Scientia Silvae Sinicae ›› 2019, Vol. 55 ›› Issue (11): 27-36.doi: 10.11707/j.1001-7488.20191104
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Chunming Li1,Lifang Zhao2,Lixue Li3
Received:
2019-04-16
Online:
2019-11-25
Published:
2019-12-21
Supported by:
CLC Number:
Chunming Li,Lifang Zhao,Lixue Li. Modeling Stand-Level Mortality of Mongolian Oak(Quercus mongolica)Based on Mixed Effect Model and Zero-Inflated Model Methods[J]. Scientia Silvae Sinicae, 2019, 55(11): 27-36.
Table 1
The statistical tables of factors in Quercus mongolica plot"
枯损影响因子 Effect factor | 指标Indicator | 平均值(标准差) Mean(standard error) | 最大值Max. | 最小值Min. | |
林分因子 Stand factor | 1999 | 胸径DBH/cm | 12.7(7.5) | 82.7 | 5.0 |
林分平均直径Mean diameter/cm | 15.3(4.2) | 30.9 | 6.3 | ||
断面积Basal area/(m2·hm-2) | 22.9(9.4) | 57.7 | 3.0 | ||
株数Number of stems/hm-2 | 1343(621) | 3 317 | 250 | ||
2004 | 胸径DBH/cm | 12.9(7.6) | 83.6 | 5 | |
林分平均直径Mean diameter/cm | 15.7(4.1) | 31.3 | 6.3 | ||
断面积Basal area/(m2·hm-2) | 24.1(8.8) | 59.7 | 3.8 | ||
株数Number of stems/hm-2 | 1 370(618) | 3 250 | 350 | ||
2009 | 胸径DBH/cm | 13.5(8.0) | 84.9 | 5.0 | |
林分平均直径Mean diameter/cm | 16.5(4.1) | 32.6 | 6.6 | ||
断面积Basal area/(m2·hm-2) | 26.2(8.5) | 61.2 | 7.3 | ||
株数Number of stems/hm-2 | 1 347(584) | 3 550 | 367 | ||
海拔Elevation/m | 596(196) | 1 280 | 100 | ||
立地因子 Site factor | 坡度Slope/(°) | 21(8.5) | 45 | 0 | |
坡向Aspect | 按方位角从0~360°,共分成9个坡向It is divided into 9 aspects according to the azimuth angle from 0° to 360° |
Table 2
The statistical table of main climate variables"
气象因子 Climate variables | 最小 Min. | 最大 Max. | 平均 Mean |
年平均温度Mean annual temperature(MAT)/℃ | 1.34 | 6.56 | 3.93 |
最暖月平均气温Mean warmest month temperature(MWMT)/℃ | 18.30 | 23.58 | 20.91 |
最冷月平均气温Mean coldest month temperature(MCMT)/℃ | -19.00 | -11.50 | -16.08 |
年降水量Mean annual precipitation(MAP)/mm | 498.60 | 1 139.20 | 675.81 |
年平均夏季(5—9月)降水量 Mean annual summer (May to Sept.) precipitation(MSP)/mm | 389.80 | 884.20 | 527.15 |
无霜期天数The number of frost-free days(NFFD)/d | 154.80 | 196.80 | 175.30 |
上一年8月至当年7月的降雪量 Precipitation as snow between Aug. in previous year and Jul. in current year(PAS)/mm | 35.20 | 154.60 | 67.73 |
Table 3
The simulation results of stand-level mortality model"
参数 Parameters | 基础模型Basic model | |||||||
标准泊松分布 Standard Poisson | 零膨胀泊松分布 ZIP | 零改变泊松分布 ZAP | 标准负二项分布 Standard NB | 零膨胀负二项分布 ZINB | 零改变负二项分布 ZANB | |||
M1 | M2 | M3 | M4 | M5 | M6 | |||
不考虑随机效应 Without random effect | 模型的零部分 Zero component of the model | α0 | -1.031 9 (0.500 4)* | -1.031 9 (0.500 4)* | -1.030 1 (0.501 4)* | -1.031 9 (0.500 4)* | ||
α1 | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | 0.064 9 (0.020 6)** | 0.064 8 (0.020 6)** | ||||
α2 | 1.620 8 (0.404 6)*** | 1.620 8 (0.404 6)*** | 1.619 9 (0.405 6)*** | 1.620 7 (0.404 6)*** | ||||
计数的部分 Positive count component of the model | β0 | 3.060 0 (0.017 6)*** | 3.408 7 (0.018 1)*** | 3.408 7 (0.018 1)*** | 2.876 1 (0.167 6)*** | 3.345 1 (0.119 6)*** | 3.345 1 (0.119 6)*** | |
β1 | 0.018 2 (0.000 5)*** | 0.012 8 (0.000 5)*** | 0.012 7 (0.000 5)*** | 0.022 1 (0.006 0)*** | 0.013 9 (0.004 1)*** | 0.013 9 (0.004 1)** | ||
β2 | 0.718 6 (0.006 9)*** | 0.633 8 (0.007 0)*** | 0.633 8 (0.007 0)*** | 0.774 9 (0.084 9)*** | 0.656 1 (0.057 2)*** | 0.656 1 (0.057 2)*** | ||
k | 1.017 2 | 0.434 7 | 0.434 7 | |||||
