A Study on the Growth Model of Individual Trees in Natural Mixed Forests of Oak and Pinus Massoniana in Hunan

doi:10.13466/j.cnki.lyzygl.2020.02.015

Abstract

Abstract:

In order to provide scientific guidance for the increment of quality of the mixed Oak and Pinus massoniana natural forest,establishing the growth model of individual volume and basal area.Twenty-three mixed Oak and Pinus massoniana natural forests in nine areas of Hunan province were selected to construct the growth models of individual volume and basal area.Through analysis,we can know that Richards model was the best model for volume and basal area growth of the two tree species,the determining coefficients (R ²) were the highest and the sum of squares of residuals (SSE) were the smallest.The result of mixed effect models show that the random effects of the Oak single-wood volume and basal area growth model are best at parameter a₁,while the volume and basal area growth model of Pinus massoniana are best at parameter b₁ and a₁+b₁.Compared with the basic model,the fitting precision (P) and determination coefficients of the mixed effect model are improved.Mean error (ME),mean absolute error (MAE),mean percent error (RME) and mean absolute percent error (RMAE) are all slumped substantially.The results show that wood volume and basal area growth of natural forests are greatly affected by the differences between tree species and site types.Mixed-effect model can take full account of the differences between sites,and solve this problem well.

Key words: mixed Oak and Pinus massoniana forest, growth model, basal area, stem volume, mixed effect

CLC Number:

S758

ENG Qilong, CHEN Zhefu, CHEN Duanlv. A Study on the Growth Model of Individual Trees in Natural Mixed Forests of Oak and Pinus Massoniana in Hunan[J]. FOREST RESOURCES WANAGEMENT, 2020, (2): 94-102.

Figures/Tables 12

Tab.1

Tab.2

Tab.3

The expression of base model and mixed-effects model

序号	模型	基础模型	混合效应模型
1	对数 Logarithm	$V (G) = a · ln (A) + b$	$V (G) = (a + a 1) · ln (A) + (b + b 1)$
2	指数Exponentin	$V (G) = a · A b$	$V (G) = (a + a 1) · A (b + b 1)$
3	二次函数Quadratic function	$V (G) = a · A 2 + b · A + c$	$V (G) = (a + a 1) · A 2 + (b + b 1) · A + (c + c 1)$
4	舒马赫Schunacher	$V (G) = a · e - b A$	$V (G) = (a + a 1) · e - (b + b 1) A$
5	理查德Richards	$V (G) = a · (1 - e - b · A) c$	$V (G) = (a + a 1) · (1 - e - (b + b 1) · A) (c + c 1)$
6	坎派兹Compertz	$V (G) = a · e - b · e - c · A$	$V (G) = (a + a 1) · e - (b + b 1) · e - (c + c 1) · A$
7	修正威布尔 Weibull modified	$V (G) = a · (1 - e - b · A c)$	$V (G) = (a + a 1) · (1 - e - (b + b 1) · A (c + c 1))$
8	逻辑斯蒂Logistic	$V (G) = a 1 + b · e - c · A$	$V (G) = a + a 1 1 + (b + b 1) · e - (c + c 1) · A$

