基于距离相关Hegyi指数的云冷杉天然林单木胸径生长模型

周泽宇; 周超凡; 胡兴国; 陈科屹; 杜满义; 张会儒; 符利勇

doi:10.12171/j.1000-1522.20210510

基于距离相关Hegyi指数的云冷杉天然林单木胸径生长模型

1.
中国林业科学研究院华北林业实验中心，北京 102300
2.
中国林业科学研究院森林生态环境与保护研究所，北京 100091
3.
吉林省汪清林业局，吉林汪清 133200
4.
中国林业科学研究院林业科技信息研究所，北京 100091
5.
中国林业科学研究院资源信息研究所，国家林业和草原局森林经营与生长模拟重点实验室，北京 100091

基金项目: 国家重点研发计划课题（2022YFD2200503）。

详细信息

作者简介:
周泽宇，博士。主要研究方向：森林生长收获预估模型。Email：zeyuzho@163.com　地址：102300北京市门头沟区水闸西路1号中国林业科学研究院华北林业实验中心

责任作者:
张会儒，研究员，博士生导师。主要研究方向：森林可持续经营。Email：huiru@ifrit.ac.cn　地址：同上。

中图分类号: S791.14；S791.18；S750
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出版历程
- 收稿日期: 2021-11-30
- 修回日期: 2023-05-24
- 录用日期: 2023-05-25
- 网络出版日期: 2023-05-30
- 刊出日期: 2023-10-30

Single tree DBH growth model of spruce-fir natural forest based on distance related Hegyi index

1.
Experimental Center of Forestry in North China, Chinese Academy of Forestry, Beijing 102300, China
2.
Ecology and Nature Conservation Institute, Chinese Academy of Forestry, Beijing 100091
3.
Wangqing Forestry Bureau, Wangqing 133200, Jinlin, China
4.
Research Institute of Forestry Policy and Information, Chinese Academy of Forestry, Beijing 100091, China
5.
Research Institute of Forest Resources Information Techniques, Chinese Academy of Forestry, Key Laboratory of Forest Management and Growth Modeling, National Forestry and Grassland Administration, Beijing 100091, China

摘要

摘要:
目的
基于与距离有关的Hegyi种内和种间竞争指数，构建以期初胸径及Hegyi竞争指数为预测变量的云冷杉天然林单木胸径生长预测模型。
方法
使用2013年金沟岭云冷杉林3块1 hm²固定样地内实测数据，以非线性Logistic模型为基础模型，逐步引入期初胸径、种内和种间竞争指数，以探究竞争和生长对于单木胸径变化的影响，并利用非线性混合效应模型进行模型精度的提升。
结果
模型拟合结果显示：以期初胸径、种内Hegyi竞争指数、种间Hegyi竞争指数为预测变量，树种水平下随机效应作用在参数a₀ 、 a₂ 、a₃上时，模型具有最优的拟合效果，且未出现异方差现象。建模数据的调整决定系数（ $R_{\rm{adj}}^2$ ）、均方根误差（RMSE）、总相对误差（TRE）分别为0.512 6、0.607 1、3.651 9%，利用检验数据对模型进行独立样本检验，检验数据的 $R_{\rm{adj}}^2$ 为0.509 8，检验RMSE均为0.624 2，检验TRE均为3.883 1%，检验数据的残差分布未出现明显的异方差现象。
结论
云冷杉天然林中影响对象木胸径生长的因素包括单木大小因子与竞争因子。期初胸径对胸径生长的影响较大，为正向作用。竞争因子中，种内竞争和种间竞争均对单木胸径的生长具有明显的调控作用，为负向抑制作用。本文所构建的基于树种水平的非线性混合效应模型能够为研究区天然云冷杉林中对象木的胸径生长预测提供一定的理论基础以及技术参考。
- Hegyi竞争指数 /
- 期初胸径 /
- 混合效应模型 /
- 胸径生长
Abstract:
Objective
Based on the Hegyi intraspecific and interspecific competition indexes related to distance, the prediction model of DBH increment of natural spruce-fir forest was constructed based on initial DBH and Hegyi competition index.
Method
In order to explore the effects of competition and growth on DBH growth of individual trees, the measured data of three permanent sample plots (each of 1 ha) of spruce-fir in Jingouling Forest Farm, Jilin Province of northeastern China in 2013 were utilized. Based on the nonlinear Logistics model, initial DBH, intraspecific and interspecific competition indexes were gradually added. The nonlinear mixed-effect model was utilized to improve the model accuracy.
Result
The results of model fitting showed that the model had the best fitting effect when initial DBH, intraspecific and interspecific Hegyi competition indexes were used as predictive variables, the best fitting efficiency occurred based on the species-level of random effect worked on parameters a₀, a₂, a₃, and without heteroscedasticity. The $R_{{\rm{adj}}}^2$ , root mean squared error (RMSE) and total relative error (TRE) of modeling data were 0.512 6, 0.607 1, 3.651 9%, respectively. The $R_{{\rm{adj}}}^2$ , RMSE and TRE of validation data were 0.509 8, 0.624 2, 3.883 1%, respectively. The residual distribution of validation data did not show obvious heteroscedasticity.
Conclusion
The factors affect the diameter growth of target trees in natural spruce-fir forest, including self-growth factors and competition factors. Among the self-growth factors, initial DBH is the main factor and plays a positive role to promote DBH increment. Among the competition factors, interspecific competition and intraspecific competition have obvious inhibition effects on the growth of individual tree DBH increment. The nonlinear mixed effect model based on species-level can provide a theoretical basis and technical reference for the DBH growth of target trees in natural spruce-fir forest in the study area.
- Hegyi competition index /
- initial diameter at breast height /
- mixed effect model /
- DBH increment

