[1]苗 铮,董利虎,李凤日*,等.基于GLMM的人工林红松二级枝条分布数量模拟[J].南京林业大学学报(自然科学版),2017,41(04):121-128.[doi:10.3969/j.issn.1000-2006.201604066]
 MIAO Zheng,DONG Lihu,LI Fengri*,et al.Modelling the vertical variation in the number of second order branches of Pinus koraiensis plantation trees through GLMM[J].Journal of Nanjing Forestry University(Natural Science Edition),2017,41(04):121-128.[doi:10.3969/j.issn.1000-2006.201604066]





Modelling the vertical variation in the number of second order branches of Pinus koraiensis plantation trees through GLMM
苗 铮董利虎李凤日*白东雪王佳慧
东北林业大学林学院,黑龙江 哈尔滨 150040
MIAO Zheng DONG Lihu LI Fengri* BAI Dongxue WANG Jiahui
School of Forestry, Northeast Forestry University, Harbin 150040, China
红松 二级枝条数量 Poisson回归模型 广义线性混合模型
Korean pine(Pinus koraiensis) number of second order branches Poisson regression model generalized linear mixed model(GLMM)
【目的】利用广义线性混合模型模拟人工林红松二级枝条分布数量,建立二级枝条分布数量广义线性混合模型,并选出最优模型。【方法】基于黑龙江省孟家岗林场人工林65棵红松955个一级枝上的二级枝条数量,通过传统Poisson回归方法选出模拟精度最高的基础模型,考虑树木效应与树木内枝条观测间的相关性,构建二级枝条分布数量广义线性混合模型,并利用R2、标准误差、平均绝对误差、相对平均绝对误差和Vuong检验对收敛模型进行比较。【结果】考虑树木效应的混合模型模拟精度均高于传统回归模型,最终将含有截距、lnRDINC(RDINC为着枝深度)、R2DINCCL(冠长)4个随机效应参数以及自相关矩阵AR(1)的广义线性混合模型选为二级枝条分布数量最优预测模型。在模型固定效应参数估计结果中,lnRDINCCLDBH(胸径)前的系数为正值,R2DINCHDR(高径比)前的系数为负值,树冠内二级枝条分布数量存在最大值。最优模型的R2为0.896 1,标准误差为5.15,平均绝对误差为3.83,相对平均绝对误差为23.25%。【结论】广义线性混合模型不仅提高了模型的拟合精度,在反映总体二级枝条分布数量变化趋势的同时,还可以反映每棵树木之间的差异。
【Objective】Establish a method for estimating the spatial distribution of branch and foliage biomass within individual Korean pine(Pinus koraiensis)crowns,the aim of the present study was to develop a predictive model for the vertical variation in number of second-order branches in farmed Korean pines.【Method】Using count data from a total of 955 branches sampled from 65 Korean pines in the Mengjiagang Forest Farm, the number of second-order branches was modeled as a function of the relative distance into the crown(RDINC), crown length(CL), diameter(DBH)and height/diameter ratio(HDR),based on a previously developed model. Subject-specific variation was captured using tree-level random coefficients, and the auto correlation among the branches sampled in consecutive whorls of the same crown were taken into account using a first-order auto regressive correlation structure AR(1) in the generalized linear mixed models. The predictive accuracy of the random-coefficient models were compared with that of the fixed-effects model using common methods for validating forest models.【Result】All of the converged models with random coefficients provided better fits than the fixed-effect model,and the model with four random coefficients(intercept, lnRDINC, R2DINC and CL)and the first-order auto regressive correlation structure AR(1) proved to be the optimum mixed model. In the fixed-effect part of this model,the parameter estimates for lnRDINC,CL and DBH were positive, whereas those for R2DINC and HDR were negative.Consequently there was a peak in the number of predicted second-order branches as RDINC increased. The Pseudo-R2, RMSE,MAE and MAE% of the optimal model were 0.896 1,5.15, 3.83, and 23.25%, respectively.【Conclusion】The generalized linear mixed models with random coefficients had greater precision than the previously developed fixed-effect model since they delineated both the mean trend of vertical variation in number of second-order branches and tree-specific deviation from the mean trend.


[1] 张小全, 徐德应, 赵茂盛. 林冠结构、辐射传输与冠层光合作用研究综述[J]. 林业科学研究,1999,12(4):411-421.DOI:10. 13275/j.cnki.lykxyj.1999.04.014. ZHANG X Q, XU D Y, ZHAO M S. Review on forest canopy structure, radiation transfer and canopy photosynthesis[J]. Forest Research, 1999,12(4): 411-421.
[2] 张智昌. 落叶松人工林枝条生长与节子大小预测模型的研究[D]. 哈尔滨:东北林业大学, 2010. ZHANG Z C. Predicting models of branch growth and knot properties for larch plantation [D]. Harbin: Northeast Forestry University, 2010.
