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基于零膨胀模型及混合效应模型相结合的蒙古栎林林木进界模拟研究

李春明 李利学

李春明, 李利学. 基于零膨胀模型及混合效应模型相结合的蒙古栎林林木进界模拟研究[J]. 北京林业大学学报, 2020, 42(6): 59-67. doi: 10.12171/j.1000-1522.20190216
引用本文: 李春明, 李利学. 基于零膨胀模型及混合效应模型相结合的蒙古栎林林木进界模拟研究[J]. 北京林业大学学报, 2020, 42(6): 59-67. doi: 10.12171/j.1000-1522.20190216
Li Chunming, Li Lixue. Simulating study on tree recruitment of Quercus mongolica based on zero-inflated model and mixed effect model methods[J]. Journal of Beijing Forestry University, 2020, 42(6): 59-67. doi: 10.12171/j.1000-1522.20190216
Citation: Li Chunming, Li Lixue. Simulating study on tree recruitment of Quercus mongolica based on zero-inflated model and mixed effect model methods[J]. Journal of Beijing Forestry University, 2020, 42(6): 59-67. doi: 10.12171/j.1000-1522.20190216

基于零膨胀模型及混合效应模型相结合的蒙古栎林林木进界模拟研究

doi: 10.12171/j.1000-1522.20190216
基金项目: 国家自然科学基金面上项目“基于混合效应模型的联立方程组及概率分布模型在模拟森林生长中的方法研究”(31570625)
详细信息
    作者简介:

    李春明,博士,副研究员。主要研究方向:森林生长模型。Email:lichunm@ifrit.ac.cn 地址:100091中国林业科学研究院资源信息研究所

  • 中图分类号: S758.5

Simulating study on tree recruitment of Quercus mongolica based on zero-inflated model and mixed effect model methods

  • 摘要: 目的林木的进界是确保森林长期维持的基本条件,而进界模型能够预测森林的发展,是量化森林生态系统未来健康和生产力的基础。方法以吉林省1995年设立的295块蒙古栎固定样地数据为例,构建基于林分因子、立地因子及气象因子的蒙古栎林林木进界模型。模型的基本形式包括泊松分布和负二项分布两种离散形式。考虑到样地中存在大量零值的问题,在这些基础模型上考虑加入零膨胀模型。为了解决模型存在的嵌套和纵向数据问题,在构建模型时把样地的随机效应考虑进去。最后利用验证数据来验证。结果林分算数平均直径和林分公顷株数是影响林木进界概率和数量最重要的影响因子,并且均与林木进界概率和数量呈反比。立地和气象因子中的各项因子对进界均没有产生明显影响。负二项分布模型由于考虑了数据过度离散问题,模拟精度要高于泊松分布;在考虑样地的随机效应后,除了标准负二项分布模型外所有模型都明显提高了模型的模拟精度;同时考虑随机效应和零膨胀的负二项分布模型,其模型的模拟效果最好,验证结果也支持此结论。结论为了确保进界的发生,在进行森林经营时,确定合理的初植和经营密度至关重要。

     

  • 表  1  蒙古栎样地各因子统计表

    Table  1.   Statistical table of factors in Quercus mongolica sample plots

    影响进界的因子
    Factor affecting recruitment
    调查年份
    Survey year
    指标
    Index
    平均值 (标准差)
    Mean (standard deviation)
    最大值
    Max.
    最小值
    Min.
    林分和单木因子
    Stand and single wood factor
    1999 胸径 DBH (d)/cm 12.7 (7.5) 82.7 5
    林分平均直径 Average stand diameter (Dg)/cm 15.3 (4.2) 30.9 6.3
    公顷断面积/(m2·hm− 2) Basal area/(m2·ha− 1) 22.9 (9.4) 57.7 3.0
    公顷株数/(株·hm− 2) Stand density/(tree·ha− 1) 1 343 (621) 3 317 250
    林分和单木因子
    Stand and single wood factor
    2004 胸径 DBH (d)/cm 12.9 (7.6) 83.6 5
    林分平均直径 Average stand diameter (Dg)/cm 15.7 (4.1) 31.3 6.3
    公顷断面积/(m2·hm− 2) Basal area/(m2·ha− 1) 24.1 (8.8) 59.7 3.8
    公顷株数/(株·hm− 2) Stand density/(tree·ha− 1) 1 370 (618) 3 250 350
    林分和单木因子
    Stand and single wood factor
    2009 胸径 DBH (d)/cm 13.5 (8.0) 84.9 5
    林分平均直径 Average stand diameter (Dg)/cm 16.5 (4.1) 32.6 6.6
    公顷断面积/(m2·hm− 2) Basal area/(m2·ha− 1) 26.2 (8.5) 61.2 7.3
    公顷株数/(株·hm− 2) Stand density/(tree·ha− 1) 1 347 (584) 3 550 367
    立地因子
    Site factor
    海拔 Elevation/m 596 (196) 1 280 100
    坡度 Slope degree/(°) 21 (8.5) 45 0
    坡向 Slope aspect 按方位角从0º ~ 360º,共分成9个坡向,每个坡向大概45º,用数字1 ~ 9表示
    According to the azimuth angle from 0−360 degrees, it is divided into 9 slope directions, each of which is about 45 degrees, represented by No. 1−9
    下载: 导出CSV

