Shrub models in a spruce-fir forest of different densities in Jingouling Plantation, Jilin Province

JI Lei; KANG Xingang; ZHANG Qing; GUO Weiwei; ZHOU Mengli

doi:10.11833/j.issn.2095-0756.2016.03.004

Volume 33 Issue 3

Oct. 2016

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JI Lei, KANG Xingang, ZHANG Qing, GUO Weiwei, ZHOU Mengli. Shrub models in a spruce-fir forest of different densities in Jingouling Plantation, Jilin Province[J]. Journal of Zhejiang A&F University, 2016, 33(3): 394-402. doi: 10.11833/j.issn.2095-0756.2016.03.004

Citation:

JI Lei, KANG Xingang, ZHANG Qing, GUO Weiwei, ZHOU Mengli. Shrub models in a spruce-fir forest of different densities in Jingouling Plantation, Jilin Province[J]. Journal of Zhejiang A&F University, 2016, 33(3): 394-402. doi: 10.11833/j.issn.2095-0756.2016.03.004

Shrub models in a spruce-fir forest of different densities in Jingouling Plantation, Jilin Province

doi: 10.11833/j.issn.2095-0756.2016.03.004

1.
College of Forestry, Beijing Forestry University, Beijing 100083, China
2.
School of Science, Beijing Forestry University, Beijing 100083, China

Received Date: 2015-06-01
Rev Recd Date: 2015-11-02
Publish Date: 2016-06-01

Abstract

In order to study the shrub biomass in the forest in Jingouling Plantation and there wasn’t a comprehensive shrub models study in this area. Three different forest densities (0.6, 0.8, 1.0) of a natural spruce-fir Picea koraiensis-Picea jezoensis-Abies nephrolepis forest in Jingouling Plantation, Jilin Province were used for this research. Based on measured data for shrub biomass under the forest canopy, 13 mixed biomass models for 13 different species and biomass models of the different shrubs’ organs were respectively constructed by R software. Then the optimal model was selected using the largest R² and F and the smallest E_SEE and E. Also differences in shrub biomass for forests of different densities and for different species distribution with the same forest density were studied. Shrub quadrat 5 m × 5 m were setted in the center and four corner at each sample plot (20 m × 20 m), then measured the diameter D, crown width C₁, C₂, and height H. According to the results of the shrub species, 13 species, were selected from the sample plots. Results showed that the optimal biomass model (R²=0.626 2-0.997 9)for different organs in each species as well as for leaves and roots of Acer tegmentosum, and the trunk of Acer ukurunduense was a power function; whereas the optimal model of the other species was a quadratic equation or binary linear equation. The independent variable of the model for stem and branch biomass was AC(AC=πC1C2/4) with the other species being D²H and CH(crown width multiply height). The independent variables in the optimal model of leaf biomass for species Spiraea pubescens, Acanthopanax senticosus and A. tegmentosum used factors of AC and CH, but other species used variables D and D²H. The optimal model for root biomass was D²H. The accuracy of the models are relatively high, and they meets the requirements of biomass model estimation, which provides the basis for the measurement of shrub biomass in this region. The research is only suitable for this area and the shrubs’ ground diameter must in a certain range, for other areas to be further studied[Ch, 2 fig. 4 tab. 27 ref.]
- forest ecology,
- shrub,
- biomass models,
- Picea forest,
- Abies forest,
- mixed forest

