基于贝叶斯模型平均法和逐步回归法构建杉木单木胸径生长模型

doi:10.11707/j.1001-7488.20210909

摘要/Abstract

摘要：

目的: 探索杉木人工林单木胸径生长量变化的驱动因子，比较不同驱动因子的重要性，构建不确定性单木胸径生长模型，为杉木经营管理者科学经营管理杉木人工林提供参考。方法: 以福建省邵武市卫闽林场杉木密度试验林为研究对象，采用贝叶斯模型平均法（BMA）和逐步回归法（SR）分析杉木单木胸径生长量与内部因子（林分变量因子）和气候因子的关系，构建杉木单木胸径生长模型。结果: 杉木单木胸径年均生长量受气候因子影响较小，主要受竞争因子和单木大小因子影响。单木胸径生长量随林分密度、林分平方平均胸径、大于对象木的断面积和、年龄、冬季平均最低温度增加而减小，随期初胸径、胸高断面积、优势木平均高、最冷月平均温度、最热月平均温度、年均降雨量增加而增加。基于SR获得模型的后验概率小于BMA获得最佳模型（最高后验概率）或SR模型不在BMA模型空间前几个后验概率高的模型中。结论: 杉木单木胸径生长量随竞争增加而减小，随温度和降雨增加而增加。贝叶斯模型平均法考虑所有可能变量的组合，能够反映出模型的不确定性。

关键词: 单木胸径生长量, 气候变量, 贝叶斯模型平均法, 逐步回归法, 林分变量因子

Abstract:

Object: Individual tree diameter growth model is one of forest growth and yield basic models. Stepwise regression is widely used in the selection of model variables. However, this method ignores the model uncertainty caused by the variable selection process. So the driving factors of individual tree diameter grouth of Chinese fir (Cunninghamia lanceolata) plantation were explored, the importance of different driving factors was compared, and the uncertain individual tree diameter growth model was constructed, in order to provide reference for Chinese fir managers to manage Chinese fir plantation scientifically. Method: Data for this study was sampled from Chinese fir stands in Weimin, Shaowu city, Fujian Province. Bayesian model averaging(BMA) and stepwise regression(SR) were used to analyze the effects of endogenous and climatic factors on the individual tree diameter growth of Chinese fir. Result: Competition and individual tree size were the main factors affecting annual diameter growth comparing with climate factors. Diameter growth decreased with the increase of tree number per hectare, quadratic mean diameter, sum of basal areas of trees larger than the subject tree(BAL), age and winter mean minimum temperature, whereas increased with the increase of diameter at the beginning of growth period, stand basal area, dominant height, mean coldest month temperature, mean warmest month temperature and mean annual precipitation. For most of the treatments of the four models, the posterior probability of the model obtained by SR was smaller than that of the best model obtained by BMA(which exhibited the highest posterior probability). In some cases, SR models did not belong to the top several models with higher posterior probability in the BMA model space. Conclusion: The diameter increment decreased with increasing competition and increased with increasing temperature and precipitation. BMA considered the combination of all possible variables and reflected the uncertainty of the model.

Key words: individual tree diameter growth, climate variables, Bayesian model averaging(BMA), stepwise regression(SR), stand variables

中图分类号:

S758.5

鲁乐乐,王震,张雄清,张建国. 基于贝叶斯模型平均法和逐步回归法构建杉木单木胸径生长模型[J]. 林业科学, 2021, 57(9): 87-97.

Lele Lu,Zhen Wang,Xiongqing Zhang,Jianguo Zhang. Individual Tree Diameter Growth Model of Chinese Fir Plantations Using Bayesian Model Averaging and Stepwise Regression Approaches[J]. Scientia Silvae Sinicae, 2021, 57(9): 87-97.

图/表 7

表1

表2

表3

BMA和SR确定的单木胸径生长模型和BMA模型的后验概率①"

