基于UAV-LiDAR数据的长白落叶松多维偏冠的邻体效应

doi:10.11707/j.1001-7488.LYKX20250603

摘要/Abstract

摘要：

目的: 基于UAV-LiDAR点云数据构建树冠多维偏冠指数，评估邻体效应对林木偏冠程度的影响，为理解树冠生长动态及其形态可塑性机制提供理论依据。方法: 以黑龙江省佳木斯市孟家岗林场的长白落叶松人工林为研究对象，利用UAV-LiDAR平台获取激光雷达点云，采用点云层次区域合并算法进行单木分割并提取树冠参数，从3个维度构建偏冠指数，用以量化树冠的不对称性：一维偏冠指数（CAI1）为树顶与树冠三维凸包中心的夹角；二维偏冠指数（CAI2）为树冠投影偏离标准圆的程度；三维偏冠指数（CAI3）为真实树冠三维体积偏离假设树冠对称理想几何体的程度。提取树冠大小、空间结构、邻体竞争因子，通过相关分析与线性混合效应模型评估不同领域特征对多维偏冠程度的影响。结果: 树冠大小因子与偏冠指标均显著负相关，即树冠偏冠程度随树冠增大而减小。在空间结构指标中，角尺度和密集度对偏冠影响不显著（P>0.05），但树高大小比数、冠幅大小比数和开敞度与3个偏冠指数均显著相关（P<0.01），直接驱动冠形发育。邻体竞争指数与CAI2和CAI3均极显著正相关，树冠偏冠程度随邻体竞争压力增大而增大，揭示出邻体竞争在驱动偏冠中的关键作用。树木为规避侧方邻体的竞争压力，会优先向空间开阔侧拓展冠层，从而导致树冠不对称生长。与CAI2和CAI3相比，CAI1分布较为集中（0~0.12），与树木大小、空间结构分布以及邻体竞争的相关关系普遍较弱。线性混合效应模型（LMM）拟合结果显示，树冠大小、空间结构、邻体竞争因子对CAI3的解释能力高达65％，远高于CAI2的19％。从各因子的标准化固定效应系数可知，偏冠指数变异主要由邻体竞争驱动，其中CAI3的变异主要受树冠大小和邻体竞争的共同作用。结论: 林木对生长空间和光资源的竞争是导致树冠不对称发育的关键因素。邻体竞争对CAI2和CAI3偏冠指数的变异起主导作用。空间结构因子与偏冠指数的相关分析表明，相较于林木水平分布格局，其大小优势关系和垂直空间竞争对偏冠的驱动更直接。LMM对CAI2和CAI3变异的解析结果证实三维空间视角能更有效捕捉树冠形态的局部调整，揭示林木相互作用的本质是对空间生态位的竞争。

关键词: 偏冠指数, 树冠结构, 林木空间结构, 邻体竞争, 无人机激光雷达

Abstract:

Objective: Traditional forest inventory methods are limited in accurately characterizing asymmetric crown growth. This study aims to develop multi-dimensional crown asymmetry indices using UAV-LiDAR point cloud data and to evaluate the effects of neighbor interactions on the degree of crown asymmetry. Method: The study was conducted in a Larix olgensis plantation in Mengjiagang Forest Farm, Jiamusi City, Heilongjiang Province. An UAV-LiDAR platform was used to acquire point cloud data. Following individual tree segmentation, crown parameters were extracted to construct asymmetry indices from three dimensions to quantify crown asymmetry. The one-dimensional crown asymmetry index (CAI1) was defined as the angle between the treetop and the centroid of the 3D convex hull of the crown. The two-dimensional index (CAI2) represented the deviation of the crown projection area from a standard circle. The three-dimensional index (CAI3) quantified the deviation of the actual 3D crown volume from an assumed ideal symmetrical geometry of tree crown. Subsequently, factors related to crown size, spatial structure, and neighbor competition were extracted. Correlation analysis and linear mixed-effects models (LMM) were employed to assess the influence of different neighbor characteristics on multi-dimensional crown asymmetry. Result: The results showed that crown size factors were all significantly negatively correlated with crown asymmetry indices, meaning that the degree of asymmetry decreased as crown size increased. Among the spatial structure indices, uniform angle index (W) and crowding (C) showed no significant effect on asymmetry (P>0.05). However, tree height and crown neighborhood comparison, as well as opening degree, were significantly correlated with all three asymmetry indices (P<0.01), directly driving crown shape development. Neighbor competition indices were very significantly positively correlated with CAI2 and CAI3, indicating that crown asymmetry was intensified with increasing competitive pressure, revealing the critical role of neighbor competition in driving crown asymmetry. Trees tend to expand their canopy preferentially towards more open spaces to avoid lateral competitive pressure from neighbors, leading to asymmetric crown development. Compared to CAI2 and CAI3, CAI1 values were more concentrated ( 0–0.12) and showed generally weaker correlations with tree size, spatial structure, and neighbor competition. LMM showed that crown size, spatial structure, and neighbor competition factors explained up to 65% of the variance in CAI3, substantially higher than the 19% explained for CAI2. Analysis of standardized fixed effect coefficients revealed that variation in crown asymmetry was primarily driven by neighbor competition, with variation in CAI3 resulting from the combined effects of both crown size and neighbor competition. Conclusion: Competition of trees for growing space and light resources is a key factor leading to asymmetric crown development. Neighbor competition plays a dominant role in driving variation in the CAI2 and CAI3 asymmetry indices. Correlation analyses between spatial structure factors and asymmetry indices indicates that, compared to the horizontal distribution pattern of trees, their size dominance relationships and vertical spatial competition have a more direct effect on crown asymmetry. The differential explanatory power of LMM for CAI2 and CAI3 variation confirms that a three-dimensional spatial perspective captures localized crown shape adjustments more effectively, revealing that the essence of tree interactions is competition for spatial niches.