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灌木层是森林生态系统的重要组成部分，它参与森林生态系统物质循环和能量转化^[1]。林下微环境是不断变化的，它对森林生态系统的稳定发展、演替进程及物种多样性起着重要作用^[2]。中国灌木林面积约为2.97×10⁷ hm2^[3]，与乔木层相比，林下植被生物量仅占总森林生物量的10%~30%，处于次要地位^[4]。虽然灌木生物量占整个森林生物量比例较小，但由于灌木层在维持森林群落稳定性、物种多样性及水土保持效益上的重要作用，其生物量的估算与研究对森林生态群落物质的循环与固定、积聚与消耗以及能量转换具有相当重要的意义^[5-9]。探讨森林群落生物量的方法主要有样地全收获、直接收获和拟合植物生物量与其形态参数的生物量模型来推算^[10]。直接收获法浪费人力物力，且对林下微环境也存在很大的不确定性，样株数又很难符合统计学大样本的要求^[11]。通过拟合生物量最优模型的方法来估算林下灌木的生物量不仅能够降低对林下植被的破坏，而且还可长期追踪样地林下灌木生物量的变化^[12-13]。特别是大范围森林生物量调查，利用生物量模型能大大减少调查工作量^[14-15]。且拟合适用于大范围的通用性立木生物量模型，是开展全国森林碳储量监测必不可少的基础工作^[16]。目前，生物量模型主要分为线性、非线性以及多项式^[17]。国内外学者对吉林省金沟岭林区林下植被生物量研究集中在地上地下生物量的研究中^[18-19]，很少考虑物种间和各物种不同器官生物量最优模型的差异及建立单一物种混合最优模型，样本量及物种个数范围较小^{[13, 20-21]}。本研究利用野外调查的大量实测数据，涵盖了该区出现频率较高的所有灌木，且运用灵活性更高的R软件^[22]拟合该区出现频率较高的13个物种生物量模型，并估算了不同密度冷杉Abies nephrolepis，鱼鳞云杉Picea jezoensis和红皮云杉Picea koraiensis林(以下称云冷杉林)灌木层的生物量，为研究金沟岭不同林型不同密度林分与灌木层生物量的关系提供基础依据。

1. 材料和方法

1.1. 研究区概况

研究区位于吉林省汪清县金沟岭林场(130°10′E，43°22′N)，经营森林面积为16 286 hm2。该区属低山丘陵地貌，海拔为300～1 200 m，坡度5°~25°。全年平均气温约为3.9 ℃，7月气温最高，在22.0 ℃左右；年降水量为600~700 mm，多集中于7月。研究区主要的乔木有冷杉，鱼鳞云杉，红皮云杉，红松Pinus koraiensis，白桦Betula platyphylla，枫桦Betula costata等。主要林下灌木有毛榛Corylus mandshurica，暴马丁香Syringa amurensis，忍冬Lonicera japonica，溲疏Deutzia scabra等。主要地被植物为少数灌木和禾本科Poaceae草类，如珍珠梅Sorbaria sorblia，柳叶绣线菊Spiraea salicifolia等。

1.2. 数据的收集

以云冷杉林为研究对象，设置3种郁闭度(0.6，0.8，1.0) 20 m × 20 m的样地，灌木样方5 m × 5 m设置在每个样地的中心及4个拐角，测量每株灌木的地径(D，mm)或胸径、冠幅(C，m )和株高(H，m)。根据灌木调查结果，在样地附近选择分布较广的13个物种，取15株·种^-1左右。样株要能代表研究灌木的地径范围，取样之前测地径D，株高H，冠幅C₁和C₂，再将整株全挖出，地上分为树干、树枝、树叶分别称出鲜质量，将根系土全部清除后再称量，将称量的各器官装入信封带回实验室，在85 ℃烘箱内烘干得到各器官干质量和含水率。取样灌木的基本参数见表 1。

物种	样本数/个	地径/mm		株高/m		冠幅/m		灌木类型
物种	样本数/个	平均值	标准差	平均值	标准差	平均值	标准差	灌木类型
土庄绣线菊	14	4.786	2.292	1.003	0.542	0.384	0.206	典型灌木
刺五力口 Acanthopanax senticosus	12	12.131	2.113	1.482	0.387	0.597	0.204	典型灌木
溲疏！	18	6.941	2.894	0.932	0.312	0.432	0.256	典型灌木
野蓄薇％osa :u;ti/Zora	8	5.601	1.557	0.721	0.231	0.379	0.157	典型灌木
山梅花 Philadelphus incanus	11	11.305	2.757	1.830	0.511	0.865	0.318	乔木型灌木
茶薦子％i+es mandshuricum	10	5.518	1.612	1.154	0.518	0.551	0.333	典型灌木
珍珠梅 Sorbaria sorbifolia.	14	12.731	6.017	1.393	0.524	0.388	0.207	典型灌木
青措械—，er te>mentosum	17	10.473	7.372	1.398	1.234	0.555	0.486	乔木型灌木
花措械—，er u?urunduense	11	8.583	7.325	1.204	0.875	0.492	0.713	乔木型灌木
暴马了香 Syninga reticulata var. mandsshuca	14	11.456	6.478	1.387	0.753	0.909	0.851	乔木型灌木
忍冬 Lonicerajaponica	14	11.721	4.713	1.679	0.644	0.945	0.363	乔木型灌木
毛棒子 Corylus mandshurica	17	11.798	8.212	1.613	1.188	0.799	0.675	乔木型灌木
惚木 Aralia chinensis	14	15.454	6.763	1.259	0.533	0.943	0.349	乔木型灌木

