林业科学 ›› 2019, Vol. 55 ›› Issue (11): 27-36.doi: 10.11707/j.1001-7488.20191104
李春明1,赵丽芳2,李利学3
收稿日期:
2019-04-16
出版日期:
2019-11-25
发布日期:
2019-12-21
基金资助:
Chunming Li1,Lifang Zhao2,Lixue Li3
Received:
2019-04-16
Online:
2019-11-25
Published:
2019-12-21
Supported by:
摘要:
目的: 基于混合效应模型和零膨胀模型方法构建林分水平枯损模型,为选择科学的经营措施提供理论依据。方法: 以吉林省1994年设置的295块蒙古栎固定样地为数据源,236块样地作为模拟数据,59块样地作为验证数据。构建基于林分因子、立地因子和气象因子的蒙古栎林分水平枯损模型,其基本形式包括泊松分布和负二项分布。考虑样地中存在大量零值问题,在基础模型上加入零膨胀和零改变模型。为解决模型的嵌套和纵向数据问题,在构建模型时考虑样地的随机效应,选择验证数据进行精度验证。结果: 样地断面积、株数和最暖月平均气温是枯损概率和数量最重要的影响因子;考虑样地随机效应后,可明显提高模型模拟精度;负二项分布模型因考虑数据过度离散问题,模拟精度高于泊松分布。结论: 同时考虑随机效应和零膨胀的负二项分布模型,其模拟效果最好。
中图分类号:
李春明,赵丽芳,李利学. 基于混合效应模型和零膨胀模型方法的蒙古栎林分水平枯损模型[J]. 林业科学, 2019, 55(11): 27-36.
Chunming Li,Lifang Zhao,Lixue Li. Modeling Stand-Level Mortality of Mongolian Oak(Quercus mongolica)Based on Mixed Effect Model and Zero-Inflated Model Methods[J]. Scientia Silvae Sinicae, 2019, 55(11): 27-36.
表1
蒙古栎样地各因子统计"
枯损影响因子 Effect factor | 指标Indicator | 平均值(标准差) Mean(standard error) | 最大值Max. | 最小值Min. | |
林分因子 Stand factor | 1999 | 胸径DBH/cm | 12.7(7.5) | 82.7 | 5.0 |
林分平均直径Mean diameter/cm | 15.3(4.2) | 30.9 | 6.3 | ||
断面积Basal area/(m2·hm-2) | 22.9(9.4) | 57.7 | 3.0 | ||
株数Number of stems/hm-2 | 1343(621) | 3 317 | 250 | ||
2004 | 胸径DBH/cm | 12.9(7.6) | 83.6 | 5 | |
林分平均直径Mean diameter/cm | 15.7(4.1) | 31.3 | 6.3 | ||
断面积Basal area/(m2·hm-2) | 24.1(8.8) | 59.7 | 3.8 | ||
株数Number of stems/hm-2 | 1 370(618) | 3 250 | 350 | ||
2009 | 胸径DBH/cm | 13.5(8.0) | 84.9 | 5.0 | |
林分平均直径Mean diameter/cm | 16.5(4.1) | 32.6 | 6.6 | ||
断面积Basal area/(m2·hm-2) | 26.2(8.5) | 61.2 | 7.3 | ||
株数Number of stems/hm-2 | 1 347(584) | 3 550 | 367 | ||
海拔Elevation/m | 596(196) | 1 280 | 100 | ||
立地因子 Site factor | 坡度Slope/(°) | 21(8.5) | 45 | 0 | |
坡向Aspect | 按方位角从0~360°,共分成9个坡向It is divided into 9 aspects according to the azimuth angle from 0° to 360° |
表2
主要气象因子统计"
气象因子 Climate variables | 最小 Min. | 最大 Max. | 平均 Mean |
年平均温度Mean annual temperature(MAT)/℃ | 1.34 | 6.56 | 3.93 |
最暖月平均气温Mean warmest month temperature(MWMT)/℃ | 18.30 | 23.58 | 20.91 |
最冷月平均气温Mean coldest month temperature(MCMT)/℃ | -19.00 | -11.50 | -16.08 |
年降水量Mean annual precipitation(MAP)/mm | 498.60 | 1 139.20 | 675.81 |
年平均夏季(5—9月)降水量 Mean annual summer (May to Sept.) precipitation(MSP)/mm | 389.80 | 884.20 | 527.15 |