HTML全文

图 1 种内、种间竞争指数和期初胸径、胸径变化之间关系

Figure 1. Relationship between intraspecific and interspecific competition index and initial DBH as well as DBH change

下载: 全尺寸图片幻灯片

图 2 树种水平下收敛模型残差图

字母代表随机参数的组合。The letters represent the combination of random parameters.

Figure 2. Residual plots of converged mixed-effect models under tree species level

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图 3 最优混合效应模型检验数据残差、拟合值−实测值图

Figure 3. Validation data residual of the optimal mixed effect model and fitted value-measured value graph

下载: 全尺寸图片幻灯片

表 1 数据统计表

Table 1 Data statistics

指标 Index		最大值 Max.	最小值 Min.	平均值 Mean	标准差 SD
建模数据 Modeling data (n = 1 983)	林分密度/（株·hm⁻²） Stand density/(tree·ha⁻¹)	826	922	877	48
	期初胸径 Initial DBH (D₁)/cm	56.0	5.0	16.2	8.1
	期末胸径 Final DBH (D₂)/cm	56.5	5.1	17.1	8.2
	胸径增长量 DBH increment (ΔDBH)/cm	4.4	0.0	0.8	0.6
	种间Hegyi竞争指数 Interspecific Hegyi competition index (I_C_inter)	36.7	0.1	4.2	3.6
	种内Hegyi竞争指数 Intraspecific Hegyi competition index (I_C_intra)	57.5	0.0	1.6	3.6
检验数据 Validation data (n = 853)	林分密度/（株·hm⁻²） Stand density/(tree·ha⁻¹)	826	922	877	48
	D₁/cm	48.3	5.0	16.5	8.3
	D₂/cm	51.3	8.4	17.4	8.5
	ΔDBH/cm	4.5	0.0	0.8	0.6
	I_C_inter	34.0	0.1	4.2	3.8
	I_C_intra	59.5	0.0	1.8	4.6

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表 3 竞争指数增加后模型拟合精度变化

Table 3 Change in model fitting accuracy after increasing competition index

变量 Variable	$R_{\rm{adj}}^2$	RMSE	TRE/%
D₁	0.408 5	0.669 2	4.470 2
D₁ + I_C_intra + I_C_inter	0.416 0	0.665 2	4.414 5

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表 2 备选模型形式

Table 2 Candidate model forms

序号 No.	模型 Model	表达式 Expression
1	Compert	$y = {a_0}\exp \left( { - {a_1}\exp \left( { - {a_2}x} \right)} \right)$
2	Mitscherlich	$y = {a_0}\left( {1 - {a_1}\exp \left( { - {a_2}x} \right)} \right)$
3	Power	$y = {a_0}{x^{{a_1}}}$
4	Weibull	$y = {a_0}\left( {1 - \exp \left( { - {a_1}{x^{{a_2}}}} \right)} \right)$
5	Korf	$y = {a_0}\exp \left( { - {a_1}{x^{ - {a_1}}}} \right)$
6	Logistic	$y = \dfrac{{{a_0}}}{{1 + {a_1}\exp \left( { - {a_2}x} \right)}}$
注：y和x分别代表模型自变量和因变量，a₀、a₁、a₂分别代表模型的待估计参数。Notes: y and x represent the independent variable and dependent variable, respectively, a₀, a₁, a₂ represent the estimated parameters of the model, respectively.