Table 1. General parameters of sampling shrubs

1.3. 数据分析

本次生物量模型的建立，选用了单因子地径D和复合因子冠幅乘株高CH，植冠面积A_C(A_C=πC₁C₂/4)及D²H为自变量，通过阅读相关文献^{[13, 15, 24-28]}，建立灌木生物量模型。不同物种生长规律不同，植物形态也会有所不同。因灌木各测树因子间存在着很强的关联性，所以希望得到灌木的生长变化和某种函数趋势接近，且选取方程和自变量时要考虑植物的形态。所以选用了指数、幂函数、二元一次和一元二次函数。选用二元一次函数的生物学意义是影响灌木生长的因素可能不止一个。在R软件中采用非线性最小二乘法拟合了灌木不同器官(干、枝、叶、根)的生物量模型和单一物种生物量混合模型。模型均进行t检验(P＜0.05)，分别使用判定系数R²，剩余标准差E_SEE，平均相对误差E以及F检验值作为评价模型优劣的指标。选出R²和F最大，E_SEE和E值最小的方程作为最优方程。将选出的模型应用于不同密度的云冷杉林，计算出灌木层的生物量，而其他没有建立生物量模型的灌木采用何列艳等^[16]建立的乔木型和典型灌木混合模型计算出生物量。4种函数形式如下^[14-27]：W＝ax^b，W＝ae^bx，W＝a＋bx＋cx²，W＝a＋bx¹＋cx₂。a，b，c为各模型参数，x为建模因子。利用Excel 2013和R软件^[22]对数据进行统计分析。

3. 结论与讨论

本研究拟合了金沟岭林场灌木层出现频率较高的13个植物的单一物种生物量混合模型和各物种不同器官生物量最优模型，并估算了3种不同密度云冷杉林下灌木层的总生物量。结果表明：每个模型均具有较高的判定系数R²值、F值和比较小的剩余标准差(E_SEE)值、平均相对误差E值，R²为0.626 2(溲疏根)～0.997 9(花楷槭干)，除了青楷槭的根外，其他物种不同器官模型的E_SEE值均小于各自单一物种混合模型的E_SEE值；各物种混合模型除了溲疏和土庄绣线菊以外，其他物种的生物量混合模型R²都达到了0.920 0以上；单一物种混合模型的 E_SEE和平均相对误差E值均较小。通过对模型的检验，模型的平均相对误差和平均拟合率也较好，综合各项指标，本次拟合的65个模型精度均较高，满足估算要求，为今后测量森林生物量提供了可靠的方法依据。不同器官生物量最优模型除青楷槭的叶根，花楷槭干为幂函数，其他不同器官最优模型多为一元二次或二元一次函数。干、枝最优模型的自变量多为D²H和CH；叶最优模型的自变量，绣线菊、刺五加和青楷槭多采用A_C和CH，其他物种多采用D和D²H；根系多采用的因子为D²H。单一物种混合模型除了土庄绣线菊为指数函数，其他的多为一元二次或者二元一次函数。将拟合的模型应用于3种密度的云冷杉林，分别得到郁闭度为0.6，0.8，1.0的林分林下灌木生物量为836.230 0，692.527 5，823.535 2 kg·hm-2。天然云冷杉林林下灌木生物量(W)随着林分郁闭度减小出现先减小后增大的趋势，即W(0.6)＞W(1.0)＞W(0.8)。郁闭度为0.8时，灌木生物量最小，是因为此密度下有较多的冷杉更新苗，导致此时灌木的生物量较小。郁闭度为0.6的林分，暴马丁香的贡献率最大，达47.94%；郁闭度为0.8和1.0时，贡献率最大的为忍冬，分别达40.53%和53.96%。在主林层密度较大时，忍冬对灌木层生物量的贡献要大于其他物种。

金沟岭林场林下灌木种类丰富，很多物种属于大灌木或者小型乔木，若采用直接收获的方法，很难估算出像青楷槭等乔木型灌木的生物量，构建这些灌木的生物量模型，不仅节省了人力物力，还有效地保护了林下微环境。本研究拟合的13个物种灌木生物量模型，涵盖了金沟岭林场出现频率较高的绝大多数物种。本研究所拟合的生物量模型仅适用于长白山区金沟岭林场林下灌木，若在研究区以外运用该模型需要通过验证，且模型中自变量超过该研究范围时也需经过验证，特别是地径较大的茶藨子。同时，各器官生物量分量总和与单一物种总生物量之间存在一定的偏差，即各器官生物量模型与总生物量模型的相容性有待进一步研究。

