest structure using neighbourhood-based variables[J]. Forest Ecology and Management, 2003, 183(1/3): 137−145.
[36]	Zhao Z H, Hui G Y, Hu Y B, et al. Testing the significance of different tree spatial distribution patterns based on the uniform angle index[J]. Canadian Journal of Forest Research, 2014, 44(11): 1419−1425. doi: 10.1139/cjfr-2014-0192
[37]	赵中华, 惠刚盈, 胡艳波, 等. 角尺度判断林木水平分布格局的新方法[J]. 林业科学, 2016, 52(2):10−16. Zhao Z H, Hui G Y, Hu Y B, et al. The new method judged horizontal distribution pattern by uniform angle index[J]. Scientia Silvae Sinicae, 2016, 52(2): 10−16.
[38]	胡艳波, 惠刚盈. 一种新的基于混交度的林木种群分布格局测度方法[J]. 北京林业大学学报, 2015, 37(1):9−14. Hu Y B, Hui G Y. A new method for measuring population distribution patterns of forest trees based on the mingling degree[J]. Journal of Beijing Forestry University, 2015, 37(1): 9−14.
[39]	惠刚盈, 张弓乔, 赵中华, 等. 林木分布格局多样性测度方法: 以阔叶红松林为例[J]. 生物多样性, 2016, 24(3):280−286. Hui G Y, Zhang G Q, Zhao Z H, et al. Measuring diversity of tree distribution patterns in natural forests[J]. Biodiversity Science, 2016, 24(3): 280−286.
[40]	Hui G Y, Zhao X H, Zhao Z H, et al. Evaluating tree species spatial diversity based on neighborhood relationships[J]. Forest Science, 2011, 57(4): 292−300.
[41]	白超, 惠刚盈. 林木直径大小多样性量化测度指数的比较研究[J]. 林业科学研究, 2016, 29(3):340−347. doi: 10.3969/j.issn.1001-1498.2016.03.005 Bai C, Hui G Y. Study on diversity indices of tree diameter size[J]. Forest Research, 2016, 29(3): 340−347. doi: 10.3969/j.issn.1001-1498.2016.03.005
[42]	惠刚盈, 胡艳波, 徐海, 等. 结构化森林经营[M]. 北京: 中国林业出版社, 2007. Hui G Y, Hu Y B, Xu H, et al. Structure-based forest management [M]. Beijing: China Forestry Publishing House, 2007.
[43]	惠刚盈, 胡艳波, 赵中华, 等. 基于交角的林木竞争指数[J]. 林业科学, 2013, 49(6):68−73. Hui G Y, Hu Y B, Zhao Z H, et al. A forest competition index based on intersection angle[J]. Scientia Silvae Sinicae, 2013, 49(6): 68−73.
[44]	Hui G Y, Wang Y, Zhang G Q, et al. A novel approach for assessing the neighborhood competition in two different aged forests[J]. Forest Ecology and Management, 2018, 422: 49−58. doi: 10.1016/j.foreco.2018.03.045
[45]	Pommerening A, Sánchez M A J. Tamm review: tree interactions between myth and reality[J]. Forest Ecology and Management, 2018, 424: 164−176. doi: 10.1016/j.foreco.2018.04.051
[46]	惠刚盈, 胡艳波, 赵中华. 结构化森林经营研究进展[J]. 林业科学研究, 2018, 31(1):85−93. Hui G Y, Hu Y B, Zhao Z H. Research progress of structure-based forest management[J]. Forest Research, 2018, 31(1): 85−93.
[47]	Li Y F, Ye S M, Hui G Y, et al. Spatial structure of timber harvested according to structure-based forest management[J]. Forest Ecology and Management, 2014, 322(3): 106−116.
[48]	Pommerening A, Stoyan D. Reconstructing spatial tree point patterns from nearest neighbour summary statistics measured in small subwindows[J]. Canadian Journal of Forest Research, 2008, 38(5): 1110−1122. doi: 10.1139/X07-222
[49]	Zhang G Q, Hui G Y, Zhao Z H, et al. Composition of basal area in natural forests based on the uniform angle index[J]. Ecological Informatics, 2018, 45: 1−8. doi: 10.1016/j.ecoinf.2018.01.002
[50]	Pommerening A, Uria-Diez J. Do large forest trees tend towards high species mingling?[J]. Ecological Informatics, 2017, 42: 139−147. doi: 10.1016/j.ecoinf.2017.10.009
[51]	Wang H X, Peng H, Hui G Y, et al. Large trees are surrounded by more heterospecific neighboring trees in Korean pine broad-leaved natural forests[J]. Scientific Reports, 2018, 8(1): 9149−9160. doi: 10.1038/s41598-018-27140-7