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基于混合效应的杂种落叶松人工幼龄林单木枯损模型

王涛 董利虎 李凤日

王涛, 董利虎, 李凤日. 基于混合效应的杂种落叶松人工幼龄林单木枯损模型[J]. 北京林业大学学报, 2018, 40(10): 1-10. doi: 10.13332/j.1000-1522.20170437
引用本文: 王涛, 董利虎, 李凤日. 基于混合效应的杂种落叶松人工幼龄林单木枯损模型[J]. 北京林业大学学报, 2018, 40(10): 1-10. doi: 10.13332/j.1000-1522.20170437
Wang Tao, Dong Lihu, Li Fengri. Individual tree mortality model for hybrid larch young plantations based on mixed effects[J]. Journal of Beijing Forestry University, 2018, 40(10): 1-10. doi: 10.13332/j.1000-1522.20170437
Citation: Wang Tao, Dong Lihu, Li Fengri. Individual tree mortality model for hybrid larch young plantations based on mixed effects[J]. Journal of Beijing Forestry University, 2018, 40(10): 1-10. doi: 10.13332/j.1000-1522.20170437

基于混合效应的杂种落叶松人工幼龄林单木枯损模型

doi: 10.13332/j.1000-1522.20170437
基金项目: 

“十二五”国家科技支撑计划课题 2015BAD09B01

详细信息
    作者简介:

    王涛,博士生。主要研究方向:林分生长模型。Email:568716463@qq.com.cn 地址:150040 黑龙江省哈尔滨市香坊区和兴路26号东北林业大学林学院

    责任作者:

    李凤日,教授,博士生导师。主要研究方向:林分生长模型。Email:fengrili@126.com 地址:同上

  • 中图分类号: S758.1

Individual tree mortality model for hybrid larch young plantations based on mixed effects

  • 摘要: 目的利用固定间隔期复测数据,运用不同方法建立杂种落叶松人工幼龄林单木枯损模型,为确定杂种落叶松合理的经营措施和推广应用提供依据。方法基于2003—2015年黑龙江省江山娇实验林场48块样地的复测数据,通过Logistic模型,利用全子集法和最大似然估计构建杂种落叶松单木枯损模型。使用列联表分析和分类率-阈值散点图,确定枯损模型预估时的最佳阈值。引入随机参数,构建样地水平广义线性混合模型。模型估计方法为自适应积分最大似然估计,模型筛选指标为Akaike信息标准(AIC)、贝叶斯信息标准(BIC)以及-2倍对数似然值。通过计算绝对平均偏差(Bias),绘制ROC曲线以及模型预估枯损率与实际枯损率直方图对两种模型的预测结果进行评价比较。结果包含单木(林木胸径,DBH;胸径平方,DBH2)、林分(林分断面积,BA)、竞争(大于对象木树木断面积之和变形,BALD)3个水平变量组合的单木枯损模型拟合效果最佳。杂种落叶松枯损主要发生在小径阶且相对竞争较大时。单木枯损概率随DBH增加逐渐减小,随BALD、BA增加而逐渐增加。最佳阈值有效提高了模型预估效果,方差-协方差结构为无结构矩阵(UN)时,四参数混合模型的拟合结果最佳,其预估的林分枯损率更接近实际林分枯损率。结论混合模型能够更有效地描述和预估杂种落叶松的单木枯损。阈值分析是提高二分类模型预测准确性的有效方法。杂种落叶松作为速生树种,幼龄时期应适时进行抚育间伐以减少枯损发生的概率。

     

  • 图  1  杂种落叶松人工幼龄林不同径阶枯损株数分布

    Figure  1.  Distribution for the number of mortality trees in different DBH classes of hybrid larch young plantations

    图  2  广义线性模型与广义线性混合模型ROC曲线比较

    Figure  2.  Comparison of the ROC curve between generalized linear model and generalized linear mixed model