Tab.3

Tab.4

Tab.5

Tab.6

Tab.7

Tab.8

Tab.9

Tab.10

Fig.1

Fig.2

References 26

[1]	唐守正, 杜纪山. 利用树冠竞争因子确定同龄间伐林分的断面积生长过程[J]. 林业科学, 1999(6):35-41.
[2]	Pretzsch H, Forrester D, Rötzer T. Representation of species mixing in forest growth models:A review and perspective[J]. Ecological Modelling, 2015,313:276-292. doi: 10.1016/j.ecolmodel.2015.06.044
[3]	Buongiorno J, Peyron J, Houllier F, et al. Growth and management of mixed-species,uneven-aged forests in the French Jura:Implications for economic returns and tree diversity[J]. Forest Science, 1995,41(3):397-429.
[4]	卢军, 张会儒, 李凤日. 大兴安岭天然林林分生长模型研究[J]. 林业资源管理, 2011(3):33-36.
[5]	赵芸, 王新杰, 江涛, 等. 基于度量误差方法的杉木储备林间伐与未间伐林分生长模型研究[J]. 西北林学院学报, 2019,34(4):185-191.
[6]	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.
[7]	徐健君. 非参数核密度估计在岷江冷杉天然林直径分布研究中的应用[J]. 甘肃林业科技, 1999(4):23-25.
[8]	吴承祯, 洪伟. 林分直径结构新模型研究[J]. 西南林学院学报, 1999(2):90-95.
[9]	Hokka H, Groot A. An individual-tree basal area growth model for black spruce in second-growth peatland stands[J]. Canadian Journal of Forest Research, 1999,5:621-629.
[10]	江希钿, 林文清, 陈兆算, 等. 柳杉人工林单木材积生长模型的研究[J]. 福建林学院学报, 1995(4):380-385.
[11]	孟宪宇, 张弘. 闽北杉木人工林单木模型[J]. 北京林业大学学报, 1996(2):1-8.
[12]	Newham R M. Development and testing of stand model for Douglas-fir[J]. Forest Chron, 1964,40:492-502.
[13]	王少杰, 邓华锋, 吕常笑, 等. 基于单木水平和林分水平的油松兼容性生长模型[J]. 西北林学院学报, 2016,31(6):243-249.
[14]	Schumacher F X. New growth curve and its application to timber-yield studies[J]. Journal of Forestry, 1939,37:819-820.
[15]	卢军. 长白山地区天然混交林单木生长模型的研究[D]. 哈尔滨:东北林业大学, 2005.
[16]	Bailey R L, Dell T R. Quantiying diameter distribution with the Weibull function[J]. Forest Science, 1973,19(2):97-104.
[17]	惠淑荣, 吕永震. Weibull分布函数在林分直径结构预测模型中的应用研究[J]. 北华大学学报:自然科学版, 2003(2):101-104.
[18]	任瑞娟, 亢新刚, 杨华. 天然林单木生长模型研究进展[J]. 西北林学院学报, 2008(6):203-206.
[19]	Cao V. Prediction of annual diameter growth and survival for individual trees from periodic measurements[J]. Forest Science, 2000,46(1):127-131.
[20]	Mabvurira D, Miina J. Individual-tree growth and mortality models for Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe[J]. Forest Ecology & Management, 2002,161(3):231-245.
[21]	林丽平, 徐期瑚, 罗勇, 等. 广东主要乡土阔叶树种单木生长模型构建[J]. 林业与环境科学, 2018,34(3):14-22.
[22]	Duan Guangshuang, Gao Zhigang, Wang Qiuyan, et al. Comparison of Different Height-Diameter Modelling Techniques for Prediction of Site Productivity in Natural Uneven-Aged Pure Stands[J]. Forest Science 2018,9(2):63-81.
[23]	Saunders M, Wagner R. Height-diameter models with random coefficients and site variables for tree species of Central Maine[J]. Annals of Forest Science, 2008,62(2):203-208.
[24]	李春明. 基于两层次线性混合效应模型的杉木林单木胸径生长量模型[J]. 林业科学, 2012,48(3):66-73. doi: 10.11707/j.1001-7488.20120311
[25]	董云飞. 福建杉木人工林单木生长模型的研究[D]. 北京:北京林业大学, 2015.
[26]	龙时胜, 曾思齐, 甘世书, 等. 基于林木多期直径测定数据的异龄林年龄估计方法[J]. 中南林业科技大学学报, 2018,38(9):1-8.

树种	株数/株	年龄(A)/a			直径(D)/cm			单株材积(V)/m³			单株断面积(G)/m²
树种	株数/株	最大值	最小值	平均值	最大值	最小值	平均值	最大值	最小值	平均值	最大值	最小值	平均值
柏木	6	20	36	31(±8.28)	7.3	15.0	12.6(±3.16)	0.011	0.074	0.051(±0.024)	0.004	0.018	0.013(±0.005)
枫香	15	15	57	29(±12.31)	5.5	16.6	9.7(±5.15)	0.008	0.108	0.037(±0.090)	0.002	0.022	0.008(±0.013)
栎类	1636	15	110	27(±12.04)	5.0	44.9	9.3(±5.11)	0.006	1.295	0.038(±0.085)	0.002	0.158	0.008(±0.013)
柳树	13	16	42	27(±11.69)	5.2	13.4	8.6(±3.73)	0.007	0.063	0.024(±0.039)	0.002	0.014	0.006(±0.007)
马尾松	796	10	95	25(±12.06)	5.1	43.0	12.8(±5.11)	0.005	1.146	0.072(±0.085)	0.002	0.145	0.016(±0.013)
杉木	104	5	67	21(±12.48)	5.0	26.2	10.4(±5.23)	0.005	0.396	0.048(±0.092)	0.002	0.054	0.010(±0.013)
油桐	10	24	43	32(±23.86)	8.7	14.8	11.3(±5.99)	0.022	0.081	0.045(±0.195)	0.006	0.017	0.010(±0.024)
樟树	43	14	50	25(±12.02)	5.0	17.6	9.5(±5.14)	0.006	0.125	0.035(±0.086)	0.002	0.024	0.008(±0.013)

特征项	柏木	枫香	栎类	柳树	马尾松	杉木	油桐	樟树	合计
株数/株	6(0.23)	15(0.57)	1636(62.35)	13(0.50)	796(30.34)	104(3.96)	10(0.38)	43(1.64)	2624(100)
总材积/m³	0.303(0.27)	0.554(0.43)	62.837(48.89)	0.318(0.25)	57.601(44.82)	4.959(3.86)	0.447(0.35)	1.511(1.18)	128.53(100)
总断面积/m²	0.078(0.28)	0.127(0.46)	13.57(48.99)	0.081(0.29)	12.35(44.59)	1.037(3.74)	0.104(0.38)	0.35(1.26)	27.698(100)