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物种及地径范围	最佳模型	参数			E	E_SEE	R²	F值	显著性
物种及地径范围	最佳模型	a	b	c	E	E_SEE	R²	F值	显著性
土庄绣线菊0.21>0.98cm	W_干=ae^b(AC)	0.018 1	2.031 2		1.8500E-05	0.003 7	0.8517	58.263 1	0.000 0
	W_枝=a+b(A_C)+c(A_C)²	0.018 4	0.000 2	0.116 1	-5.84E-10	0.002 0	0.9452	134.7740	0.000 0
	W_叶=a+b(A_C)+c(CH)	0.018 1	0.024 2	-0.003 1	-9.66E-10	0.000 7	0.8989	87.819 1	0.000 0
	W_根=a+b(D)+c(A_C)	0.015 3	0.000 9	0.026 9	-1.09E-10	0.003 6	0.7458	29.893 4	0.000 0
	W_总=ae^b(A_c)	0.071 1	1.609 9		0.0000424	0.008 7	0.8882	80.560 4	0.000 0
刺五加0.28~1.58cm	W_干=a+b(A_C)+c(D²H)	0.015 7	0.026 5	0.000 1	-7.4800E-17	0.004 6	0.9626	403.133 7	0.000 0
	W_枝=a+b(A_C)+c(CH)	0.011 7	-0.063 1	0.045 9	6.9700E-10	0.005 8	0.8302	84.057 4	0.000 0
	W_叶=a+b(A_C)+c(CH)	0.013 9	-0.068 5	0.046 5	7.9900E-10	0.006 5	0.7765	67.985 2	0.000 0
	W_根=a+b(cH)+c(CH)²	0.045 4	-0.036 6	0.036 3	2.8300E-09	0.007 5	0.8860	116.2644	0.000 0
	W_总=a+b(A_C)+c(CH)	0.059 4	-0.135 8	0.173 0	2.2400E-09	0.018 8	0.9242	221.681 6	0.000 0
溲疏0.22~1.35cm	W_干=a+b(D²H)+c(D²H)²	-0.000 7	0.000 2	-1.760 0E-07	4.4100E-11	0.002 2	0.9727	482.007 7	0.000 0
	W_枝=a+b(D²H)+c(D²H)²	-0.0022	0.000 3	-4.600 0E-07	-7.4100E-11	0.007 0	0.7257	35.492 0	0.000 0
	W_叶=a+b(D)+c(D²H)	0.001 8	-0.0004	7.7300E-05	8.6000E-12	0.001 4	0.9025	109.219 0	0.000 0
	W_根=a+b(D²H)+c(D²H)²	-0.003 2	0.000 5	-1.260 0E-06	1.7900E-11	0.011 2	0.6262	20.650 5	0.001 0
	W_总=a+b(D²H)+c(D²H)²	-0.006	0.001 0	-1.8500E-06	9.7300E-12	0.018 6	0.8374	70.028 2	0.000 0
青楷槭2.98~23.31cm	W_干=a+b(A_c)+c(CH)	-0.002 4	-0.051 9	0.0523	-5.6000E-09	0.008 2	0.9827	728.609 3	0.000 0
	W_枝=a+b(D)+c(D)²	0.005 4	-0.002 3	0.003	-2.56E-11	0.008 8	0.9452	223.781 7	0.000 0
	W_叶=aD^b	2.740 0E-05	2.309 0		9.6600E-05	0.002 7	0.9796	707.487 3	0.000 0
	W_根=aD^b	2.510 0E-14	9.110 5		0.0101	0.023 5	0.9527	154.291 8	0.000 0
	W_总=aD(D²H)+c(D²H)²	0.0021	0.003	-7.67E-08	-1.100 5E-09	0.0140	0.9892	1 242.204 7	0.000 0
花楷槭2.88~28.90 mm	W_干=a(CH)^b	0.0250	1.1229		-0.0007	0.0034	0.9979	4050.3455	0.0000
	W_枝=a+b(A_c)+c(CH)	-0.0010	0.0194	0.0046	-5.2000E-09	0.0032	0.9932	1070.311	0.0000
	W_叶=a+b(D²H)+c(D²H)²	0.0012	2.4600E-05	2.5900E-09	1.3800E-11	0.0032	0.9872	545.4946	0.0000
	W_根=a+b(A_c)+c(CH)	-0.0044	-0.0378	0.0408	1.2000E-11	0.0052	20.9897	723.6879	0.0000
	W_总=a+b(D²H)+c(CH)	0.0060	4.2900E-05	0.0634	-6.5800E-11	0.0108	0.9970	2476.331	0.0000
暴马丁香4.20~23.13 mm	W_干=a+b(D²H)+c(CH)	0.0115	0.0001	0.0103	-1.8202E-12	0.0119	0.9772	282.1242	0.0000
	W_枝=a+b(CH)+c(D²H)	0.0106	0.0001	0.0103	-1.8200E-12	0.0119	0.9577	210.5066	0.0000
	W_叶=a+b(A_c)+c(CH)	0.0134	-0.0087	0.0197	-7.0101E-10	0.0038	0.9772	282.1242	0.0000
	W_根=a+b(D²H)+c(CH)	0.0265	0.0001	0.0087	2.3200E-11	0.0192	0.8654	63.0999	0.0000
	W_总=a+b(D²H)+c(CH)	0.0618	0.0003	0.0489	1.4000E-07	0.0397	0.9656	257.5155	0.0000
忍冬3.84~20.75 mm	W_干=a+b(D²H)+c(CH)	-0.0219	-0.0001	0.0869	1.5400E-10	0.0271	0.8881	67.8130	0.0000
