华北落叶松人工林林分枯损株数随机效应预测模型

doi:10.11707/j.1001-7488.20221007

Abstract

Abstract:

Objective: This study aimed to develope counting model that can accurately predict the number of dead trees in Larix principis-rupprechtii plantation, explore the main reasons affecting the number of dead trees in L. principis-rupprechtii plantation, and provide decision-making basis for the scientific management of L. principis-rupprechtii plantation in the core area of the Winter Olympic Games. Method: 45 sample plots of L. principis-rupprechtii plantation in the core area of Winter Olympic Games in Chongli District of Zhangjiakou City were chosen as the research material. Poisson regression model, negative binomial regression model, zero-inflated Poisson regression model, zero-inflated negative binomial regression model, hurdle passion regression model, and hurdle negative binomial regression model were used to develop the models of L. principis-rupprechtii plantation stand mortality number, and the optimal model would be selected in terms of the AIC value. Based on the optimal model, the random effect of different levels and the combination of various random parameters lying on the intercepts were taken into consideration, and the optimal mixed effect model of stand dead number was constructed. The best random effect level and the most optimal combination of random parameters would be determined according to the model convergence situation and AIC value, and the optimal mixed effect model of stand mortality number would be developed. Result: Stand average diameter, mean height of dominant trees, stand age, stand basal area, stand diameter Gini coefficient were the stand factors affecting stand mortality numbers, and site factors had little effect on stand death. When too many zeros were not considered, the fitting effect of negative binomial regression model was much better than Poisson regression model. After considering the phenomenon of zero expansion, the zero expansion model and hurdle model were used for simulation. It was found that the fitting effect of hurdle negative binomial regression model(HNB) and zero expansion negative binomial regression model(ZINB) were better than other models. Finally, the order of goodness of fit of several counting models considering lots of zero values was HNB regression model ≈ ZINB regression model > HP regression model > ZIP regression model. HNB model and ZINB model were selected for further mixed effect model construction. When the random effect level was specified at plot, the number of random parameters had only one, and the model cannot converge when acting on other covariates except for intercept. Only when the random parameters acted on the intercept at plot level, the model could get to converge and the fitting accuracy was further improved, and the evaluation error ME of HNB model and ZINB model were 14 and 11 trees·hm^-2 respectively. Conclusion: In the core area of the Winter Olympic Games, the main factors affecting the death of L. principis-rupprechtii plantation were stand factors rather than site factors. HNB regression model and ZINB regression model had more advantages than Poisson regression model and negative binomial regression model when fitting too many zeros. The generalized linear mixed effect model considering random intercept effect can improve the fitting accuracy of the model and reduce fitting error.

Key words: mortality trees number, Poisson model, negative binomial model, zero expansion model, Hurdle model, random effect

CLC Number:

S757

Zeyu Zhou,Linyan Feng,Xingrong Yan,Xiaofang Zhang,Xuping Yang,Liyong Fu,Huiru Zhang. Prediction Model of Stand Mortality of Larix principis-rupprechtii Plantation in the Core Area of Winter Olympic Games[J]. Scientia Silvae Sinicae, 2022, 58(10): 67-78.

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References 0

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变量 Variable	最大 Max.	最小 Min.	均值 Mean	标准误 Standard error
林分平均胸径Sand mean DBH/cm	24.71	4.08	13.44	4.97
优势木平均高Mean height of stand dominant trees/m	21.25	4.55	12.67	4.54
林龄Stand age/a	49.0	11.0	28.0	12.0
林分断面积Basal area of stand/m²	46.88	0. 92	20.05	13.11
林分密度Stand density/hm^-2	2 444	422	1 264	522
林分胸径Gini系数Stand diameter Gini coefficient	0.30	0.08	0.18	0.05
枯死木株数Dead trees number/hm^-2	167	0	32	49
枯死概率Dead probability(%)	0.10	0.00	0.02	0.03
海拔Elevation/m	2 097	1 626	1 841	153
坡度Slope/(°)	23.00	9.00	16.60	3.5
坡向Aspect	东East：67.5°~112.5°; 南South：157.5°~202.5°; 西West：247.5°~292.5°; 北North：337.5°~22.5°; 东南Southeast：112.5°~157.5°; 东北Northeast：22.5°~67.5°; 西南Southwest：202.5°~247.5°; 西北Northwest：292.5°~337.5°