[3] NEWTON M, LACHENBRUCH B, ROBBINS J M,et al. Branch diameter and longevity linked to plantation spacing and rectangularity in young Douglas-fir [J]. Fuel & Energy Abstracts, 2012, 266:75-82. DOI:10.1016/j.foreco.2011.11.009.
[4] 郑杨, 董利虎, 李凤日. 黑龙江省红松人工林枝条分布数量模拟[J]. 应用生态学报, 2016, 27(7):2172-2180. DOI:10.13287/j.1001-9332.201607.21. ZHENG Y, DONG L H, LI F R. Branch quantity distribution simulation for Pinus koraiensis plantation in Heilongjiang Province, China[J]. Chinese Journal of Applied Ecology, 2016, 27(7):2172-2180.
[5] DAVIDIAN M, GILTINAN D. Nonlinear models for repeated measurement data: an overview and update [J]. Journal of Agricultural Biological & Environmental Statistics, 2003, 8(4):387-419. DOI: 10.1198/1085711032697.
[6] FANG Z, BAILEY R L, SHIVER B D. A multivariate simultaneous prediction system for stand growth and yield with fixed and random effects [J]. Forest Science, 2001, 47(4): 550-562.
[7] 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. DOI:10.11707//j.1001-7488.2100716. LI C M, TANG S Z. The basal area model of mixed stands of Larix olgensis,Abies nephrolepis and Picea jezoensis based on nonlinear mixed model [J]. Scientia Silvae Sinicae, 2010,46(7): 106-113.
[8] 杨志雄, 袁岱菁. 非线性混合效应模型和广义线性模型拟合随机效应logistic回归的应用比较[J]. 中国卫生统计, 2011(3):321-323. DOI:10.3969/j.issn.1002-3674.2011.03.038.
[9] HEIN S, MäKINEN H, YUE C, et al. Modelling branch characteristics of Norway spruce from wide spacings in Germany [J]. Forest Ecology and Management, 2007, 242(2-3):155-164. DOI:10.1016/j.foreco.2007.01.014.
[10] NEMEC A F L, GOUDIE J W, PARISH R. A Gamma-Poisson model for vertical location and frequency of buds on lodgepole pine(Pinus contorta)leaders [J]. Canadian Journal of Forest Research, 2010, 40(10):2049-2058. DOI:10.1016/j.foreco.2007.01.0140
[11] KINT V, HEIN S, CAMPIOLI M, et al. Modelling self-pruning and branch attributes for young Quercus robur L. and Fagus sylvatica L. trees [J]. Forest Ecology and Management, 2010, 260(11):2023-2034. DOI:10.1016/j.foreco.2010.09.008.
[12] NEMEC A F L, PARISH R, GOUDIE J W. Modelling number, vertical distribution, and size of live branches on coniferous tree species in British Columbia [J]. Canadian Journal of Forest Research, 2012, 42(42): 1072-1090. DOI:10.1139/X2012-06.
[13] SATTLER D F, COMEAU P G, ACHIM A. Branch models for white spruce (Picea glauca(Moench)Voss)in naturally regenerated stands [J]. Forest Ecology and Management, 2014, 325: 74-89. DOI:http://dx.doi.org/10.1016/j.foreco.2014.03.051.
[14] 贺宝龙. 广义线性混合模型在精算分析中的应用[D]. 武汉:武汉理工大学, 2008. HE B L. The application of generalized linear mix models in actuarial analysis [D]. Wuhan: Wuhan University of Technology, 2008.
[15] 陈丹萍. 广义线性混合效应模型(GLMM)与复杂抽样的logistics回归模型在分层整群抽样数据分析中的比较[D]. 上海:复旦大学, 2010. CHEN D P. Comparison of generalized linear mixed models(GLMM)and logistic regression in complex sampling for analyzing data obtain from stratified cluster random sampling [D]. Shanghai: Fudan University, 2010.
[16] WOLFINFER R, O'CONNELL M. Generalized linear mixed model: a pseudo-likelihood approach [J].Journal of Statistical Computation and Simulation, 1993, 48(3):233-243. DOI: 10.1080/00949659308811554.
[17] 杨肇, 朱凯旋. Logistic回归分析中的过度离散现象及纠正[J].中国卫生统计, 2003(4):48-49. DOI:10.3969/j.issn.1002-3674.2003.04.016.
[18] MAGUIRE D A, MOEUR M, BENNETT W S. Models for describing basal diameter and vertical distribution of primary branches in young Douglas-fir [J]. Forest Ecology and Management, 1994, 63(1):23-55.
[19] ISHII H, MCDOWELL N. Age-related development of crown structure in coastal Douglas-fir trees [J]. Forest Ecology and Management, 2002, 169(3):257-270.