	W_枝=a+b(CH)+c(CH)²	-0.0131	0.0630	-0.0058	9.4200E-09	0.0283	0.7431	25.9984	0.0000
	W_叶=a+b(D)+c(A_c)	0.0152	0.0007	0.0125	7.3400E-10	0.0040	0.8830	65.2186
	W_根=a+b(A_c)+c(CH)	-0.0023	-0.0416	0.0608	1.2700E-10	0.0220	0.8608	49.4119	0.0000
	W_总=a+b(D²H)+c(CH)	0.0002	-0.0001	0.1784	9.9900E-08	0.0549	0.9205	101.6929	0.0000
毛榛子2.19~26.58mm	W_干=a+b(A_c)+c(CH)	-0.008	-0.0136	0.0439	4.1300E-09	0.0184	0.9690	285.0368	0.0000
	W_枝=a+b(CH)+c(CH)²	-0.0025	0.0157	-0.0007	2.3500E-10	0.0094	0.8983	97.4586	0.0000
	W_叶=a+b(A_C)+c(D²H)²	-9.6400E-05	1.4600E-14	-6.8800E-08	-7.2600E-11	0.0096	0.9041	101.2987	0.0000
	W_根=a+b(D²H)+c(D²H)²	-9.6400E-05	1.460E-04	-6.8800E-08	-7.2600E-11	0.0096	0.9041	101.2987	0.0000
	W_总=a+b(D²H)+c(CH)	0.0035	6.7500E-05		0.0470	3.0000E-09	0.0235	0.9798	540.8142	0.0000
茶藨子2.82~7.60mm	W_干=ae^b(D)	0.00003	1.0541		-0.0002	0.0088	0.8996	48.3694	0.0000
	W_枝=ae^b(D)	3.000E-6	1.3083		0.00036	0.9645	124.6582	0.0000
	W_叶=ae^b(D)	0.0002	0.4997		-0.0001	0.0008	0.9145	81.3773	0.0000
	W_根=ae^b(D)	0.0007	0.5182		-0.0005	0.0036	0.9206	93.0817	0.0000
	W_总=ae^b(D)	0.0002	0.8198		0.0002	0.0082	0.9812	309.8734	0.0000
楤木6.10~27.33	W_干=a(D²H)^b	0.0002	1.0251		-1.3100E-03	0.0275	0.9506	202.9919	0.0000
	W_枝=ae^b(D)	0.0014	0.1567		-1.7500E-05	0.0123	0.8760	70.6008	0.0000
	W_叶=a+b(D)+c(A_c)	-0.0037	0.0008	0.0205	-1.000E-7	-1.1600E-10	0.0181	0.8430	57.4457	0.0000
	W_根=a+b(D²H)+c(D²H)²	0.0013	0.0002	-1.0000E-7	-1.1600E-10	0.0181	0.8430	57.4457	0.0000
	W_总=a(D²H)^b	0.0002	1.1742		6.4400E-04	0.0280	0.9419	128.7706	0.0000
山梅花5.72~15.70mm	W_干=a+b(A_c)+c(D²H)	-0.0111	0.0102	0.0002	-3.0100E-11	0.0070	0.9771	302.6944	0.0000
	W_枝=a+b(A_c)+c(D²H)	-0.0131	0.0092	0.0002	3.1900E-11	0.0186	0.8169	31.6464	0.0000
	W_叶=a+b(CH)+c(CH)²	0.0082	-0.0100	0.0044	6.2400E-13	0.0023	0.8112	3.8272	0.0000
	W_根=a+b(D²H)+c(CH)	0.0080	0.0002	-0.0125	2.8100E-12	0.0066	0.9553	135.1367
	W_总=a(D²H)^b	0.0002	1.1742		6.4400E-04	0.0280	0.9419	128.7706	0.0000
野蔷薇3.66~8.33mm	W_干=a+b(D²H)+c(D²H)²	-0.0011	0.0003	-6.0000E-7	3.9800E-12	0.0007	0.9925	611.4494	0.0000
	W_枝=a+b(D)+c(D)²	-0.0168	0.0059	-0.0004	-4.7000E-14	60.7921	17.2780	0.0000
	W_叶=a+b(A_C)+c(CH)	-0.0023	0.0078	0.0252	-2.6900E-10	0.0013	0.9755	177.1763	0.0000
	W_根=a+b(D)+c(A_c)	-0.0128	0.0041	0.1099	2.6100E-09	0.0058	0.9349	67.8752	0.0000
	W_总=a+b(D)+c(A_c)	-0.0386	0.0108	0.1533	2.3000E-09	0.0054	0.9823	2.688038	0.0000
珍珠梅4.21~24.53mm	W_干=a+b(D²H)+c(D²H)²	-0.0109	0.0004	0.0000	1.0700E-09	0.0199	0.9430	164.9001	0.0000
	W_枝=a+b(D)+c(A_c)	-0.0193	0.0022	0.0720	8.5500E-09	0.0093	0.8962	88.9694	0.0000
	W_叶=a+b(A_c)+c(D²H)	-0.0008	0.0442	0.00003	2.4400E-10	0.0059	0.9466	172.1479	0.0000
	W_根=a+b(D)+c(CH)	-0.0288	0.0057	-0.0168	-1.0600E-09	0.0164	0.7612	34.1580	0.0000
	W_总=a+b(D²H)+c(D²H)²	-0.0055	0.0006	-2.0000E-7	4.6500E-11	0.0262	0.9735	389.0325	0.0000

