数据点选择与参数估计方法对杉木人工林自疏边界线的影响

doi:10.3773/j.issn.1005-264x.2010.04.006

摘要/Abstract

摘要：

自疏边界线是指植物种群发生密度依赖死亡时种群最大收获量的上边界线。已有研究由于在拟合自疏边界线的过程中对数据点的选择和参数估计的方法存在诸多的差异, 进而导致产生对自疏法则的争议。该研究采用26年生杉木(Cunninghamia lanceolata)人工林的定位观测数据, 对视觉法、死亡率法、等距区间法和相对密度法等4种数据点选择方法以及最小二乘法、降维分析法、分位数回归法和随机边界方程等4种参数拟合方法进行对比分析, 以探寻客观选择自疏拟合数据和正确拟合方法的途径。比较4种不同的数据选择方法得出: 视觉法具有较强的主观性; 对于没有发生非密度依赖死亡的林分, 死亡率法可以准确地确定林分自疏的起始点; 等距区间法可以减少非密度依赖死亡的影响, 得到的数据点能充分反映林分的自疏过程; 相对密度法可以保证临界密度阈值以上的数据点拟合林分自疏边界线的有效性, 并能排除非密度依赖死亡的影响。比较分析4种不同的拟合方法发现: 最小二乘法和降维分析法拟合的林分自疏边界线均从实测数据“中心”穿过, 与林分自疏边界线为林分收获量上边界线的涵义不相符合, 无法真实反映林分的自疏进程; 分位数回归和随机边界方程的拟合结果均与实测数据一致, 能够较为准确地反映林分自疏的真实过程, 但二者的统计推断要求都比较严格。分位数值的正确选取和残差足够小且趋于0, 是分位数回归法和随机边界方程能否正确反映林分自疏动态的前提。

关键词: 杉木, 参数估计方法, 数据点选择, 自疏边界线

Abstract:

Aims The self-thinning boundary line represents the upper boundary of possible yield-density combinations in crowded stands. Our aim was to elucidate how to objectively select data points and the most appropriate regression method for estimating the self-thinning boundary line.

Methods We compare alternatives for selecting data points and fitting coefficients that have been or can be used to estimate the self-thinning boundary line. The selecting data point methods include visualized inspection, mortality criterion, equal intervals method and relative density method; the fitting coefficients methods include ordinary least squares regression, reduced major axis method, quantile regression and stochastic frontier function. We used data from an even-aged Cunninghamia lanceolata stand as example.

Important findings Visualized inspection is subjective. Mortality criterion can precisely determine onset of the self-thinning without the independent-density stand. The equal intervals method has the potential to reduce independent-density mortality effect and the selected data points may adequately reflect stand self-thinning dynamics. The relative density method can avoid influence of independent-density mortality and ensure stand density threshold value. Stand self-thinning span is a limiting factor with equal intervals and relative density. The slope and intercept estimates used in ordinary least squares regression and reduced major axis differ from the stand self-thinning upper boundary line. Both the quantile regression technique and stochastic frontier function produce the self-thinning boundary line because the method can easily perform that there are no significant departures based on the adequate selection of quantile value and residual converge to zero with underlying distributional assumptions.

Key words: Cunninghamia lanceolata, fitting coefficients methods, selection of data points, self-thinning boundary line

孙洪刚, 张建国, 段爱国. 数据点选择与参数估计方法对杉木人工林自疏边界线的影响. 植物生态学报, 2010, 34(4): 409-417. DOI: 10.3773/j.issn.1005-264x.2010.04.006

SUN Hong-Gang, ZHANG Jian-Guo, DUAN Ai-Guo. A comparison of selecting data points and fitting coefficients methods for estimating self-thinning boundary line. Chinese Journal of Plant Ecology, 2010, 34(4): 409-417. DOI: 10.3773/j.issn.1005-264x.2010.04.006

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https://www.plant-ecology.com/CN/Y2010/V34/I4/409

