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人工长白落叶松枝条存活模型

王烁 董利虎 李凤日

王烁, 董利虎, 李凤日. 人工长白落叶松枝条存活模型[J]. 北京林业大学学报, 2018, 40(1): 57-66. doi: 10.13332/j.1000-1522.20170203
引用本文: 王烁, 董利虎, 李凤日. 人工长白落叶松枝条存活模型[J]. 北京林业大学学报, 2018, 40(1): 57-66. doi: 10.13332/j.1000-1522.20170203
Wang Shuo, Dong Li-hu, Li Feng-ri. Branch survival models of planted Larix olgensis tree[J]. Journal of Beijing Forestry University, 2018, 40(1): 57-66. doi: 10.13332/j.1000-1522.20170203
Citation: Wang Shuo, Dong Li-hu, Li Feng-ri. Branch survival models of planted Larix olgensis tree[J]. Journal of Beijing Forestry University, 2018, 40(1): 57-66. doi: 10.13332/j.1000-1522.20170203

人工长白落叶松枝条存活模型

doi: 10.13332/j.1000-1522.20170203
基金项目: 

国家自然科学基金项目 31570626

详细信息
    作者简介:

    王烁。主要研究方向:森林经理学。Email: wangshuo1504@163.com 地址: 150040黑龙江省哈尔滨市和兴路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:林分生长与收获模型。Email: fengrili@126.com 地址:同上

  • 中图分类号: S757.9

Branch survival models of planted Larix olgensis tree

  • 摘要: 目的木材的质量决定了它在生产中的价值, 优质的木材往往可以获得更高的利润。但是树干上节子的大小会严重影响木材的质量, 而节子是在枝条死亡后形成的, 所以通过研究枝条属性, 寻找合适的营林控制方式将对提高木材质量具有重要意义。方法本研究根据黑龙江省佳木斯市孟家岗林场、林口林业局和东京城林业局的10块长白落叶松人工林标准地中的70株落叶松枝解析数据, 分别建立传统的Logistic基础模型以及相应的广义线性混合模型(GLMM)来预测该地区长白落叶松的枝条存活状况, 并对模型进行拟合效果评价和独立性检验。结果枝条存活状态受树木自然整枝程度、枝条生长位置和树木间竞争等因素的影响, 在模型中, 冠长率(CR)可以反映树木自然整枝程度, 其参数值为正说明树木自然整枝程度较低时, 枝条大多处于存活状态。枝条相对位置(BRH)和枝条轮数(WHOLE)可以反映枝条的生长位置, 其参数值为负说明处于树冠上部的枝条由于受光充分而长势良好, 而处于树冠下部的枝条由于相互遮蔽而死亡。树高胸径比(HD)可以反映林木间的竞争情况, 其参数值为负说明激烈的竞争环境会使枝条存活概率降低。AIC、RMSE、AUC和模型判断正确率可以用于比较基础模型和广义线性混合模型的预测效果。经计算, 广义线性混合模型的AIC=801.67, RMSE=0.126, 均小于基础模型, AUC=0.9975, 模型判断正确率为97.9%, 均大于基础模型, 说明广义线性混合模型可以有效解决不同个体间存在差异的问题, 有利于提高枝条存活状态的预测精度。独立性检验结果显示模型预测精度良好。结论本研究可为长白落叶松人工林确定合理的经营措施, 提高木材质量提供理论依据。

     

  • 图  1  Logistic基础模型残差图

    Figure  1.  Residuals of the basic Logistic model

    图  2  Logistic广义线性混合模型残差图

    Figure  2.  Residuals of GLMM

    图  3  ROC曲线

    Figure  3.  ROC curve for model

    图  4  阈值点与分类率关系图

    FNR.假阴性率False nagative rate;FPR.假阳性率False positive rate;MCR.总错误分类率Total misclassification rate

    Figure  4.  Relationship of classification rate and threshold

    图  5  不同变量对枝条存活概率的影响

    Figure  5.  Effects of different variables on the probability of alive branches

    表  1  长白落叶松样木及枝条属性因子统计表

    Table  1.   Statistics for the variables of sample trees and branches for Larix olgensis

    变量
    Variable
    平均值
    Mean
    标准差
    Standard deviation
    最小值
    Min.
    最大值
    Max.
    胸径Diameter at breast height (DBH)/cm 12.7162 5.0454 2.0000 24.2000
    树高Tree height (HT)/m 12.6704 3.7268 3.8000 19.9200
    冠长Crown length (CL)/m 7.5661 2.3245 2.3000 14.7200
    基径Ground diameter (BD)/mm 11.1315 6.6462 1.0800 41.7800
    枝条位置Branch height (BH)/m 4.8071 3.5719 0.0100 17.7300
    枝条轮数Whole number of the branch (WHOLE) 6.9087 5.0261 1.0000 29.0000
    下载: 导出CSV

    表  2  符号解释

    Table  2.   Explanation of symbols

    变量
    Variable
    解释
    Definition
    Ps 枝条存活概率(1:活;0:死)Branch status(1:living;0:death)
    DBH 胸径Diameter at breast height,cm
    HT 树高Tree height,m
    HD 树高胸径比Tree height and diameter ratio(HD=HT/DBH)
    CW 冠幅Crown width,m
    HBLC 活冠的高度(第一活枝的高度)Tree height to crown base (height of the lowest live branch),m
    CL 活冠的长度Live crown length(CL=HT-HBLC),m
    CR 冠长率Crown length ratio(CR=CL/HT)
    BD 枝条的基径Ground diameter of branch,mm
    BH 枝条位置(树梢到枝条基部的距离)Branch height(distance from the tree apex to the base of the branch),m
    BRH 枝条相对位置Relative BH(BRH=BH/HT)
    WHOLE 枝条轮数(枝条所处伪轮的序号)Whole number of the branch
    下载: 导出CSV