    表  2  主要气象变量统计表

    Table  2.   Satistical table of main climate variables

    气象因子
    Climate factor
    最大值
    Max.
    最小值
    Min.
    平均值 (标准差)
    Mean (standard deviation)
    年份
    Year
    年平均温度
    Mean annual temperature (MAT)/℃
    6.56 1.8 4.2 (0.8) 1999—2004
    6.96 2.3 4.6 (0.8) 2004—2009
    6 1.3 3.7 (0.8) 2009—2014
    最暖月平均气温
    Mean temperature of the warmest month (MWMT)/℃
    23.58 18.6 21.1 (0.9) 1999—2004
    22.68 18.4 20.8 (0.8) 2004—2009
    22.78 18.3 20.8 (0.8) 2009—2014
    最冷月平均气温
    Mean temperature of the coldest month (MCMT)/℃
    − 11.5 − 18.4 − 15.7 (1.1) 1999—2004
    − 10.1 − 16.9 − 14.4 (1.1) 2004—2009
    − 12.1 − 19 − 16.5 (1.1) 2009—2014
    年平均降水量
    Mean annual precipitation (MAP)/mm
    920.6 498.6 646.3 (75.3) 1999—2004
    1 038.8 475.2 640.9 (113.3) 2004—2009
    1 139.2 518.2 705.3 (126.4) 2009—2014
    年平均夏季 (5月至9月)降水量
    Mean annual summer (from May to September) precipitation (MSP)/mm
    731.4 399.2 514.9 (53.7) 1999—2004
    827.6 379.2 512.9 (88.9) 2004—2009
    884.2 389.8 539.4 (99.0) 2009—2014
    无霜期天数
    Number of frost-free days (NFFD)
    196.8 156.6 176.6 (7.9) 1999—2004
    200.2 158.6 178.9 (8.1) 2004—2009
    194.6 154.8 174.0 (7.7) 2009—2014
    上一年8月至当年7月的降雪量
    Snowfall between August in previous year and July in current year (PAS)/ mm
    115.8 35.2 54.9 (16.3) 1999—2004
    123.2 35 60.9 (14.8) 2004—2009
    154.6 52.4 80.5 (19.7) 2009—2014
    下载: 导出CSV