    图  3  广义线性模型、广义线性混合模型预测枯损率与实际枯损率比较

    Figure  3.  Comparison of the actual mortality rate in the result of generalized linear model and generalized linear mixed model predicted

    图  4  杂种落叶松人工幼龄林枯损模型阈值点与分类率关系

    Figure  4.  Relationship of classification rate and threshold for the mortality model of hybrid larch young plantations

    表  1  杂种落叶松人工幼龄林基本因子统计表

    Table  1.   Statistics of basic characteristics about hybrid larch young plantations

    数据类别
    Data class
    样地数
    Sample plot number(N)
    林分平均胸径
    Mean DBH(Dg)/cm
    林分平均高
    Mean stand height(H)/m
    林分断面积/
    (m2·hm-2)
    Stand basal area (BA)/
    (m2·ha-1)
    每公顷存活株数/
    (株·hm-2)
    Living tree number per hectare(NHAL)/
    (plant·ha-1)
    存活树木蓄积/
    (m3·hm-2)
    Living tree volume per hectare(VOLL)/
    (m3·ha-1)
    每公顷枯死株数/
    (株·hm-2)
    Dead tree number per hectare(NHAD)/
    (plant·ha-1)
    枯死树木蓄积/
    (m3·hm-2)
    Dead tree volume per hectare(VOLD)/
    (m3·ha-1)
    建模数据
    Modeling data
    40 3.07~15.12
    (13.29±2.67)
    2.41~14.12
    (8.95±2.41)
    2.05~38.74
    (19.49±8.39)
    1775~4875
    (2707±758)
    6.19~200.82
    (95.60±4.65)
    0~1100
    (71±119)
    0~14.19
    (0.89±2.08)
    检验数据
    Testing data
    8 4.33~14.56
    (13.16±2.67)
    2.44~14.08
    (8.81±2.44)
    3.92~34.66
    (19.90±8.59)
    1642~4275
    (2633±627)
    10.27~184.18
    (98.10±5.18)
    0~475
    (50±88)
    0~10.99
    (0.63±1.96)
    注:括号内为平均值±标准差。Note: that in bracket is the mean value ± standard deviation.
    下载: 导出CSV

    表  2  阈值检验指标计算公式描述

    Table  2.   Formula description for the threshold test index

    检验指标Testing index 缩写Abbreviation 公式Formula
    真阳性率/灵敏度True positive rate/sensitivity TPR TPR=TP/(TP+FN)
    假阴性率False negative rate FNR FNR=FN/(TP+FN)=1-TPR
    真阴性率/特异度True negative rate/specificity TNR TNR=TN/(FP+TN)
    假阳性率False positive rate FPR FPR=FP/(FP+TN)=1-TNR
    错误分类率Mistake classification rate MCR MCR=FPR+FNR
    正确分类率Accuracy classification rate ACR ACR=(TP+TN)/(TP+TN+FP+FN)
    下载: 导出CSV

    表  3  杂种落叶松人工幼龄林不同间隔期建模结果

    Table  3.   Modeling results with different intervals for hybrid larch young plantations

    间隔期/a Interval/year AUC
    1 0.856
    2 0.861
    3 0.870
    4 0.836
    5 0.845
    下载: 导出CSV

    表  4  杂种落叶松人工幼龄林全子集模型筛选结果

    Table  4.   Results of model selection with All-sets for hybrid larch young plantations