    表  3  Logistic模型变量的统计量

    Table  3.   Statistics of variables used in the Logistic model

    变量
    Variable
    平均值
    Mean
    标准差
    Standard
    deviation
    最小值
    Min.
    最大值
    Max.
    HD 1.0678 0.2398 0.6595 1.9111
    CR 0.6167 0.1622 0.2674 0.9735
    BRH 0.3952 0.2795 0.0012 0.9954
    WHOLE 6.9087 5.0261 1.0000 29.0000
    下载: 导出CSV

    表  4  Logistic模型拟合结果的混淆矩阵

    Table  4.   Confusion matrix of fitting results for Logistic model

    观测值
    Observation value
    预测值Prediction value 总计
    Total
    正确率
    Accuracy rate/%
    事件发生
    Event occurred (Y=1)
    事件未发生No event
    occurred (Y=0)
    事件发生Event occurred (Y=1) a b a+b a/(a+b)
    事件未发生No event occurred (Y=0) c d c+d d/(c+d)
    总计Total a+c b+d a+b+c+d (a+d)/(a+b+c+d)
    注: a为预测事件发生,且观测事件也发生; b为预测事件未发生,但观测事件发生; c为预测事件发生,但观测事件未发生; d为预测事件未发生且观测事件也未发生。Notes: a, event occurred in both predicted and observed data; b, event occurred in observed data, but not in predicted data; c, event occurred in predicted data, but not in observed data; d, event occurred neither in predicted nor in observed data.
    下载: 导出CSV

    表  5  Logistic基础模型参数估计值、标准误差和显著性检验

    Table  5.   Model coefficient estimates, standard error(SE) and P-values of the basic Logistic model

    变量
    Variable
    估计值
    Estimated value
    标准误差
    Standard error(SE)
    P
    P-value
    截距Intercept 12.2773 0.9638 < 0.0001
    HD -3.6072 0.3984 < 0.0001
    CR 10.9067 0.9362 < 0.0001
    BRH -19.0603 0.9415 < 0.0001
    WHOLE -0.3264 0.0364 < 0.0001
    下载: 导出CSV

    表  6  Logistic广义线性混合模型拟合结果

    Table  6.   Fitting results of GLMM

    固定参数Fixed parameter 估计值Estimated value 标准误差Standard error(SE) PP-value
    截距Intercept 20.3051 3.0873 < 0.0001
    HD -4.4430 1.1623 0.0003
    CR 13.3754 3.3764 0.0002
    BRH -27.9856 2.5131 < 0.0001
    WHOLE -0.6084 0.1342 < 0.0001
    随机效应方差-协方差结构
    Random effect variance-covariance structure(G)
    $\left(\begin{array}{ccc}{93.4010} & {-83.9933} & {-0.2798} \\ {-83.993} & {87.9502} & {-0.8689} \\ {-0.2798} & {-0.8689} & {0.1207}\end{array}\right)$
    注: CR、BRH、WHOLE为随机效应参数。Notes: CR, BRH, WHOLE are random effect parameters.
    下载: 导出CSV

    表  7  Logistic基础模型和Logistic广义线性混合模型的AIC值、RMSE值和AUC值比较

    Table  7.   Comparison of AICs, RMSEs and AUCs of classic and GLMM Logistic models

    模型Model AIC RMSE AUC
    基础模型Classic model 1047.68 0.176 0.9905
    广义线性混合模型GLMM 801.67 0.126 0.9975
    下载: 导出CSV

    表  8  Logistic基础模型拟合结果混淆矩阵

    Table  8.   Confusion matrix of fitting results for basic Logistic model

    观测值
    Observation value
    预测值Prediction value 总计
    Total
    正确率
    Accuracy rate/%
    枝条存活Lived branch (Y=1) 枝条死亡Dead branch (Y=0)
    事件发生Event occurred (Y=1) 3573 209 3782 94.5
    事件未发生No event occurred (Y=0) 50 1132 1182 95.8
    总计Total 3623 1341 4964 94.8
    下载: 导出CSV

    表  9  Logistic广义线性混合模型拟合结果混淆矩阵

    Table  9.   Confusion matrix of fitting results for GLMM

    观测值
    Observation value
    预测值Prediction value 总计
    Total
    正确率
    Accuracy rate/%
    枝条存活Lived branch (Y=1) 枝条死亡Dead branch (Y=0)
    事件发生Event occurred (Y=1) 3732 56 3788 98.5
    事件未发生No event occurred (Y=0) 50 1126 1176 95.7
    总计Total 3782 1182 4964 97.9
    下载: 导出CSV

    表  10  Logistic基础模型和Logistic广义线性混合模型的独立性检验结果

    Table  10.   Results of independence test of classic and GLMM Logistic models

    模型Model ME MAE Pa/%
    基础模型Classic model 0.0036 0.0608 98.89
    广义线性混合模型GLMM 0.0032 0.0373 99.13
    下载: 导出CSV
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  • 收稿日期:  2017-06-12
  • 修回日期:  2017-11-01
  • 刊出日期:  2018-01-01

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