    表  3  林分进界模型模拟结果

    Table  3.   Simulation results of stand-level recruitment models

    参数
    Parameter
    基础模型 Basic model
    M1M2M3M4
    不考虑随机效应
    No random effect
    模型的零部分
    Zero component of the model
    $ {\alpha _0}$ 5.730 8 (0.990 3)*** 5.726 6 (1.000 1)***
    $ {\alpha _1}$ − 0.203 8 (0.046 4)*** − 0.202 4 (0.046 8)***
    $ {\alpha _2}$ − 1.110 0 (0.265 1)*** − 1.110 3 (0.267 7)***
    计数的部分
    Positive count component of the model
    $\; {\beta _0}$ 9.713 9 (0.026 7)*** 9.237 8 (0.027 6)*** 8.446 8 (0.469 7)*** 8.065 1 (0.295 0)***
    $\; {\beta _1}$ − 0.313 0 (0.001 7)*** − 0.274 4 (0.001 7)*** − 0.214 1 (0.021 4)*** − 0.187 4 (0.013 8)***
    $\; {\beta _2}$ − 0.756 0 (0.008 3)*** − 0.621 9 (0.008 5)*** − 0.771 5 (0.149 9)*** − 0.583 3 (0.095 2)***
    $ k$ 2.437 2 0.753 2
    AIC 55 314 39 871 4 877.6 4 671.8
    BIC 55 327 39 896 4 894.2 4 700.9
    − 2logL 55 308 39 859 4 869.6 4 657.8
    参数
    Parameter
    考虑混合效应模型 With mixed effect model
    M5 M6 M7 M8
    考虑随机效应部分
    With random effect
    模型的零部分
    Zero component of the model
    $ {\alpha _0}$ 5.729 5 (0.990 3)*** 5.716 6 (0.993 3)***
    $ {\alpha _1}$ − 0.203 8 (0.046 4)*** − 0.202 6 (0.046 5)***
    $ {\alpha _2}$ − 1.109 8 (0.265 2)*** − 1.108 0 (0.265 9)***
    计数的部分
    Positive count component of the model
    $\; {\beta _0}$ 10.453 3 (0.150 7)*** 9.587 2 (0.113 4)*** 8.995 2 (0.552 7)*** 8.263 9 (0.354 6)***
    $\; {\beta _1}$ − 0.391 3 (0.006 4)*** − 0.259 9 (0.006 3)*** − 0.240 6 (0.026 7)*** − 0.202 0 (0.017 8)***
    $\; {\beta _2}$ − 0.992 8 (0.017 5)*** − 1.220 0 (0.020 8)*** − 0.926 2 (0.169 5)*** − 0.687 1 (0.107 8)***
    $ k$ 2.292 2 0.525 7
    AIC 21 504 15 054 4 882.4 4 645.0
    BIC 21 518 15 078 4 899.8 4 672.7
    − 2logL 21 496 15 040 4 872.4 4 629.0
    随机效应方差协方差矩阵 Covariance matrix of random effect variance 2.976 0 0.673 0 0.000 1 0.254 7
    注:k是负二项分布的待估参数;M1为标准泊松分布进界模型,即公式 (1);M2为零膨胀泊松分布进界模型,即公式 (2);M3为标准负二项分布进界模型,即公式 (3);M4为零膨胀负二项分布进界模型,即公式 (4);M5为考虑随机效应的标准泊松分布进界模型;M6为考虑随机效应的零膨胀泊松分布进界模型;M7为考虑随机效应的标准负二项分布进界模型;M8为考虑随机效应的零膨胀负二项分布进界模型。表中括号内的值为标准差;*为0.01 < P < 0.05,**为0.001 < P < 0.01,***P < 0.001;$ {\alpha _0}$和$\; {\beta _0}$为截距参数,$ {\alpha _1}$和$\; {\beta _1}$为林分算数平均直径参数值,$ {\alpha _2}$和$\; {\beta _2}$为林分公顷株数参数值。Notes: k is a parameter to be estimated in negative binomial distribution; M1 is Poisson distribution recruitment model, i.e. formula (1); M2 is zero-inflated Poisson distribution recruitment model, i.e. formula (2); M3 is negative binomial distribution recruitment model, i.e. formula (3); M4 is zero-inflated negative binomial distribution recruitment model, i.e. formula (4); M5 is Poisson distribution recruitment model based on mixed effect model; M6 is zero-inflated Poisson distribution recruitment model based on mixed effect model; M7 is negative binomial distribution recruitment model based on mixed effect model; M8 is zero-inflated negative binomial distribution recruitment model based on mixed effect model. Values in brackets are standard deviation; * is 0.01 < P < 0.05,** is 0.001 < P < 0.01,*** is P < 0.001; $ {\alpha _0}$ and $\; {\beta _0}$ are intercept parameters, $ {\alpha _1}$ and $\; {\beta _1}$ are stand arithmetic average diameter parameters, $ {\alpha _2}$ and $\; {\beta _2}$ are stand number of per hectare parameters.
    下载: 导出CSV

    表  4  利用LRT指标对模型进行比较的结果

    Table  4.   Comparing results of the model based on LRT index

    模型 ModelLRT值 LRT valueP模型 ModelLRT 值 LRT valueP模型 ModelLRT值 LRT valueP
    M1/M2 15 449 < 0.000 1 M1/M5 33 812 < 0.000 1 M3/M4 211.8 < 0.000 1
    M2/M6 24 819 < 0.000 1 M3/M7 2.8 > 0.05 M4/M8 28.8 < 0.000 1
    下载: 导出CSV

    表  5  模型验证结果

    Table  5.   Validation results of models

    评价指标
    Evaluating index
    不考虑随机效应 No random effect考虑随机效应 With random effect
    M1M2M3M4M5M6M7M8
    $ {R^2}$ 0.40 0.55 0.50 0.65 0.75 0.91 0.54 0.84
    RMSE/株 RMSE/tree
    163.8 146.2 158.7 139.2 125.3 161.8 153.8 116.5
    $ |\bar E|$/株 $ |\bar E|$/tree 98.8 95.9 83.9 81.7 65 70.2 85 61.7
    下载: 导出CSV
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  • 收稿日期:  2019-05-09
  • 修回日期:  2019-09-05
  • 网络出版日期:  2020-05-27
  • 刊出日期:  2020-07-01

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