初植密度Planting density	BMA		SR	2种方法的模型是否相似SR model = BMA model or not
初植密度Planting density	后验概率Posterior probability	选择的模型变量Selected model variables	选择的模型变量Selected model variables	2种方法的模型是否相似SR model = BMA model or not
A	模型1 Model 1 (0.656)	N, D_g, DBH, lnDBH, lnA, MWMT, MCMT, AP, AHM, SMMT, WMMT	N, BA, DBH, lnDBH, lnA, MWMT, MCMT, AP, AHM, DD0, SMMT, WMMT, SMT	模型2 Model 2
	模型2 Model 2(0.069)	N, BA, DBH, lnDBH, lnA, MWMT, MCMT, AP, AHM, DD0, SMMT, WMMT, SMT
	模型3 Model 3(0.062)	N, D_g, DBH, lnDBH, lnA, MAT, MWMT, MCMT, AP, DD0, SMMT, WMMT
	模型4 Model 4(0.062)	N, D_g, DBH, lnDBH, lnA, MWMT, MCMT, AP, AHM, DD0, SMMT, WMMT
	模型5 Model 5(0.043)	N, D_g, DBH, lnDBH, lnA, MWMT, MCMT, AP, AHM, DD0, SMMT, WMMT, SMT
B	模型1 Model 1(0.743)	N, D_g, H_d, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, SMMT, WMMT	N, D_g, H_d, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, DD0, SMMT, WMMT, SMT	否No
B	模型2 Model 2 (0.257)	N, D_g, H_d, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, WMMT		否No
C	模型1 Model 1 (0.447)	N, BA, D_g, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, DD0, SMMT, WMMT	N, BA, D_g, H_d, DBH, lnDBH, lnA, BAL, MAT, MWMT, MCMT, AP, AHM, DD0, SMMT, WMMT, SMT	否No
	模型2 Model 2 (0.228)	N, BA, D_g, H_d, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, DD0, SMMT, WMMT
	模型3 Model 3 (0.155)	N, BA, D_g, DBH, lnDBH, lnA, BAL, MCMT, AP, DD0, WMMT
	模型4 Model 4 (0.095)	N, BA, D_g, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, SMMT, WMMT
	模型5 Model 5 (0.038)	N, BA, D_g, DBH, lnDBH, lnA, BAL, MWMT, MCMT, AP, WMMT
D	模型1 Model 1(0.825)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, AHM, DD0, WMMT, SMT	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, MWMT, AP, AHM, DD0, SMMT, WMMT, SMT	模型2 Model 2
	模型2 Model 2(0.069)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, MWMT, AP, AHM, DD0, SMMT, WMMT, SMT
	模型3 Model 3 (0.062)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, AP, DD0, WMMT, SMT
	模型4 Model 4 (0.043)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, AHM, WMMT, SMT
E	模型1 Model 1(0.594)	BA, D_g, DBH, lnDBH, lnA, BAL, MAT, MWMT, MCMT, AHM, DD0, SMMT, WMMT, SMT	BA, D_g, DBH, lnDBH, lnA, BAL, MAT, MWMT, MCMT, AHM, DD0, SMMT, WMMT, SMT	模型1 Model 1
E	模型2 Model 2 (0.406)	BA, D_g, DBH, lnDBH, lnA, BAL, MAT, MWMT, MCMT, AP, DD0, SMMT, WMMT, SMT		模型1 Model 1
全样本数据All data	模型1 Model 1(0.679)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, MWMT, MCMT, AP, AHM, DD0, WMMT, SMT	N, BA, D_g, H_d, DBH, lnDBH, lnA, BAL, MAT, MWMT, MCMT, AP, AHM, DD0, WMMT, SMT	否No
全样本数据All data	模型2 Model 2(0.321)	N, BA, D_g, H_d, DBH, lnA, BAL, MAT, MWMT, MCMT, AP, DD0, WMMT, SMT		否No

表3

表4

表5

SR和BMA构建单木胸径生长模型的参数估计值①"