变量Variable	Poisson回归模型 Poisson regression model			负二项回归模型 Negative binomial regression model
变量Variable	估计值 Estimation	标准误 Standard error	P	估计值 Estimation	标准误 Standard error	P
截距Intercept	-1.846 9	0.257 0	< 0.000 1	-
林分平均胸径Stand mean DBH	-0.166 4	0.015 3	< 0.000 1	-0.183 0	0.077 9	0.023 5
优势木平均高Mean height of dominant trees	-0.049 5	0.026 6	0.063 1	-
林分断面积Stand basal area	0.125 0	0.006 0	< 0.000 1	0.152 6	0.035 1	< 0.000 1
林龄Stand age	0.063 6	0.004 9	< 0.000 1	-
林分胸径Gini系数Stand DBH Gini coefficient	15.967 0	0.746 7	< 0.000 1	10.581 8	3.074 8	0.001 3

变量 Variable	零膨胀Poisson回归模型 Zero-inflated Poisson model (ZIP)			零膨胀负二项回归模型 Zero-inflated negative binomial model(ZINB)			Hurdle-Poisson回归模型 Hurdle-Poisson model (HP)			Hurdle负二项回归模型 Hurdle negative binomial model(HNB)
变量 Variable	估计值 Estimate	标准误 Standard error	P	估计值 Estimate	标准误 Standard error	P	估计值 Estimate	标准误 Standard error	P	估计值 Estimate	标准误 Standard error	P
计数模型Count model
截距Intercept	0.845 7		0.268 0	0.001 6		—	0.845 7		0.268 0	0.001 6		—
林分平均胸径Stand mean DBH	-0.092 9		0.016 1	< 0.000 1		—	-0.092 9		0.016 1	< 0.000 1		—
林龄Stand age	0.046 2	0.004 7	< 0.000 1	0.050 2	0.019 3	0.009 3	0.046 2	0.004 7	< 0.000 1	0.050 2	0.019 3	0.000 9
优势木平均高Mean height of dominant trees	-0.134 4	0.025 6	< 0.000 1	-0.195 7	0.069 0	0.004 6	-0.134 4	0.025 6	< 0.000 1	-0.195 6	0.069 0	0.004 6
林分断面积Stand basal area	0.088 1	0.006 0	< 0.000 1	0.070 7	0.018 9	0.000 2	0.088 1	0.006 0	< 0.000 1	0.070 6	0.018 9	0.000 2
林分胸径Gini系数Stand DBH Gini coefficient	13.614 9	0.767 3	< 0.000 1	17.614 1	1.871 1	< 0.000 1	13.614 9	0.767 3	< 0.000 1	17.607 0	1.871 3	< 0.000 1
零模型Zero model
截距Intercept	4.184 3	1.469 7	0.004 4	4.181 0	1.469 8	0.004 5	-3.892 5	1.279 7	0.002 4	-3.894 2	1.280 2	0.002 4
林分平均胸径Stand mean DBH	0.667 5	0.261 9	0.010 8	0.666 8	0.262 0	0.010 9	-0.494 1	0.204 0	0.015 5	-0.494 1	0.204 1	0.015 5
优势木平均高Mean height of dominant trees	-1.033 4	0.314 9	0.001 0	-1.032 5	0.314 9	0.001 0	0.787 4	0.244 3	0.001 3	0.787 6	0.244 4	0.001 3
AIC	352.5			251.2			350.6			251.3
BIC	368.8			265.6			366.9			267.5
-2Loglikehood	334.5			235.2			332.6			233.3

