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    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

    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。

       

      Abstract:
      ObjectiveFor evaluating the self-thinning theory, selecting the optimum fitting method that can truly describe self-thinning dynamics is a hot topic and a difficult task.
      MethodIn this study, we compared different approaches for fitting self-thinning equations, including three traditional methods, i.e., hand-fitting method, interval method and relative density (RD) method; three regression methods, i.e., ordinary least squares regression (OLS) method, reduced major axis regression (RMA) method and quantile regression (QR) method; and three frontier model methods, i.e., corrected OLS (COLS) method, deterministic frontier function (DFF) method and stochastic frontier function (SFF) method. The data from 553 sample plots of even-aged Chinese fir (Cunninghamia lanceolata) plantations in Fujian Province, eastern China was employed.
      ResultThe results indicated that hand-fitting method was easy but subjective. The coefficients estimated by interval method can be influenced significantly by interval length, and the estimated slope tended to be flatter than the real slope. The RD method can avoid influence of independent-density mortality, but the result would be affected by the predetermined theoretical constant for the slope. The maximum size-density lines fitted by the OLS, RMA and COLS methods tended to inaccurately match the actual boundaries of data points, and differed from the stand self-thinning upper boundary line. The maximum size-density line fitted by QR method can be close to the stand self-thinning upper boundary line when the quantile value approached 100%. The maximum size-density line fitted by linear programming approach was more suitable than the line fitted by quadratic programming approach. However, statistical inference was very difficult with the DFF and QR methods. SFF method was relatively objective, however, the fitted maximum size-density line can truly describe self-thinning process only when variance of stochastic error terms was small enough and close to zero.
      ConclusionFinally, the optimum self-thinning equation for Chinese fir plantations in Fujian Provence is determined as ln(QMD) = 7.795 − 0.620ln(N), which can provide a reference for developing efficient measures of stand density control.

       

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