Research on Growth Mixed Effect Model for Basal Area of Cunninghamia lanceolata Plantation Based on Site Factors

doi:10.13466/j.cnki.lyzygl.2021.02.011

Abstract

Abstract:

Based on data of 150 Cunninghamia lanceolata Plantation plots in Central China's Hunan Province,this study attempt to construct a mixed effect model of Cunninghamia lanceolata Plantation growth with site factors through using methods such as variance analysis,regression analysis,nonlinear mixed effects model and K-means clustering.The results show that:(1)Altitude (HB),slope (PD),slope position (PW),soil thickness (TH) and soil type (TL)have a significant impact on the growth of the basal area,and the order of significance is TL>TH>PD> PW>HB.(2)Among the eight commonly used theoretical growth equations,Schumacher (M5)has the highest coefficient of determination (R²=0.7636),and was selected as the basic model for forest basal area growth simulation.(3)A nonlinear mixed effects model was constructed by taking 107 site types (ST)of different site factor combinations as random effects and the coefficient of determination (R²)increased to 0.895 1.(4)The 107 site types (ST)were clustered into 5 site type groups (STG),and the mixed effect model of Cunninghamia lanceolata cross-sectional basal area growth was further constructed,and the determination coefficient (R²)increased to 0.920 2.Studies have shown that the nonlinear mixed effect model based on site factors objectively explains the impact of site factors on the growth of Cunninghamia lanceolata Plantation,which helps improve the simulation accuracy of the stand growth model.

Key words: Cunninghamia lanceolata, basal area, site typ, mixed effect model, cluster analysis

CLC Number:

S791.27
S711

WU Xuping, LV Yong, ZHANG Xiongqing, YI Xuan, ZHU Guangyu. Research on Growth Mixed Effect Model for Basal Area of Cunninghamia lanceolata Plantation Based on Site Factors[J]. FOREST RESOURCES WANAGEMENT, 2021, 0(2): 75-82.

Figures/Tables 11

Tab.1

Tab.2

Tab.3

Basic models candidates

序号	模型名称	表达式
M1	理查德(Richards)	G=a×(1-e^(-^b^×^T⁾)×(SDI/1000)^c
M2	理查德(Richards)	G=a×(1-e^(-^b^×^T⁾)×(N/1000)^c
M3	舒马克(Schumacher)	G=a×e^(-^b^×^T⁾)×(SDI/1000)^c
M4	舒马克(Schumacher)	G=a×e^(-^b^×^T⁾)×(N/1000)^c
M5	舒马克(Schumacher)	G=HT⁽^a⁺^b/T⁾×(SDI/1000)⁽^c⁺^d/T⁾×e⁽^q⁺^w/T⁾
M6	舒马克(Schumacher)	G=HT⁽^a⁺^b/T⁾×(N/1000)⁽^c⁺^d/T⁾×e⁽^q⁺^w/T⁾
M7	舒马克(Schumacher)	G=e⁽^a⁺^b/T⁾×(SDI/1000)^c+d/T
M8	单分子(Mitscherlish)	G=a×(1- $e (- b × (SDI / 1000) c)$ ×T)