图/表 6

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样地 Plot	初植密度 Planting density (trees·hm^-2)	2006年林分密度 Stand density in 2006 (trees·hm^-2)	林分平均胸径 Mean diameter of breast height (cm)	标准差 SD	胸径最小值 Minimum diameter of breast height (cm)	胸径最大值 Maximum diameter of breast height (cm)
B₂	3 333	2 517	10.65	2.42	6.49	13.80
B₃	3 333	2 483	12.29	2.71	7.58	16.23
C₂	5 000	3 467	9.57	2.44	5.51	13.16
C₃	5 000	2 417	10.21	2.74	6.04	14.04
D₁	6 667	3 317	8.76	2.02	5.53	11.90
D₂	6 667	4 267	8.85	2.67	4.95	13.14
D₃	6 667	3 800	9.13	2.62	5.33	13.26
E₁	10 000	5 117	8.39	2.01	5.55	11.70
E₂	10 000	3 183	8.42	2.50	4.80	13.08
E₃	10 000	5 217	8.75	2.71	5.10	13.11

样地 Plot	初植密度 Planting density (trees·hm^-2)	2006年林分密度 Stand density in 2006 (trees·hm^-2)	林分平均胸径 Mean diameter of breast height (cm)	标准差 SD	胸径最小值 Minimum diameter of breast height (cm)	胸径最大值 Maximum diameter of breast height (cm)
B₂	3 333	2 517	10.65	2.42	6.49	13.80
B₃	3 333	2 483	12.29	2.71	7.58	16.23
C₂	5 000	3 467	9.57	2.44	5.51	13.16
C₃	5 000	2 417	10.21	2.74	6.04	14.04
D₁	6 667	3 317	8.76	2.02	5.53	11.90
D₂	6 667	4 267	8.85	2.67	4.95	13.14
D₃	6 667	3 800	9.13	2.62	5.33	13.26
E₁	10 000	5 117	8.39	2.01	5.55	11.70
E₂	10 000	3 183	8.42	2.50	4.80	13.08
E₃	10 000	5 217	8.75	2.71	5.10	13.11

数据点选择方法及数量 Selecting data points and numbers (n)	斜率(标准误差) Slope (SE)	截距(标准误差) Intercept (SE)	R²
死亡率法 Mortality criterion
开始死亡 Zero mortality (83)	-0.56 (0.046)	7.28 (0.612)	0.817
10%死亡 10% mortality (51)	-0.51 (0.037)	6.79 (0.435)	0.931
20%死亡 20% mortality (37)	-0.49 (0.029)	6.19 (0.367)	0.934
等距区间法 Equal intervals
5株 5 stems (43)	-0.62 (0.071)	7.91 (0.610)	0.917
10株 10 stems (31)	-0.55 (0.069)	7.26 (0.583)	0.922
20株 20 stems (19)	-0.54 (0.089)	7.23 (0.762)	0.939
相对密度法 Relative density (RD)
RD > 0.7 (71)	-0.58 (0.069)	7.14 (0.583)	0.883
RD > 0.8 (62)	-0.54 (0.056)	7.09 (0.472)	0.929
RD > 0.9 (57)	-0.53 (0.057)	6.70 (0.478)	0.900

数据点选择方法及数量 Selecting data points and numbers (n)	斜率(标准误差) Slope (SE)	截距(标准误差) Intercept (SE)	R²
死亡率法 Mortality criterion
开始死亡 Zero mortality (83)	-0.56 (0.046)	7.28 (0.612)	0.817
10%死亡 10% mortality (51)	-0.51 (0.037)	6.79 (0.435)	0.931
20%死亡 20% mortality (37)	-0.49 (0.029)	6.19 (0.367)	0.934
等距区间法 Equal intervals
5株 5 stems (43)	-0.62 (0.071)	7.91 (0.610)	0.917
10株 10 stems (31)	-0.55 (0.069)	7.26 (0.583)	0.922
20株 20 stems (19)	-0.54 (0.089)	7.23 (0.762)	0.939
相对密度法 Relative density (RD)
RD > 0.7 (71)	-0.58 (0.069)	7.14 (0.583)	0.883
RD > 0.8 (62)	-0.54 (0.056)	7.09 (0.472)	0.929
RD > 0.9 (57)	-0.53 (0.057)	6.70 (0.478)	0.900

回归方法 Regression technique	斜率 Slope	截距 Intercept
随机边界方程 Stochastic frontier function	-0.52	7.03
最小二乘法 Ordinary least squares regression	-0.54	7.63
降维分析法 Reduced major axis	-0.57	7.39
分位数回归法 Quantile regression	-0.52	7.05