[20] WEISKITTEL A R, MAGUIRE D A, MONSERUD R A. Response of branch growth and mortality to silvicultural treatments in coastal Douglas-fir planations: implications for predicting tree growth [J]. Forest Ecology and Management, 2007, 251(3):182-194. DOI:10.1016/j.foreco.2007.06.007.
[21] MAKINEN H, OJANSUU R, SAIRANEN P, et al. Predicting branch characteristics of Norway spruce(Picea abies(L.)Karst.)from simple stand and tree measurements [J]. The Journal of the Society of Foresters of Great Britain, 2003, 76(5):525-546.
[22] 康萌萌. 广义线性混合模型及其SAS实现[J]. 统计教育, 2009(10):50-54. KANG M M. Generalized linear mixed models and implementation with SAS [J] Statistical Thinktank, 2009(10):50-54.


 CHEN Yong liang,HAN Shi jie.Distribution characteristics of elements in rootsoil interface of Pinus koraiensis seedlings by electron probe Xray microanalysis[J].Journal of Nanjing Forestry University(Natural Science Edition),2009,33(04):065.[doi:10.3969/j.jssn.1000-2006.2009.03.015]
[2]朱 磊,张厚江*,孙燕良,等.基于应力波和微钻阻力的红松类木构件力学性能的无损检测[J].南京林业大学学报(自然科学版),2013,37(02):156.[doi:10.3969/j.issn.1000-2006.2013.02.028]
 ZHU Lei,ZHANG Houjiang*,SUN Yanliang,et al.Mechanical properties non-destructive testing of wooden components of Korean pine based on stress wave and micro-drilling resistance[J].Journal of Nanjing Forestry University(Natural Science Edition),2013,37(04):156.[doi:10.3969/j.issn.1000-2006.2013.02.028]
 CHEN Yong-liang,LIU Ming-he,LI Xiu-ling.Effects of Different Nitrogen Forms and Ratios on the Photosynthetic Characteristics of Pinus koraiensis Seedlings[J].Journal of Nanjing Forestry University(Natural Science Edition),2005,29(04):077.[doi:10.3969/j.jssn.1000-2006.2005.03.020]
 Peng Shujing,Tan Boqi,Zhang Dacheng,et al.THE COMPREHENSIVE UTILIZATION OF PINUS KORAIENSIS (SIEB. ET ZUCC.) SEED I. ANALYSIS OF THE COMPOSITION OF KERNEL OIL[J].Journal of Nanjing Forestry University(Natural Science Edition),1986,10(04):024.[doi:10.3969/j.jssn.1000-2006.1986.04.004]
 Li Xuewen Wang Qingjun Nian Xiuhong.STUDIES ON THE EFFECT OF DIFFERENT MIXED PROPORTION ON STAND QUALITY IN KOREAN PINE PLANTATION[J].Journal of Nanjing Forestry University(Natural Science Edition),1992,16(04):115.[doi:10.3969/j.jssn.1000-2006.1992.03.031]
 CHEN Yong-liang.The Effects of Different Nitreon Sources on pH and the Nutrient Availability in the Rhizosphere of Korean Pine[J].Journal of Nanjing Forestry University(Natural Science Edition),2004,28(04):042.[doi:10.3969/j.jssn.1000-2006.2004.01.010]
 XU Huadong,XU Guoqi,WANG Lihai*.Effect of low temperature on the mechanical properties of Pinus koraiensis and Populus ussuriensis timber[J].Journal of Nanjing Forestry University(Natural Science Edition),2014,38(04):025.[doi:10.3969/j.issn.1000-2006.2014.05.006]
[8]高 芳,沈海龙*,刘春苹,等.红松成熟胚愈伤组织诱导外植体选择及培养条件优化[J].南京林业大学学报(自然科学版),2017,41(03):043.[doi:10.3969/j.issn.1000-2006.201605034]
 GAO Fang,SHEN Hailong*,LIU Chunping,et al.Optimization of culture conditions and selection of suitable explants for callus induction from mature embryo of Pinus koraiensis[J].Journal of Nanjing Forestry University(Natural Science Edition),2017,41(04):043.[doi:10.3969/j.issn.1000-2006.201605034]
 GAO Huilin,DONG Lihu,LI Fengri*.Modelling outer crown profile for planted Pinus koraiensis andLarix olgensis trees in Heilongjiang Province, China[J].Journal of Nanjing Forestry University(Natural Science Edition),2018,42(04):010.[doi:10.3969/j.issn.1000-2006.201703112]


收稿日期:2016-04-30 修回日期:2016-12-07
基金项目:国家自然科学基金项目(31570626); 国家级大学生创新创业训练计划项目(201410225057)
引文格式:苗铮,董利虎,李凤日,等. 基于GLMM的人工林红松二级枝条分布数量模拟[J]. 南京林业大学学报(自然科学版),2017,41(4):121-128.
更新日期/Last Update: 1900-01-01