AIC | 27 132 | 21 228 | 21 228 | 5 167.6 | 4 916.2 | 4 916.2 | ||
BIC | 27 144 | 21 253 | 21 253 | 5 184.2 | 4 945.3 | 4 945.3 | ||
-2LogL | 27 126 | 21 216 | 21 216 | 5 159.6 | 4 902.2 | 4 902.2 | ||
考虑随机效应 With random effect | M7 | M8 | M9 | M10 | M11 | M12 | ||
模型的零部分 Zero component of the model | α0 | -1.007 3 (0.506 3)* | -1.031 9 (0.500 4)* | -1.030 4 (0.501 0)* | -1.031 9 (0.500 4)* | |||
α1 | 0.064 1 (0.020 7)** | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | ||||
α2 | 1.615 4 (0.405 9)*** | 1.620 8 (0.404 6)*** | 1.620 1 (0.405 1)*** | 1.620 8 (0.404 6)*** | ||||
计数的部分 Positive count component of the model | β0 | -0.276 6 (0.121 2)* | 0.692 2 (0.112 0)*** | 0.696 6 (0.111 5)*** | 2.758 9 (0.282 7)*** | 3.218 7 (0.137 5)*** | 3.221 5 (0.137 7)*** | |
β1 | 0.1310 (0.002 5)*** | 0.111 5 (0.002 6)*** | 0.111 4 (0.002 6)*** | 0.023 0 (0.007 1)** | 0.016 2 (0.004 4)** | 0.016 2 (0.004 4)** | ||
β2 | 0.895 2 (0.033 4)*** | 0.686 3 (0.033 9)*** | 0.685 6 (0.033 8)*** | 0.824 3 (0.112 1)*** | 0.677 1 (0.061 8)*** | 0.676 8 (0.061 7)*** | ||
k | 1.053 9 | 0.370 3 | 0.371 4 | |||||
AIC | 11 680 | 9 597.4 | 9 597.7 | 5 170.6 | 4 912.7 | 4 913.1 | ||
BIC | 11 694 | 9 621.6 | 9 621.9 | 5 188.0 | 4 940.5 | 4 940.8 | ||
-2logL | 11 672 | 9 583.4 | 9 583.7 | 5 160.6 | 4 896.7 | 4 897.1 | ||
随机效应方差协方差矩阵D | 1.779 8 | 1.084 5 | 1.082 2 | 0.001 0 | 0.074 1 | 0.072 0 |
Table 4
The compare the results of the model based on LRT"
模型Model | LRT | P |
M1/M2 | 5 910 | < 0.000 1 |
M4/M5 | 257.4 | < 0.000 1 |
M1/M7 | 15 454 | < 0.000 1 |
M4/M10 | 1 | >0.05 |
M1/M3 | 5 910 | < 0.000 1 |
M4/M6 | 257.4 | < 0.000 1 |
M2/M8 | 11 632.6 | < 0.000 1 |
M5/M11 | 5.5 | 0.023 |
M2/M3 | 0 | 1 |
M5/M6 | 0 | 1 |
M3/M9 | 11 632.3 | < 0.000 1 |
M6/M12 | 5.1 | 0.028 |
Table 5
The simulation results of model considering climate variables"
参数 Parameter | 考虑气象因子的零膨胀负二项分布模拟结果M13 ZINB with climate variables | 考虑气象因子及随机效应的零膨胀负二项分布模拟结果M14 Random ZINB with climate variables | |||
模拟值Simulated value | P | 模拟值Simulated value | P | ||
α0 | -133.57 (44.324 1) | 0.002 7 | -133.56 (44.316 3) | 0.002 9 | |
α1 | 0.169 5 (0.065 6) | 0.010 2 | 0.169 5 (0.065 6) | 0.010 5 | |
α2 | 4.152 6 (1.771 7) | 0.019 5 | 4.152 7 (1.771 4) | 0.019 9 | |
α3 | 5.985 0 (1.999 2) | 0.002 9 | 5.984 7 (1.998 9) | 0.003 0 | |
β0 | 3.345 5 (0.957 8) | 0.000 5 | 3.373 5 (1.026 8) | 0.001 2 | |
β1 | 0.013 9 (0.004 3) | 0.001 6 | 0.016 0 (0.004 7) | 0.000 8 | |
β2 | 0.655 8 (0.058 6) | < 0.000 1 | 0.675 2 (0.062 9) | < 0.000 1 | |
β3 | 0.000 1(0.038 91) | 0.999 6 | -0.006 3 (0.041 9) | 0.879 3 | |
AIC | 4 681.2 | 4 677.6 | |||
BIC | 4 718.6 | 4 712.3 | |||
-2logL | 4 663.2 | 4 657.6 | |||
k | 0.433 6 | 0.369 1 | |||
随机效应方差 Random effect matrix | 0.074 8 |
Table 6
The validation result of models"
评价指标 Evaluating indicator | 不考虑随机效应 Without random effect | 考虑随机效应 With random effect | |||||||||||||
M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | M9 | M10 | M11 | M12 | M13 | M14 | ||
R2 | 0.87 | 0.89 | 0.89 | 0.87 | 0.89 | 0.89 | 0.89 | 0.85 | 0.85 | 0.89 | 0.89 | 0.89 | 0.88 | 0.83 | |
RMSE | 82.1 | 85.7 | 85.7 | 75.7 | 83.4 | 83.4 | 73.9 | 76.1 | 76.1 | 78.9 | 74.8 | 78.8 | 85.2 | 87.8 | |
|${\bar E}$| | 60.5 | 61.6 | 61.6 | 55.2 | 59.8 | 59.8 | 48.4 | 51.7 | 51.7 | 53.4 | 51.6 | 53.6 | 64.6 | 67.6 |
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