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表 4 样地水平下收敛的混合效应模型评价指标

Table 4 Evaluation indexes of converged mixed-effect models under sample plot level

参数 Parameter	AIC	BIC	−2Loglike	LRT	P
a₀ + a₄	3 523.8	3 572.9	3 505.8	40.5	< 0.000 1
a₃ + a₄	3 523.8	3 573.0	3 505.8	40.5	< 0.000 1
a₂ + a₃	3 523.8	3 573.0	3 505.8	40.5	< 0.000 1
a₀ + a₁ + a₂	3 529.8	3 595.4	3 505.8	36.4	< 0.000 1
a₂ + a₃ + a₄	3 523.8	3 589.4	3 499.8	40.5	< 0.000 1

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表 5 树种水平下收敛的混合效应模型评价指标

Table 5 Evaluation indexes of converged mixed-effect models under tree species level

参数 Parameter	AIC	BIC	−2Loglike	LRT	P
a₀	3 417.8	3 455.9	3 403.8	110.5	< 0.000 1
a₁	3 429.9	3 468.1	3 415.9	98.4	< 0.000 1
a₃	3 416.9	3 455.1	3 402.9	111.4	< 0.000 1
a₄	3 416.4	3 454.6	3 402.4	111.9	< 0.000 1
a₀ + a₁	3 368.9	3 418.1	3 350.9	163.3	< 0.000 1
a₀ + a₂	3 389.2	3 438.3	3 371.2	143.1	< 0.000 1
a₀ + a₃	3 367.1	3 416.2	3 349.1	165.2	< 0.000 1
a₀ + a₄	3 358.9	3 408.0	3 340.9	173.4	< 0.000 1
a₁ + a₃	3 377.7	3 426.9	3 359.7	154.6	< 0.000 1
a₁ + a₄	3 368.8	3 417.9	3 350.8	163.5	< 0.000 1
a₂ + a₄	3 393.2	3 442.3	3 375.2	139.1	< 0.000 1
a₃ + a₄	3 386.8	3 435.9	3 368.8	145.4	< 0.000 1
a₀ + a₁ + a₂	3 348.7	3 414.3	3 324.7	189.5	< 0.000 1
a₀ + a₂ + a₃	3 327.2	3 392.8	3 303.2	211.0	< 0.000 1
a₁ + a₂ + a₄	3 355.1	3 420.6	3 331.1	183.2	< 0.000 1
a₁ + a₃ + a₄	3 383.7	3 449.2	3 359.7	154.6	< 0.000 1

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表 6 单木水平下收敛的混合效应模型评价指标

Table 6 Evaluation indexes of converged mixed-effect models under single tree level

参数 Parameter	AIC	BIC	−2Loglike	LRT	P
a₁	3 519.8	3 558.1	3 505.8	45.4	< 0.000 1
a₃	3 518.8	3 556.1	3 503.2	43.6	< 0.000 1
a₀	3 517.8	3 555.1	3 499.4	40.1	< 0.000 1
a₂	3 512.8	3 551.1	3 502.6	39.1	< 0.000 1

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表 7 树种水平下最优混合效应模型参数估计

Table 7 Parameter estimation of best mixed-effect models under tree species level

参数 Parameter	估计（标准误） Estimation (SE)	T值 T value	P 值 P value
a₀	5.118 3（0.273 0）	18.745 2	0.000 0
a₁	1.190 5（0.092 6）	12.860 8	0.000 0
a₂	−0.053 0（0.006 1）	−8.700 4	0.000 0
a₃	0.054 2（0.017 3）	3.130 9	0.001 8
a₄	0.045 5（0.014 1）	3.230 7	0.001 3
方差−协方差结构 Variance-covariance structure	$\left[ \begin{gathered} 0.191\;4\quad 0.595\;0\quad 0.576\;0 \\ 0.595\;0\quad 0.002\;3\quad 0.388\;0 \\ 0.576\;0\quad 0.388\;0\quad 0.001\;8 \\ \end{gathered} \right]$
误差方差 Variance of error	0.374 4
$R_{\rm{adj}}^2$	0.512 6
RMSE	0.607 1
TRE/%	3.651 9

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