    模型编号
    Model No.
    变量Variable AIC BIC -2倍对数似然值
    -2 log likelihood
    AUC VIF
    1 BALD 7170.6 7186.2 7166.6 0.795 2.71
    2 NHAL BALD 7053.3 7061.5 7033.2 0.806 2.86
    3 DBH DBH2 BALD 6903.7 6934.8 6895.7 0.826 3.16
    4 DBH DBH2 BALD BA 6804.3 6843.3 6794.3 0.870 4.43
    5 DBH DBH2 NHAL BALD RD 6932.9 6923.7 6918.2 0.865 4.60
    6 DBH DBH2 BA NHAL BALD DBA 6931.3 6939.7 6932.5 0.852 4.87
    7 DBH DBH2 BA NHAL BALD DBA RD 6921.3 6918.8 6912.3 0.852 5.26
    8 DBH DBH2 BA NHAL BAL BALD RD DBA 6885.1 6879.2 6875.3 0.854 6.02
    注:DBH为林木胸径,BAL指所有大于对象木的树木断面积之和,BALD为BAL与DBH的变形,RD为相对直径, DBA为胸径和林分断面积之比,BA为林分断面积,NHAL为每公顷存活株数。下同。Notes: DBH, tree diameter at breast height; BAL, sum of stand basal area of all greater than object wood; BALD, transformation of BAL and DBH; RD, relative diameter; DBA, ratio of DBH to stand basal area; BA, stand basal area; NHAL, NHAL is number of living trees per hectare. The same below.
    下载: 导出CSV

    表  5  杂种落叶松人工幼龄林Logistic广义线性模型参数估计

    Table  5.   Parameter estimation for Logistic generalized linear model of hybrid larch young plantations

    变量Variable 参数Parameter 自由度Freedom 估计值
    Estimated value
    标准误差SD Wald χ2 P
    截距Intercept b0 1 -2.5321 0.2282 123.0760 < 0.0001
    DBH b1 1 -0.6185 0.0648 90.9819 < 0.0001
    DBH2 b2 1 0.0260 0.0030 74.1734 < 0.0001
    BALD b3 1 0.3411 0.0338 101.9940 < 0.0001
    BA b4 1 0.0238 0.0205 15.3487 < 0.0001
    下载: 导出CSV

    表  6  杂种落叶松人工幼龄林广义线性混合模型模拟

    Table  6.   Simulation of the Logistic generalized linear mixed model of hybrid larch young plantations

    模型编号
    Model No.
    参数个数
    Number of parameters
    随机参数
    Random parameter
    筛选指标
    Screening criteria
    b0 b1 b2 b3 b4 AIC BIC -2倍对数似然值
    -2 log likelihood
    1 5 6804.30 6843.30 6794.30
    2 6 6313.60 6323.74 6301.60
    3 6 6282.87 6293.00 6270.87
    4 6 6420.65 6430.78 6408.65
    5 6 6523.29 6533.43 6511.29
    6 6 6392.90 6403.03 6380.90
    7 8 6240.89 6254.40 6224.89
    8 8 6247.94 6261.45 6231.94
    9 8 6259.96 6273.47 6243.96
    10 8 6235.31 6248.83 6219.31
    11 8 6259.53 6273.04 6243.53
    12 8 6281.58 6295.09 6265.58
    13 8 6215.97 6212.46 6210.46
    14 8 6349.88 6363.40 6333.88
    15 11 6284.48 6292.93 6274.48
    16 11 6203.66 6212.10 6193.66
    17 11 6205.95 6214.40 6195.95
    18 11 6208.55 6217.00 6198.55
    19 11 6214.05 6222.50 6204.05
    20 11 6225.70 6234.14 6215.70
    21 11 6271.29 6279.73 6261.29
    22 11 6242.72 6251.17 6232.72
    23 15 6203.10 6211.54 6193.10
    23 15 6204.59 6213.03 6194.59
    24 15 6207.70 6216.14 6197.70
    25 15 6186.54 6194.98 6176.54
    26 20 6236.21 6244.32 6226.13
    注:▲表示包括这个随机参数;b0b1b2b3b4分别为截矩、DBH、DBH2、BALD、BA的模型参数。Notes:▲ means it is included in the random parameters; b0, b1, b2, b3, b4 are model parameters of intercept, DBH, DBH2, BALD, BA.
    下载: 导出CSV