Tab.3

Tab.4

Tab.5

Tab.6

Tab.7

Tab.8

Tab.9

Fig.1

Fig.2

References 20

[1]	胡松. 湖南栎类天然林断面积生长模型研究[D]. 长沙: 中南林业科技大学, 2019.
[2]	张雄清, 雷渊才, 陈新美, 等. 组合预测法在林分断面积生长预估中的应用[J]. 北京林业大学学报, 2010,32(4):6-11.
[3]	李春明, 唐守正. 基于非线性混合模型的落叶松云冷杉林分断面积模型[J]. 林业科学, 2010,46(7):106-113.
[4]	李永慈, 唐守正. 度量误差对全林整体模型的影响研究[J]. 林业科学, 2005(6):169-172.
[5]	符利勇, 唐守正, 张会儒, 等. 基于多水平非线性混合效应蒙古栎林单木断面积模型[J]. 林业科学研究, 2015,28(1):23-31.
[6]	许冰冰, 边更战, 易烜, 等. 湖南杉木人工林单木干形特征及影响因子研究[J]. 林业资源管理, 2020(5):82-88.
[7]	龚召松, 曾思齐, 贺东北, 等. 湖南楠木次生林断面积生长模型研究[J]. 林业资源管理, 2020(2):87-93.
[8]	孟宪宇. 测树学[M].3版. 北京: 中国林业出版社, 2006: 43-66.
[9]	李春喜. 生物统计学[M].5版. 北京: 科学出版社, 2013: 95-104.
[10]	吴恒, 党坤良, 田相林. 秦岭林区天然次生林与人工林立地质量评价[J]. 林业科学, 2015,51(4):78-88.
[11]	Saud Pradip, Lynch Thomas B, Cram Douglas S, et al. An Annual basal area growth model with multiplicative climate modifier fitted to longitudinal data for shortleaf pine[J]. Forestry:An International Journal of Forest Research, 2019(5):5.
[12]	朱光玉, 胡松, 符利勇. 基于哑变量的湖南栎类天然林林分断面积生长模型[J]. 南京林业大学学报:自然科学版, 2018,42(2):155-162.
[13]	Pinherio J C, Bates D M. Mixed-Effects Models in S and S-PLUS[M]. New York: Spring-Verlag, 2000.
[14]	Chafa D, Concordet D. A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models[J]. Statistics & Computing, 2009,19(2):129-138.
[15]	冉啟香, 邓华锋, 吕常笑, 等. 油松林分断面积与蓄积量生长模型研究[J]. 西北林学院学报, 2016,31(5):217-223.
[16]	李杨, 亢新刚. 长白山云冷杉针阔混交林林木空间利用率混合模型[J]. 北京林业大学学报, 2020,42(5):71-79.
[17]	李希菲, 唐守正, 王松林. 大岗山实验局杉木人工林可变密度收获表的编制[J]. 林业科学研究, 1988(4):382-389.
[18]	Sharma M, Parton J. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach[J]. Forest Ecology and Management, 2007,249(3):187-198. doi: 10.1016/j.foreco.2007.05.006
[19]	Pandhard X, Samson A. Extension of the SAEM algorithm for non-linear mixed models with 2 levels of random effects[J]. Biostatis-tics, 2009,10(1):121-135.
[20]	刘飞虎. 基于林层效应的湖南栎类次生林断面积生长模型研究[D]. 长沙: 中南林业科技大学, 2020.

因子	断面积(G)/(m²/hm²)	年龄(Age)/a	密度指数(SDI)	单位面积株数(N)/株/hm²)	海拔(HB)/m
平均值	26.78	18	2079	2580	469
标准差	8.95	3	974	1000	268
最小值	9.63	11	969	780	49
最大值	52.91	27	5536	5175	1250

立地因子	符号	等级划分
海拔	HB	100m为一级
坡度	PD	缓坡	斜坡	陡坡	急坡	险坡
坡位	PW	上坡	中坡	下坡
坡向	PX	阳坡	阴坡
土壤类型	TL	红壤	黄壤	山地黄壤
土壤厚度	TH	薄	中	厚

因子组	平方和	自由度	均方	F值	Pr>F	备注
HB	1182.38	11	107.49	2.12	0.02300	显著
PD	966.22	4	241.55	4.77	0.00128	显著
PW	461.26	2	230.63	4.56	0.01228	显著
PX	11.75	1	11.74	0.23	0.63084	不显著
TH	730.34	2	365.17	7.21	0.00108	显著
TL	1196.30	2	598.15	11.82	0.00002	显著

模型	a	b	c	d	q	w	R²	P/%	MAE	RMSE
M1	12.455	473.41	0.8146	—	—	—	0.6376	97	3.61	4.85
M2	20.551	472.66	0.3863	—	—	—	0.2187	95	6.16	8.01
M3	19.143	9.3464	0.8945	—	—	—	0.7118	97	3.63	4.86
M4	33.455	9.9705	0.4674	—	—	—	0.2982	95	5.76	7.59
M5	1.4039	-17.978	0.8222	0.8792	-0.3722	33.868	0.7636	97	3.08	4.40
M6	1.7490	-20.861	0.0382	8.3653	-0.3535	34.106	0.4226	95	5.12	6.88
M7	2.9448	-9.9929	0.9145	10.881	—	—	0.7119	97	3.62	4.86
M8	61.762	0.0088	1.3313	—	—	—	0.7014	97	3.84	4.95

随机效应	添加位置	a	b	c	d	q	w	AIC	BIC	R²
ST	a	1.205	-13.66	0.731	2.906	0.175	22.03	877.41	901.49	0.8857
ST	b	1.254	-14.49	0.772	2.324	0.035	24.29	877.91	901.99	0.8794
ST	c	1.212	-13.81	0.762	2.566	0.119	22.90	872.41	896.50	0.8951
ST	d	1.286	-15.12	0.818	1.686	-0.091	26.51	873.88	897.97	0.8871
ST	q	1.256	-14.68	0.749	2.594	0.044	24.62	879.17	903.26	0.8785
ST	w	1.306	-15.57	0.786	2.037	-0.099	27.07	879.65	903.74	0.8713