树种	林分变量	建模数据
树种	林分变量	样本量			最大值		最小值	平均值		标准差		样本量	最大值			最小值		平均值	标准差
栎类	年龄(A)/a		1088	135		15			26	10.896	548			91	16		27			10.692
	直径(D)/cm		1088	35.4		5.0			9.1	4.111	548			30.2	5.0		9.4			4.155
	材积(V)/m³		1088	0.721		0.006			0.035	0.057	548			0.485	0.006		0.037			0.054
	断面积(G)/m²		1088	0.098		0.002			0.008	0.009	548			0.072	0.002		0.008			0.009
马尾松	年龄(A)/a		528	95		10			25	11.315	268			50	11		23			8.873
	直径(D)/cm		528	43.0		5.1			13.1	5.950	268			27.0	5.1		12.2			5.178
	材积(V)/m³		528	1.146		0.005			0.078	0.116	268			0.347	0.005		0.061			0.068
	断面积(G)/m²		528	0.145		0.002			0.016	0.017	268			0.057	0.002		0.014			0.012

树种	方程序号		参数					指标
树种	方程序号		a		b	c		R²	SSE
栎类	1	0.16866(±0.00372)		-0.50288(±0.01202)			0.557			4.198
	2	0.00007(±0.00000)		1.90001(±0.01248)			0.873			1.199
	3	0.00003(±0.00000)		0.00194(±0.00012)		-0.03960(±0.00247)	0.885			1.090
	4	1.91577(±0.03867)		126.10227(±1.34834)			0.840			1.515
	5	1.20318(±0.10381)		0.01369(±0.00111)		3.09178(±0.12107)	0.887			1.068
	6	1.42190(±0.03881)		6.21277(±0.06351)		0.18458(±0.00396)	0.873			1.205
	7	1.67263(±0.10172)		0.00232(±0.00010)		2.18514(±0.02864)	0.883			1.112
	8	1.05344(±0.01917)		104.31849(±3.69011)		0.47873(±0.00722)	0.836			1.554
马尾松	1	0.18573(±0.00630)		-0.50742(±0.01984)			0.523			4.004
	2	0.00005(±0.00001)		2.20912(±0.03073)			0.804			1.647
	3	0.00013(±0.00000)		-0.00072(±0.00046)		-0.00562(±0.00720)	0.805			1.632
	4	2.62627(±0.11859)		103.20307(±2.00159)			0.768			1.948
	5	7.28237(±3.99675)		0.00715(±0.00252)		2.66767(±0.18742)	0.805			1.631
	6	2.07629(±0.21976)		6.55694(±0.12845)		0.02431(±0.00146)	0.799			1.683
	7	2.12563(±0.36265)		140.98612(±40.10094)		1.11202(±0.09743)	0.759			2.022
	8	1.10377(±0.05014)		107.47063(±7.02958)		0.07316(±0.00230)	0.784			1.814

树种	方程序号		参数						指标
树种	方程序号		a		b		c		R²	SSE
栎类	1	0.02711(±0.00045)		-0.07872(±0.00147)				0.685			0.063
	2	0.00004(±0.00000)		1.59895(±0.01066)				0.860			0.028
	3	0.00002(±0.00000)		0.00060(±0.00002)		-0.00917(±0.00036)		0.879			0.024
	4	1.75671(±0.00322)		88.52108(±0.89458)				0.839			0.032
	5	0.12090(±0.00710)		0.17403(±0.01143)		2.80860(±0.09905)		0.884			0.023
	6	0.14740(±0.00384)		5.34338(±0.05482)		2.17172(±0.04515)		0.865			0.027
	7	0.17380(±0.00076)		0.57425(±0.03849)		1.92531(±0.02449)		0.876			0.025
	8	0.11690(±0.00219)		56.22297(±1.80148)		51.00943(±0.83070)		0.826			0.035
马尾松	1	0.03096(±0.00079)		-0.08112(±0.00250)				0.657			0.064
	2	0.00005(±0.00001)		1.74066(±0.02481)				0.815			0.034
	3	0.00001(±0.00000)		0.00059(±0.00007)		-0.00650(±0.00103)		0.816			0.034
	4	0.20645(±0.00806)		68.32779(±1.43521)				0.779			0.041
	5	0.66325(±0.30482)		0.65953(±0.23592)		2.03500(±0.12000)		0.819			0.034
	6	0.19207(±0.01438)		5.24315(±0.10016)		0.07682(±0.00144)		0.809			0.035
	7	0.64705(±0.20216)		26.59188(±3.52349)		0.66159(±0.06525)		0.805			0.036
	8	0.12868(±0.00518)		48.29720(±2.73098)		0.07029(±0.00213)		0.792			0.038