灌木名称	平均相对误差/%	平均拟合率/4
暴马丁香(6)	10.29	90.56
刺五加(7)	11.61	90.43
忍冬(8)	18.28	84.97
绣线菊(>)	11.85	89.32
茶薦子(5)	5.32	95.66
山梅花(6)	4.37	95.64
珍珠梅(7)	14.43	87.53
毛榛(9)	11.43	90.75
青揩槭（10)	14.74	86.51
花楷槭(8)	12.22	89.56
溲疏(6)	18.29	82.77
惚木(7)	1.82	98.19
野蔷薇(6)	6.38	94.47

说明：括号里数据为检验样本个数。

灌木名称	生物量/kg
灌木名称	暴马丁香	16.036 6	4.412 9	0.485 3
刺五加	2.4149	2.679 3	3.697 7
花楷槭	3.322 3	0.186 2	0.000 0
青楷槭	5.741 6	0.577 5	2.955 1
忍冬	0.172 4	11.227 2	18.153 7
毛榛子	0.969 4	0.809 1	0.256 1
溲疏	0.000 0	0.152 1	1.852 3
绣线菊	0.000 0	5.308 8	5.265 6
其他	4.792 1	2.348 1	0.475 5
合计	33.449 2	27.701 1	33.141 3
说明：郁闭度 0.6 生物量为 836.230 0 kg.hm ^-2,郁闭度 0.8 为 692.527 5 kg.hm^-2,郁闭度 1.0 为 828.535 2 kg.hm^-2。
郁闭度0.6	郁闭度0.8	郁闭度1.0

Shrub models in a spruce-fir forest of different densities in Jingouling Plantation, Jilin Province

doi: 10.11833/j.issn.2095-0756.2016.03.004