无霜期天数The number of frost-free days(NFFD)/d | 154.80 | 196.80 | 175.30 |
上一年8月至当年7月的降雪量 Precipitation as snow between Aug. in previous year and Jul. in current year(PAS)/mm | 35.20 | 154.60 | 67.73 |
表3
林分水平枯损模型模拟结果①"
参数 Parameters | 基础模型Basic model | |||||||
标准泊松分布 Standard Poisson | 零膨胀泊松分布 ZIP | 零改变泊松分布 ZAP | 标准负二项分布 Standard NB | 零膨胀负二项分布 ZINB | 零改变负二项分布 ZANB | |||
M1 | M2 | M3 | M4 | M5 | M6 | |||
不考虑随机效应 Without random effect | 模型的零部分 Zero component of the model | α0 | -1.031 9 (0.500 4)* | -1.031 9 (0.500 4)* | -1.030 1 (0.501 4)* | -1.031 9 (0.500 4)* | ||
α1 | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | 0.064 9 (0.020 6)** | 0.064 8 (0.020 6)** | ||||
α2 | 1.620 8 (0.404 6)*** | 1.620 8 (0.404 6)*** | 1.619 9 (0.405 6)*** | 1.620 7 (0.404 6)*** | ||||
计数的部分 Positive count component of the model | β0 | 3.060 0 (0.017 6)*** | 3.408 7 (0.018 1)*** | 3.408 7 (0.018 1)*** | 2.876 1 (0.167 6)*** | 3.345 1 (0.119 6)*** | 3.345 1 (0.119 6)*** | |
β1 | 0.018 2 (0.000 5)*** | 0.012 8 (0.000 5)*** | 0.012 7 (0.000 5)*** | 0.022 1 (0.006 0)*** | 0.013 9 (0.004 1)*** | 0.013 9 (0.004 1)** | ||
β2 | 0.718 6 (0.006 9)*** | 0.633 8 (0.007 0)*** | 0.633 8 (0.007 0)*** | 0.774 9 (0.084 9)*** | 0.656 1 (0.057 2)*** | 0.656 1 (0.057 2)*** | ||
k | 1.017 2 | 0.434 7 | 0.434 7 | |||||
AIC | 27 132 | 21 228 | 21 228 | 5 167.6 | 4 916.2 | 4 916.2 | ||
BIC | 27 144 | 21 253 | 21 253 | 5 184.2 | 4 945.3 | 4 945.3 | ||
-2LogL | 27 126 | 21 216 | 21 216 | 5 159.6 | 4 902.2 | 4 902.2 | ||
考虑随机效应 With random effect | M7 | M8 | M9 | M10 | M11 | M12 | ||
模型的零部分 Zero component of the model | α0 | -1.007 3 (0.506 3)* | -1.031 9 (0.500 4)* | -1.030 4 (0.501 0)* | -1.031 9 (0.500 4)* | |||
α1 | 0.064 1 (0.020 7)** | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | 0.064 8 (0.020 6)** | ||||
α2 | 1.615 4 (0.405 9)*** | 1.620 8 (0.404 6)*** | 1.620 1 (0.405 1)*** | 1.620 8 (0.404 6)*** | ||||
计数的部分 Positive count component of the model | β0 | -0.276 6 (0.121 2)* | 0.692 2 (0.112 0)*** | 0.696 6 (0.111 5)*** | 2.758 9 (0.282 7)*** | 3.218 7 (0.137 5)*** | 3.221 5 (0.137 7)*** | |
β1 | 0.1310 (0.002 5)*** | 0.111 5 (0.002 6)*** | 0.111 4 (0.002 6)*** | 0.023 0 (0.007 1)** | 0.016 2 (0.004 4)** | 0.016 2 (0.004 4)** | ||
β2 | 0.895 2 (0.033 4)*** | 0.686 3 (0.033 9)*** | 0.685 6 (0.033 8)*** | 0.824 3 (0.112 1)*** | 0.677 1 (0.061 8)*** | 0.676 8 (0.061 7)*** | ||
