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自然稀疏方程不同拟合方法的对比研究

孟京辉

孟京辉. 自然稀疏方程不同拟合方法的对比研究[J]. 北京林业大学学报, 2019, 41(12): 58-68. doi: 10.12171/j.1000-1522.20190434
引用本文: 孟京辉. 自然稀疏方程不同拟合方法的对比研究[J]. 北京林业大学学报, 2019, 41(12): 58-68. doi: 10.12171/j.1000-1522.20190434
Meng Jinghui. A comparison of different methods for fitting the self-thinning equation[J]. Journal of Beijing Forestry University, 2019, 41(12): 58-68. doi: 10.12171/j.1000-1522.20190434
Citation: Meng Jinghui. A comparison of different methods for fitting the self-thinning equation[J]. Journal of Beijing Forestry University, 2019, 41(12): 58-68. doi: 10.12171/j.1000-1522.20190434

自然稀疏方程不同拟合方法的对比研究

doi: 10.12171/j.1000-1522.20190434
基金项目: 国家重点研发计划(2017YFC0505604)
详细信息
    作者简介:

    孟京辉,副教授。主要研究方向:森林生长与收获模型。Email:jmeng@bjfu.edu.cn 地址:100083 北京市清华东路35号北京林业大学林学院

  • 中图分类号: S757.1

A comparison of different methods for fitting the self-thinning equation

  • 摘要: 目的选择能够真实反映种群自疏动态的拟合方法是评估自然稀疏法则的难点和热点问题。方法本研究基于福建省553块杉木同龄林样地数据,对前人用于估计自然稀疏方程的手绘法、区间法和相对密度法3种传统方法,普通最小二乘法回归(OLS)、简化主轴回归(RMA)和分位数回归(QR)3种以回归为基础的方法,修正最小二乘法(COLS)、确定性前沿函数(DFF)和随机前沿函数(SFF)3种边界模型构建方法进行对比分析,得出最大密度线的适宜拟合方法。结果手绘法简单易行,但主观性较强;区间法拟合结果会受到区间长度的显著影响,得到的最大密度线斜率往往比真实斜率平缓;相对密度法能排除非密度依赖死亡的干扰,但会受选点过程中预设斜率理论值的影响;OLS法、COLS法、RMA法拟合的直线容易出现与实际的数据点边界不吻合的问题,与自然稀疏直线为数据点上边界线的定义不相符;当分位数值越接近100%,QR法拟合得到的直线就越接近林分自疏上边界线;DFF法中,采用线性规划途径拟合直线优于非线性规划途径,但QR法和DFF法进行统计推断比较困难。SFF法拟合结果比较客观,但只有随机误差项的方差足够小且趋近于零时,拟合所得直线才能真实反映种群自疏过程。结论本文最后筛选得出福建省杉木人工林最优自然稀疏方程为ln(QMD) = 7.795 − 0.620ln(N),可为当地杉木经营实践中制定有效密度调控措施提供参考。

     

  • 图  1  清查样地杉木纯林的地理分布

    Figure  1.  Geographical distribution of the inventory sample plots within pure Chinese fir stands

    图  2  由手绘法得到的最大密度线

    Figure  2.  The maximum size-density line obtained from the hand-fitting method

    图  3  由区间法得到的最大密度线

    Figure  3.  The maximum size-density lines obtained from the interval method

    图  4  由相对密度(RD)法得到的最大密度线

    Figure  4.  The maximum size-density lines obtained from the relative density (RD) method

    图  5  6种拟合方法得到的最大密度线

    Figure  5.  The maximum size-density lines obtained from the six fitting methods

    图  6  由分位数回归(QR)法得到的最大密度线

    Figure  6.  The maximum size-density lines obtained from the quantile regression (QR) method

    图  7  由确定性前沿分析(DFF)法得到的最大密度线

    Figure  7.  The maximum size-density lines obtained from the deterministic frontier function (DFF) method

    表  1  杉木人工纯林林分和立地变量统计(样地数为553个)

    Table  1.   Descriptive statistics of stand and site variables for pure Chinese fir plantations (n = 553)

    变量
    Variable
    平均值 Mean标准差 SD最小值 Min.最大值 Max.
    林分年龄/a
    Stand age/year
    19 10 4 46
    林分密度/(株·hm− 2
    Stand density/(tree·ha− 1)
    1 801 1 047 104 6 791
    平方平均胸径
    Quadratic mean DBH/cm
    12.1 3.8 5.7 25.0
    海拔
    Elevation/m
    483 222 43 1350
    土壤厚度
    Soil depth/cm
    93.8 18.8 9.0 160.0
    腐殖层厚度
    Humus depth/cm
    9.5 5.2 0 42.0
    枯落物厚度
    Litter depth/cm
    3.8 5.5 0 30.0
    坡度
    Slope/(°)
    25.9 7.1 3.0 46.0
    方位角
    Azimuth/(°)
    194.8 104.4 45.0 360.0
    下载: 导出CSV

    表  2  6种拟合方法的回归系数和检验结果

    Table  2.   Regression coefficients of the six fitting methods

    回归方法
    Regression method
    所选数据点
    Selected data
    斜率
    Slope
    截距
    Intercept
    普通最小二乘法
    Ordinary least squares regression (OLS)
    RD ≥ 0.70 − 0.582 7.345
    简化主轴回归
    Reduced major axis regression (RMA)
    RD ≥ 0.70 − 0.600 7.490
    分位数回归
    Quantile regression (QR)
    全部
    All plots
    − 0.420 6.193
    修正最小二乘法
    Corrected OLS (COLS)
    RD ≥ 0.70 − 0.582 7.489
    确定性前沿函数
    Deterministic frontier function (DFF)
    全部
    All plots
    − 0.420 6.193
    随机前沿函数
    Stochastic frontier function (SFF)
    RD ≥ 0.70 − 0.620 7.795
    注:RD,相对密度。Note: RD, relative density.
    下载: 导出CSV

    表  3  基于RD ≥ 0.70数据点拟合的OLS和RMA模型统计量和验证结果

    Table  3.   Fitting statistics and validation results of the OLS and RMA models fitted by RD ≥ 0.70 data

    回归方法
    Regression method
    回归模型的拟合统计量
    Fitting statistics of the regression models
    交叉验证
    Cross-validation
    dfAICRMSER2 NMSEtePRESS
    OLS− 99.830 (3)− 93.8300.0580.9400.1330.096
    RMA− 100.250 (5) − 90.2510.0590.9850.1350.090
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-10-12
  • 修回日期:  2019-12-03
  • 网络出版日期:  2019-12-11
  • 刊出日期:  2019-12-01

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