变量Variable	A		B		C		D		E		全样本数据All data
变量Variable	SR	BMA	SR	BMA	SR	BMA	SR	BMA	SR	BMA	SR	BMA
N	0.000 9^*	-0.000 9 (1.00)	0.000 2^*	0.000 2 (1.00)	0.000 2^*	0.000 2 (1.00)	0.000 2^*	0.000 1 (1.00)	—	—	0.000 03^*	0.000 03 (1.00)
BA	0.004 1^*	—	—	—	0.005 5^*	0.005 1 (1.00)	0.004 6^*	0.004 7 (1.00)	0.003 7^*	0.003 7 (1.00)	0.001 8^*	0.002 0 (1.00)
D_g	—	-0.016 5 (0.89)	0.056 5^*	0.063 4 (1.00)	0.069 8^*	0.086 9 (1.00)	0.090 5^*	0.086 0 (1.00)	0.024 6^*	0.024 2 (1.00)	-0.027 5^*	-0.027 0 (1.00)
H_d	—	—	0.014 3^*	0.016 6 (1.00)	0.008 5^*	—	0.014 2^*	0.014 0 (1.00)	—	—	0.005 1^*	0.005 1 (1.00)
DBH	0.034 2^*	0.034 0 (1.00)	0.022 9^*	0.024 3 (1.00)	0.012 0^*	0.012 9 (1.00)	0.017 9^*	0.017 0 (1.00)	0.014 9^*	0.014 9 (1.00)	0.016 3^*	0.015 0 (1.00)
lnDBH	0.153 2^*	-0.151 8 (1.00)	0.096 3^*	0.103 0 (1.00)	0.064 9^*	0.061 6 (1.00)	—	—	0.088 96^*	0.088 2 (1.00)	-0.011 4^*	—
lnA	0.727 6^*	-0.735 8 (1.00)	0.262 0^*	0.228 2 (1.00)	0.195 2^*	0.172 8 (1.00)	0.320 5^*	0.280 0 (1.00)	-0.405 8^*	0.397 9 (1.00)	-0.291 0^*	-0.300 0 (1.00)
BAL	—	—	0.003 3^*	0.003 1 (1.00)	0.003 8^*	0.003 6 (1.00)	0.004 5^*	0.004 7 (1.00)	-0.006 1^*	0.006 1 (1.00)	-0.004 2^*	-0.004 3 (1.00)
MAT	0.139 3	—	—	—	0.208 4^*	—	0.264 9^*	0.100 0 (1.00)	-0.149 1^*	0.195 0 (1.00)	-0.198 5^*	-0.180 0 (1.00)
MWMT	0.128 1^*	0.129 4 (1.00)	0.071 7^*	0.048 9 (1.00)	0.053 9^*	0.037 9 (0.81)	0.038 7^*	—	0.091 8^*	0.090 2 (1.00)	0.028 7^*	0.027 0 (1.00)
MCMT	0.195 3^*	0.178 0 (1.00)	0.098 4^*	0.083 5 (1.00)	0.076 6^*	0.049 1 (1.00)	—	—	0.078 6^*	0.078 5 (1.00)	0.059 0^*	0.056 0 (1.00)
AP	0.001 0^*	0.000 7 (1.00)	0.000 2^*	0.000 2 (1.00)	0.000 6^*	0.000 2 (1.00)	0.000 4^*	—	—	—	0.000 4^*	0.000 3 (1.00)
AHM	0.078 2^*	0.051 4 (0.87)	—	—	0.051 2^*	—	0.056 6^*	0.015 0 (0.94)	-0.032 5^*	—	0.002 3^*	—
DD0	0.869 3^*	—	0.037 4^*	—	0.082 0^*	0.025 6 (0.83)	0.054 2^*	0.041 0 (0.96)	0.111 8^*	0.116 9 (1.00)	0.081 3^*	0.082 0 (1.00)
SMMT	0.206 8^*	-0.227 6 (1.00)	0.098 2^*	0.052 8 (0.74)	0.059 8^*	0.059 3 (0.77)	0.089 3^*	—	-0.107 3^*	0.097 9 (1.00)	—	—
WMMT	0.156 3^*	-0.172 6 (1.00)	0.106 6^*	0.104 5 (1.00)	0.052 0^*	0.067 9 (1.00)	0.063 3^*	0.041 0 (1.00)	-0.070 4^*	0.066 6 (1.00)	-0.050 3^*	-0.051 0 (1.00)
SMT	0.069 8^*	—	0.016 7^*	—	0.065 9^*	—	0.084 6^*	0.045 0 (1.00)	0.112 6^*	0.123 7 (1.00)	0.090 4^*	0.088 0 (1.00)

表5

图1

图2

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初植密度Planting density	胸高断面积Basal area (BA)/(m²·hm^-²)		林分密度Number (N)/(trees·hm^-²)		优势木平均高Dominant height (H_d)/(m)		大于对象木的断面积和Sum of basal areas of trees larger than the subject tree (BAL)/(m²·hm^-²)		胸径Diameter at breast height (DBH)/(cm)
初植密度Planting density	均值Mean	标准差SD	均值Mean	标准差SD	均值Mean	标准差SD	均值Mean	标准差SD	均值Mean	标准差SD
A	31.57	19.66	1 630	107.22	13.71	6.44	19.13	16.81	14.38	6.67
B	37.01	21.27	3 190	325.67	12.52	5.79	22.96	18.70	11.27	5.22
C	38.75	22.24	4 635	685.83	12.35	5.96	24.86	19.70	9.64	4.87
D	41.19	21.15	6 084	966.38	11.52	5.85	27.01	21.86	8.95	4.75
E	39.50	20.35	8 739	2 073.10	10.65	5.11	25.96	18.65	7.53	4.12

气候变量Climate variable	含义Description	最小值Min	最大值Max	平均值Mean	标准差SD
MAT/℃	年均气温Mean annual temperature	18.10	19.80	18.96	0.45
MWMT/℃	最热月平均温度Mean warmest month temperature	26.50	30.30	28.26	0.94
MCMT/℃	最冷月平均温度Mean coldest month temperature	5.20	10.20	8.34	1.17
AP/mm	年均降雨量Mean annual precipitation	1 390.00	2 416.00	1 795.79	271.39
AHM	年均干旱指数Annual heat-moisture index	11.90	21.40	16.45	2.35
DD0/d	低于0℃天数Degree-days below 0 ℃	1.00	3.00	1.48	0.63
SMMT/℃	夏季平均最高温度Summer mean maximum temperature	30.30	33.80	32.10	0.81
WMMT/℃	冬季平均最低温度Winter mean minimum temperature	2.50	6.60	4.95	0.96
SMT/℃	春季平均气温Spring mean temperature	16.90	19.60	18.53	0.75

初植密度Planting density	R²		MAD
初植密度Planting density	BMA	SR	BMA	SR
A	0.793 4	0.793 7	0.227 4	0.226 6
B	0.732 4	0.733 1	0.204 3	0.203 2
C	0.714 3	0.714 5	0.194 5	0.193 9
D	0.676 7	0.688 5	0.191 2	0.190 8
E	0.340 0	0.340 1	0.235 0	0.235 5
全样本数据All data	0.612 1	0.611 8	0.220 4	0.220 4

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