k | 1.053 9 | 0.370 3 | 0.371 4 | |||||
AIC | 11 680 | 9 597.4 | 9 597.7 | 5 170.6 | 4 912.7 | 4 913.1 | ||
BIC | 11 694 | 9 621.6 | 9 621.9 | 5 188.0 | 4 940.5 | 4 940.8 | ||
-2logL | 11 672 | 9 583.4 | 9 583.7 | 5 160.6 | 4 896.7 | 4 897.1 | ||
随机效应方差协方差矩阵D | 1.779 8 | 1.084 5 | 1.082 2 | 0.001 0 | 0.074 1 | 0.072 0 |
表5
考虑气象因子的模型模拟结果"
参数 Parameter | 考虑气象因子的零膨胀负二项分布模拟结果M13 ZINB with climate variables | 考虑气象因子及随机效应的零膨胀负二项分布模拟结果M14 Random ZINB with climate variables | |||
模拟值Simulated value | P | 模拟值Simulated value | P | ||
α0 | -133.57 (44.324 1) | 0.002 7 | -133.56 (44.316 3) | 0.002 9 | |
α1 | 0.169 5 (0.065 6) | 0.010 2 | 0.169 5 (0.065 6) | 0.010 5 | |
α2 | 4.152 6 (1.771 7) | 0.019 5 | 4.152 7 (1.771 4) | 0.019 9 | |
α3 | 5.985 0 (1.999 2) | 0.002 9 | 5.984 7 (1.998 9) | 0.003 0 | |
β0 | 3.345 5 (0.957 8) | 0.000 5 | 3.373 5 (1.026 8) | 0.001 2 | |
β1 | 0.013 9 (0.004 3) | 0.001 6 | 0.016 0 (0.004 7) | 0.000 8 | |
β2 | 0.655 8 (0.058 6) | < 0.000 1 | 0.675 2 (0.062 9) | < 0.000 1 | |
β3 | 0.000 1(0.038 91) | 0.999 6 | -0.006 3 (0.041 9) | 0.879 3 | |
AIC | 4 681.2 | 4 677.6 | |||
BIC | 4 718.6 | 4 712.3 | |||
-2logL | 4 663.2 | 4 657.6 | |||
k | 0.433 6 | 0.369 1 | |||
随机效应方差 Random effect matrix | 0.074 8 |
表6
模型验证结果"
评价指标 Evaluating indicator | 不考虑随机效应 Without random effect | 考虑随机效应 With random effect | |||||||||||||
M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | M9 | M10 | M11 | M12 | M13 | M14 | ||
R2 | 0.87 | 0.89 | 0.89 | 0.87 | 0.89 | 0.89 | 0.89 | 0.85 | 0.85 | 0.89 | 0.89 | 0.89 | 0.88 | 0.83 | |
RMSE | 82.1 | 85.7 | 85.7 | 75.7 | 83.4 | 83.4 | 73.9 | 76.1 | 76.1 | 78.9 | 74.8 | 78.8 | 85.2 | 87.8 | |
|${\bar E}$| | 60.5 | 61.6 | 61.6 | 55.2 | 59.8 | 59.8 | 48.4 | 51.7 | 51.7 | 53.4 | 51.6 | 53.6 | 64.6 | 67.6 |
杜纪山. 落叶松林木枯损模型. 林业科学, 1999. 35 (2): 45- 49.
doi: 10.3321/j.issn:1001-7488.1999.02.008 |
|
Du J S . Tree mortality model of Larix. Scientia Silvae Sinicae, 1999. 35 (2): 45- 49.
doi: 10.3321/j.issn:1001-7488.1999.02.008 |
|
刘平, 马履一, 贾黎明, 等. 油松林木枯损率模型研究. 林业资源管理, 2008. (2): 51- 56.
doi: 10.3969/j.issn.1002-6622.2008.02.012 |
|
Liu P , Ma L Y , Jia L M , et al. Study on tree mortality model for Pinus tabulaeformis plantation. Forest Resources Management, 2008. (2): 51- 56.