Key words: crown asymmetry index, crown structure, tree spatial structure, neighbor competition, unmanned aerial vehicle

中图分类号:

S757

张诺,郝元朔,董利虎,赵颖慧,李凤日. 基于UAV-LiDAR数据的长白落叶松多维偏冠的邻体效应[J]. 林业科学, 2026, 62(7): 27-37.

Nuo Zhang,Yuanshuo Hao,Lihu Dong,Yinghui Zhao,Fengri Li. Neighbor Effects on Multi-Dimensional Crown Asymmetry in Larix olgensis Based on UAV-LiDAR Data[J]. Scientia Silvae Sinicae, 2026, 62(7): 27-37.

图/表 9

表1

图1

表2

表3

邻体效应指标①"

指标Index	公式Equation		公式编号Equation number
空间结构指数Spatial structure indices
角尺度Uniform angle index (W)	$ \dfrac{1}{N}\displaystyle \sum\limits_{j=1}^{N}{Z}_{ij} $	$ {Z}_{ij}=\begin{cases} 1，\mathrm{当}{\alpha }_{j}{< \alpha }_{0}\mathrm{时}\\0，\mathrm{否则}\end{cases} $	（4）
密集度Crowding index (C)	$ \dfrac{1}{N}\displaystyle \sum\limits_{j=1}^{N}{y}_{ij} $	$ {y}_{ij}=\begin{cases} 1，\mathrm{当}{\text{CR}}_{i}+{\text{CR}}_{j}> {L}_{ij}\mathrm{时}\\0，\mathrm{否则}\end{cases} $	（5）
树高大小比数Neighborhood comparison index based on treeheight ($ {U}_{\left[\mathrm{H}\right]} $)	$ \dfrac{1}{N}\displaystyle \sum\limits_{j=1}^{N}{k}_{ij} $	$ {k}_{ij}=\begin{cases} 1，\mathrm{当}{H}_{j}{\geq H}_{i}\mathrm{时}\\0，\mathrm{否则}\end{cases} $	（6）
树冠大小比数Neighborhood comparison index based on crown diameter ($ {U}_{\left[\text{CD}\right]} $)	$ \dfrac{1}{N}\displaystyle \sum\limits_{j=1}^{N}{k}_{ij} $	$ {k}_{ij}=\begin{cases} 1，\mathrm{当}{\text{CD}}_{j}{\geq \text{CD}}_{i}\mathrm{时}\\0，\mathrm{否则}\end{cases} $	（6）
开敞度Openness index (B)	$ \dfrac{1}{N}\displaystyle \sum\limits_{j=1}^{N}\dfrac{{L}_{ij}}{{H}_{j}} $		（7）
竞争指数Competition indices
$ {\text{Hegyi}}_{\left[\mathrm{H}\right]} $	$ \displaystyle \sum\limits_{j=1}^{N}{\text{CI}}_{j\left[\mathrm{H}\right]} $	$ \mathit{\mathit{\mathrm{CI}}}_{j\left[\mathrm{H}\right]} $= $ \dfrac{{H}_{j}}{{H}_{i}\times {L}_{ij}} $	（8）
$ {\text{CVC}}_{\left[\mathrm{H}\right]} $	$ \sqrt{\dfrac{\displaystyle \sum\limits_{j=1}^{N}{\left({\text{CI}}_{j\left[\mathrm{H}\right]}-\overline{{\text{CI}}_{\left[\mathrm{H}\right]}}\right)}^{2}}{N}} $		（9）
$ {\text{Hegyi}}_{\left[\text{CD}\right]} $	$ \displaystyle \sum\limits_{j=1}^{N}{CI}_{j\left[\text{CD}\right]} $	$ {\text{CI}}_{j\left[\text{CD}\right]} $=$ \dfrac{{\text{CD}}_{j}}{{\text{CD}}_{i}\times {L}_{ij}} $	（10）
$ {\text{CVC}}_{\left[\text{CD}\right]} $	$ \sqrt{\dfrac{\displaystyle \sum\limits_{j=1}^{N}{\left({\text{CI}}_{j\left[\text{CD}\right]}-\overline{{\text{CI}}_{\left[\text{CD}\right]}}\right)}^{2}}{N}} $		（11）
CVR	$ \dfrac{{V}_{\text{cone}j}}{{V}_{\text{cone}i}} $		（12）