    表  7  基于不同方差-协方差结构的模型比较

    Table  7.   Comparison of model based on different variance-covariance structures

    模型编号
    Model No.
    方差-协方差结构
    Variance-covariance structure
    参数个数
    Number of parameters
    AIC BIC -2倍对数似然值
    -2 log likelihood
    Pearson χ2
    25 无结构矩阵Unstructured matrix(UN) 15 6186.54 6194.98 6176.54 0.93
    对角矩阵Diagonal matrix(VC) 9 6270.39 6285.59 6252.39 0.88
    复合矩阵Compound symmetry(CS) 7 6362.29 6374.11 6348.29 0.91
    一阶自回归结构First-order autoregressive(AR(1)) 16 6221.74 6225.09 6211.44 0.92
    一阶移动平移结构First-order moving-average(MA(1))
    一阶自回归移动平均结构
    First-order autoregressive moving-average(ARMA(1, 1))
    下载: 导出CSV

    表  8  杂种落叶松人工幼龄林枯损模型拟合与检验结果

    Table  8.   Fitting and testing results of mortality model of hybrid larch young plantations

    固定参数Fixed parameter 基础模型Basic model 混合模型Mixed model
    b0 -2.5321 -2.6368
    b1 -0.6185 -1.4545
    b2 0.0260 0.0392
    b3 0.3411 0.3456
    b4 0.0238 0.0522
    随机效应方差-协方差结构Random effect variance-covariance structure(G) $\left[\begin{array}{cccc}{0.2297} & {-0.0034} & {0.0851} & {-0.0945} \\ {-0.0034} & {0.0001} & {-0.0001} & {0.0012} \\ {0.0851} & {-0.0001} & {0.0357} & {-0.0373} \\ {-0.0945} & {0.0012} & {-0.0373} & {0.0405}\end{array}\right]$
    Pearson χ2 1.36 0.93
    AUC 0.8701 0.9178
    Wald χ2 < 0.0001 < 0.0001
    Bias 5.375 1.375
    下载: 导出CSV

    表  9  杂种落叶松人工幼龄林枯损模型阈值预测列联表分析

    Table  9.   Confusion matrix of the hybrid larch mortality model for four cut points

    列联表分析
    Confusion matrix
    实际变量分类Actual variety classification
    Positive 0=枯损Dead Negative 1=存活Living
    预测变量分类
    Classification of predicted variety
    Positive
    0=枯损Dead
    TPR 83.6%(A=0.08) FPR 17.4%(A=0.08)
    82.3%(B=0.06) 17.9%(B=0.06)
    32.4%(C=0.5) 0.8%(C=0.5)
    86.1%(D=0.1) 10%(D=0.1)
    Negative
    1=存活Living
    FNR 16.4%(A=0.08) TNR 82.6%(A=0.08)
    17.7%(B=0.06) 82.1%(B=0.06)
    67.6%(C=0.5) 99.2%(C=0.5)
    13.9%(D=0.1) 90.0%(D=0.1)
    注:ABCD为阈值点。Note:A, B, C, D are threshold points.
    下载: 导出CSV

    表  10  杂种落叶松人工幼龄林枯损模型不同阈值预测分类率

    Table  10.   Classification of the hybrid larch young plantation mortality model for four cut points

    阈值Threshold ACR MCR
    A=0.08 82.9% 33.7%
    B=0.06 82.1% 35.7%
    C=0.5 81.2% 68.4%
    D=0.1 88.9% 23.9%
    注:ACR(正确分类率):正确预测枯损与存活株数占总株数比率; MCR(错误分类率):假阳性率与假阴性率之和。Notes:ACR(accurate classification rate): correctly predicting the ratio of mortality and living trees to total trees; MCR(misclassification rate): the sum of false positive rate and false negative rate.
    下载: 导出CSV
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  • 收稿日期:  2017-12-06
  • 修回日期:  2018-07-23
  • 刊出日期:  2018-10-01

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