doi: 10.3969/j.issn.1002-6622.2008.02.012 |
|
金凤伟, 刘微, 王黑子来. 兴安落叶松人工林单木枯损模型的研究. 林业勘查设计, 2011. (3): 59- 61. | |
Jin F W , Liu W , Wang H Z L . Study on individual tree mortality probability model of Larix olgensis plantation. Forest Survey and Design, 2011. (3): 59- 61. | |
张雄清, 雷渊才, 雷相东, 等. 基于计数模型方法的林分枯损研究. 林业科学, 2012. 48 (8): 54- 61. | |
Zhang X Q , Lei Y C , Lei X D , et al. Predicting stand-level mortality with count data models. Scientia Silvae Sinicae, 2012. 48 (8): 54- 61. | |
郑治刚. 关于建立林分枯损模型的探讨. 中南林业调查规划, 1998. (3): 5- 8, 30. | |
Zheng Z G . Discussion on the establishment of a stand-level mortality model. Forestry Survey Planning in Central and South China, 1998. (3): 5- 8, 30. | |
Affleck D L R . Poisson mixture models for regression analysis of stand-level mortality. Canadian Journal of Forest Research, 2006. 36 (11): 2994- 3006.
doi: 10.1139/x06-189 |
|
Akaike H . A new look at statistical model indentification. IEEE Translate on Automatic Control, 1992. 716- 722. | |
Calama R , Montero G . Interregional nonlinear height-diameter model with random coefficients for stone pine in spain. Canadian Journal of Forest Research, 2004. 34, 150- 163.
doi: 10.1139/x03-199 |
|
Chen C , Weiskittel A , Bataineh M , et al. Evaluating the influence of varying levels of spruce budworm defoliation on annualized individual tree growth and mortality in Maine, USA and New Brunswick, Canada. Forest Ecology and Management, 2017. 396, 184- 194.
doi: 10.1016/j.foreco.2017.03.026 |
|
Crocker S J, Liknes G C, McKee F R, et al. 2016. Stand-level factors associated with resurging mortality from eastern larch beetle (Dendroctonus simplex LeConte). Forest Ecology and Management, 375: 27-34. | |
Das A J , Stephenson N L . Improving estimates of tree mortality probability using potential growth rate. Canadian Journal of Forest Research, 2015. 45, 920- 928.
doi: 10.1139/cjfr-2014-0368 |
|
Fontes C G , Chambers J Q , Higuchi N . Revealing the causes and temporal distribution of tree mortality in central Amazonia. Forest Ecology and Management, 2018. 424 (15): 177- 183. | |
Ganio L M , Progar R A . Mortality predictions of fire-injured large Douglas-fir and ponderosa pine in Oregon and Washington, USA. Forest Ecology and Management, 2017. 390, 47- 67.
doi: 10.1016/j.foreco.2017.01.008 |
|
Groom J D , Hann D W , Temesgen H . Evaluation of mixed-effects models for predicting Douglas-fir mortality. Forest Ecology and Management, 2012. 276, 139- 145.
doi: 10.1016/j.foreco.2012.03.029 |
|
Hamilton D A, Edwards B M.1976. Modelling the probability of individual tree mortality. USDA Forest Service Research Paper, INT-185. | |
Hallinger M , Johansson V , Schmalholz M , et al. Factors driving tree mortality in retained forest fragments. Forest Ecology and Management, 2016. 368, 163- 172.
doi: 10.1016/j.foreco.2016.03.023 |
|
Hurst J M , Stewart G H , Perry George L W , et al. Determinants of tree mortality in mixed old-growth Nothofagus forest. Forest Ecology and Management, 2012. 270, 189- 199.
doi: 10.1016/j.foreco.2012.01.029 |
|
Kim M , Lee W K , Cho G M , et al. Modeling stand-level mortality based on maximum stem number and seasonal temperature. Forest Ecology and Management, 2017. 386, 37- 50.
doi: 10.1016/j.foreco.2016.12.001 |
|
Kuehne C , Weiskittel A R , Fraver S , et al. Effects of thinning induced changes in structural heterogeneity on growth, in growth, and mortality in secondary coastal Douglas-fir forests. Canadian Journal of Forest Research, 2015. 45, 1448- 1461.
doi: 10.1139/cjfr-2015-0113 |
|
Lambert D . Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 1992. 34 (1): 1- 14.
doi: 10.2307/1269547 |
|
Li R , Weiskittel A R , Kershaw Jr J A . Modeling annualized occurrence, frequency, and composition of in growth using mixed-effects zero-inflated models and permanent plots in the Acadian forest region of north America. Canadian Journal of Forest Research, 2011. 41, 2077- 2089.
doi: 10.1139/x11-117 |
|
Monserud R A , Sterba H . Modeling individual tree mortality for Austrian forest species. Forest Ecology and Management, 1999. 113, 109- 123.