表3

图2

图3

图4

表4

表5

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样地编号 Plot No.	林分密度 Stand density/ （tree?hm^–2）	平均胸径 Mean DBH/cm	平均树高 Mean tree height/m	平均冠幅 Mean crown diameter/m	平均冠长 Mean crown length/m
1	2 132	12.38	14.65	2.61	5.87
2	1 848	13.33	15.59	2.65	6.52
3	2 043	13.01	15.69	2.57	6.56
4	2 421	11.77	14.48	2.13	5.87
5	2 425	11.26	14.59	2.18	6.55
6	2 012	12.62	16.63	2.03	7.17
7	2 021	12.91	15.68	2.04	6.05
8	1 622	13.68	16.77	2.42	6.20
9	2 620	13.07	16.25	2.31	7.06
10	2 343	12.74	16.18	2.68	6.58
11	1 721	13.51	16.48	2.71	7.18
12	2 318	12.40	15.55	2.55	6.75

指标 Index	公式 Equation	公式编号 Equation number
CAI1	$ \arctan \left(\dfrac{{y}_{\mathrm{t}}-{y}_{\mathrm{c}}}{\left\| {x}_{\mathrm{t}}-{x}_{\mathrm{c}}\right\| }\right)\div \dfrac{{\text{π}}}{2} $	（1）
CAI2	$ 1-\dfrac{1}{N}\displaystyle \sum\limits_{i=1}^{N}\dfrac{\overline{R}}{\left\| {R}_{i}-\overline{R}\right\| +\overline{R}} $	（2）
CAI3	$ 100-\left(\dfrac{{V}_{\mathrm{I}}}{{V}_{\mathrm{m}}}\times 100\right) $	（3）

模型 Model	参数和系数 Parameters and coefficients	线性模型 Linear model (R²)	混合效应模型 Linear mixed model (R²)
CAI2	$ {\beta }_{0}+{\beta }_{1}{U}_{\left[\text{CD}\right]}+{\beta }_{2}{\text{CVC}}_{\left[\mathrm{H}\right]}+{\beta }_{3}{\text{CVC}}_{\left[\text{CD}\right]}+{\beta }_{4}\text{CVR}+\varepsilon $	0.17	0.19
CAI3	$ {\beta }_{0}+{{{\beta }_{1}}\text{CPA}+{{\beta }_{2}}\text{CV}+\beta }_{3}{U}_{\left[\text{CD}\right]}+{\beta }_{4}B+{\beta }_{5}{\text{Hegyi}}_{\left[\text{CD}\right]}+{\beta }_{6}\text{CVR}+\varepsilon $	0.62	0.65

项目 Item	β	95% CI ?	95% CI +	P
CAI2
$ {U}_{\left[\text{CD}\right]} $	0.08	0.05	0.11	<0.001
$ {\text{CVC}}_{\left[H\right]} $	0.19	0.08	0.31	<0.001
$ {\text{CVC}}_{\left[\text{CD}\right]} $	0.20	0.11	0.28	<0.001
CVR	0.62	0.49	0.74	<0.001
CAI3
CPA	–0.25	–0.35	–0.15	<0.001
CV	–0.30	–0.37	–0.23	<0.001
$ {U}_{\left[\text{CD}\right]} $	0.05	0.03	0.07	<0.001
B	–0.12	–0.17	–0.07	<0.001
$ {\text{Hegyi}}_{\left[\text{CD}\right]} $	0.34	0.28	0.39	<0.001
CVR	0.30	0.22	0.38	<0.001

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