模型 Model	Vuong检验值 Vuong value	P
ZIP，HP	-2.83	0.002 3
ZINB，HNB	-2.83	0.002 3
ZIP，ZINB	-1.73	0.042 0
HP，HNB	-1.73	0.042 0
ZIP，HNB	-1.75	0.039 5
ZINB，HP	1.69	0.044 6

随机效应水平 Random-effects level	HNB	ZINB
样地类型 Plot type	收敛 Converged	收敛 Converged
样地 Plot	不收敛 False converged	不收敛 False converged
样地/样地类型嵌套 Plot/plot type nested	不收敛 False converged	不收敛 False converged

Prediction Model of Stand Mortality of Larix principis-rupprechtii Plantation in the Core Area of Winter Olympic Games

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变量Variable	估计 Estimation	标准误 Standard error	P
计数模型Count model
截距Intercept	—
林分平均胸径Stand mean DBH	-0.089 3	0.042 4	0.035 1
优势木平均高Mean height of dominant trees	-0.119 5	0.067 7	0.077 6
林龄Stand age	0.048 1	0.012 3	< 0.000 1
林分断面积Stand basal area	0.090 5	0.017 6	< 0.000 1
林分胸径Gini系数Stand DBH Gini coefficient	15.562 0	1.645 9	< 0.000 1
零模型Zero model
截距Intercept	—
林分平均胸径Stand mean DBH	0.327 2	0.099 2	0.001 0
林分断面积Stand basal area	-0.222 3	0.062 3	0.000 3
AIC	248.9
BIC	265.2
-2Loglikehood	230.9
ME	-14
方差协方差矩阵D Variance-covariance matrix D	1.58×10^-10

变量Variable	估计Estimation	标准误Standard arror	P
计数模型Count model
截距Intercept	—
优势木平均高Mean height of dominant trees	-0.177 9	0.060 3	0.003 2
林龄Stand age	0.036 8	0.011 5	0.001 3
林分断面积Stand basal area	0.084 2	0.018 7	< 0.000 1
林分胸径Gini系数Stand DBH Gini coefficient	16.222 9	1.645 5	< 0.000 1
零模型Zero model
截距Intercept	—
林分平均胸径Stand mean DBH	0.317 5	0.100 8	0.001 6
林分断面积Stand basal area	-0.217 1	0.063 1	0.000 6
AIC	251.0
BIC	265.5
-2Loglikehood	235.0
ME	-11
方差协方差矩阵D Variance-covariance matrix D	1.48×10^-10

样地编号 Plot No.	实测枯死木株数 Measured dead trees	预测枯死木株数 Predicted dead trees		样地编号 Plot No.	实测枯死木株数 Measured dead trees	预测枯死木株数 Predicted dead trees
样地编号 Plot No.	实测枯死木株数 Measured dead trees	ZINB	HNB	样地编号 Plot No.	实测枯死木株数 Measured dead trees	ZINB	HNB
1	89	27	26	24	0	0	0
2	122	125	133	25	0	3	2
3	33	47	39	26	0	1	1
4	0	0	0	27	0	2	1
5	56	73	69	28	0	22	22
6	11	12	12	29	11	6	5
7	0	1	0	30	167	113	127
8	33	22	20	31	122	81	83
9	11	21	16	32	11	23	25
10	56	33	33	33	122	113	125
11	11	20	19	34	0	3	3
12	133	113	99	35	0	9	8
13	22	3	3	36	0	21	20
14	0	2	2	37	0	31	25
15	0	2	2	38	11	1	1
16	0	3	3	39	0	13	11
17	0	1	1	40	133	95	130
18	0	1	1	41	122	109	111
19	0	5	4	42	33	27	31
20	22	1	1	43	0	23	23
21	0	3	3	44	0	12	9
22	0	35	24	45	100	114	87
23	0	8	5

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