doi: 10.1016/S0378-1127(98)00419-8 |
|
Moore J A , Hamilton Jr D A , Xiao Y , et al. Bedrock type significantly affects individual tree mortality for various conifers in the inland Northwest, U.S.A. Canadian Journal of Forest Research, 2004. 34, 31- 42.
doi: 10.1139/x03-196 |
|
Pothier D , Mailly D . Stand-level prediction of balsam fir mortality in relation to spruce budworm defoliation. Canadian Journal of Forest Research, 2006. 36, 1631- 1640.
doi: 10.1139/x06-062 |
|
Taylor S L, MacLean D A. 2007. Spatiotemporal patterns of mortality in declining balsam fir and spruce stands. Forest Ecology and Management, 253: 188-201. | |
Temesgen H , Mitchell S J . An individual-tree mortality model for complex stands of southeastern British Columbia. Western Journal of Applied Forestry, 2005. 20 (2): 101- 109.
doi: 10.1093/wjaf/20.2.101 |
|
Thapa R , Burkhart H E . Modeling stand-level mortality of loblolly pine (Pinus taeda) using stand, climate, and soil variables. Forest Science, 2014. 61 (5): 834- 846. | |
Timilsina N , Staudhammer C L . Individual tree mortality model for slash pine in Florida:a mixed modeling approach. Southern Journal of Applied Forestry, 2012. 36 (4): 211- 219.
doi: 10.5849/sjaf.11-026 |
|
Vanoni M , Bugmann H , Nötzli M , et al. Drought and frost contribute to abrupt growth decreases before tree mortality in nine temperate tree species. Forest Ecology and Management, 2016. 382, 51- 63.
doi: 10.1016/j.foreco.2016.10.001 |
|
Vonesh E F, Chinchilli V M. 1997. Linear and nonlinear models for the analysis of repeated measurements. New York: Marcel Dekker. | |
Wang W F , Peng C H , Kneeshaw D D , et al. Drought-induced tree mortality:ecological consequences, causes, and modeling. Environmental Reviews, 2012. 20 (2): 109- 121.
doi: 10.1139/a2012-004 |
|
Wang T , Wang G , Innes J L , et al. Climate AP:an application for dynamic local downscaling of historical and future climate data in Asia Pacific. Frontiers of Agricultural Science and Engineering, 2017. 4 (4): 448- 458.
doi: 10.15302/J-FASE-2017172 |
|
Weiskittel A R , Crookston N L , Radtke P J . Linking climate, gross primary productivity, and site index across forests of the western United States. Canadian Journal of Forest Research, 2011. 41, 1710- 1721.
doi: 10.1139/x11-086 |
|
Woollons R C . Even-aged stand mortality estimation through a two-step regression process. Forest Ecology and Management, 1998. 105 (2): 189- 195. | |
Wu H , Franklin S B , Liu J M , et al. Relative importance of density dependence and topography on tree mortality in a subtropical mountain forest. Forest Ecology and Management, 2017. 384, 169- 179.
doi: 10.1016/j.foreco.2016.10.049 |
|
Xiang W , Lei X D , Zhang X Q . Modelling tree recruitment in relation to climate and competition in semi-natural Larix-Picea-Abies forests in northeast China. Forest Ecology and Management, 2016. 382, 100- 109.
doi: 10.1016/j.foreco.2016.09.050 |
|
Yang Y , Huang S . A generalized mixed logistic model for predicting individual tree survival probability with unequal measurement intervals. Forest Science, 2013. 59 (2): 177- 187.
doi: 10.5849/forsci.10-092 |
|
Yaussy D A , Iverson L R , Matthews S N . Competition and climate affects US hardwood-forest tree mortality. Forest Science, 2012. 59 (4): 416- 430. | |
Yao X H, Titus S J, Ellen MacDonald S. 2001. A generalized logistic model of individual tree mortality for aspen, white spruce, and lodgepole pine in Alberta mixed wood forests. Canadian Journal of Forest Research, 31: 283-291. | |
Zhang X Q , Cao Q V , Duan A G , et al. Modeling tree mortality in relation to climate, initial planting density, and competition in Chinese fir plantations using a Bayesian logistic multilevel method. Canadian Journal of Forest Research, 2017. 47, 1278- 1285.
doi: 10.1139/cjfr-2017-0215 |
|
Zhang X , Lei Y , Pang Y , et al. Tree mortality in response to climate change induced drought across Beijing, China. Climatic Change, 2014. 124 (1/2): 179- 190. | |
Zhao D , Borders B , Wilson M . Individual-tree diameter growth and mortality models for bottomland mixed-species hardwood stands in the lower Misssissippi alluvial valley. Forest Ecology and Management, 2004. 199 (2): 307- 322. | |
Zhao D , Borders B , Wang M , et al. Modeling mortality of second-rotation loblolly pine plantations in the piedmont/upper coastal plain and lower coastal plain of the southern United States. Forest Ecology and Management, 2007. 252 (1/3): 132- 143. | |
Zuur A F, Ieno E N, Walker N J, et al. 2009. Mixed effects models and extensions in ecology with R. Springer Science+Business Media, LLC. |
[1] | 竹万宽,许宇星,王志超,杜阿朋. 中国桉树人工林生物量估算系数及影响要素[J]. 林业科学, 2020, 56(5): 1-11. |
[2] | 万盼,刘文桢,刘瑞红,王鹏,王宏翔,惠刚盈. 结构化经营对栎松混交林林分空间结构及稳定性的影响[J]. 林业科学, 2020, 56(4): 35-45. |
[3] | 曹小玉, 李际平, 委霞. 中亚热带典型林分空间结构对土壤养分含量的影响[J]. 林业科学, 2020, 56(1): 20-28. |
[4] | 邓磊,朱春云,于世川,祁银燕,张文辉,杜盛,关晋宏. 祁连山青海云杉中龄林混交度对细根形态特征的影响[J]. 林业科学, 2020, 56(1): 191-200. |
[5] | 王文杰, 杜红居, 肖路, 张建宇, 仲召亮, 周伟, 张波, 王洪元. 凉水自然保护区3种森林类型的植物组成和林分结构特征[J]. 林业科学, 2019, 55(9): 166-176. |
[6] | 胡瑞瑞, 梁军, 谢宪, 黄咏槐, 王俊, 苑晓雯, 张英军, 张星耀. 昆嵛山赤松纯林赤枯病特征及与林分因子的关系[J]. 林业科学, 2019, 55(7): 95-104. |
[7] | 朱嘉磊, 薄慧娟, 李璇, 文春燕, 王江, 聂立水, 田菊, 宋莲君. 不同毛白杨无性系林分蓄积量的长期水氮耦合效应[J]. 林业科学, 2019, 55(5): 27-35. |
[8] | 刘宝, 王民煌, 余再鹏, 林思祖, 林开敏. 中亚热带天然林改造成人工林后土壤呼吸的变化特征[J]. 林业科学, 2019, 55(4): 1-12. |
[9] | 吕振刚, 李文博, 黄选瑞, 张志东. 气候变化情景下河北省3个优势树种适宜分布区预测[J]. 林业科学, 2019, 55(3): 13-21. |
[10] | 张雄清, 王翰琛, 鲁乐乐, 陈传松, 段爱国, 张建国. 杉木单木枯损率与初植密度、竞争和气候因子的关系[J]. 林业科学, 2019, 55(3): 72-78. |
[11] | 何怀江, 张忠辉, 张春雨, 郝珉辉, 姚杰, 解蛰, 高海涛, 赵秀海. 采伐强度对东北针阔混交林林分生长和物种多样性的短期影响[J]. 林业科学, 2019, 55(2): 1-12. |
[12] | 杨桂娟,胡海帆,孙洪刚,张建国,段爱国. 林分年龄、造林密度和林分自然稀疏对杉木人工林个体大小分化和生产力关系的影响[J]. 林业科学, 2019, 55(11): 126-136. |
[13] | 耿林, 李明泽, 范文义, 王斌. 基于机载LiDAR的单木结构参数及林分有效冠的提取[J]. 林业科学, 2018, 54(7): 62-72. |
[14] | 刘生冬, 孟昕, 孟庆繁, 李燕, 赵红蕊, 高文韬. 阔叶红松林不同林分对地表甲虫群落的影响[J]. 林业科学, 2018, 54(2): 110-118. |
[15] | 吴鞠, 陈瑜, 刘海轩, 许丽娟, 金桂香, 徐程扬. 林分密度及混交度对长白山天然风景林树木形态的影响[J]. 林业科学, 2018, 54(12): 12-21. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||