【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)、R2DINC和CL(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,lnRDINC、CL和DBH(胸径)前的系数为正值,R2DINC、HDR(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。
Abstract
【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.
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基金
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)
第一作者:苗铮(18745068128@163.com),博士生。*通信作者:李凤日(fengrili@126.com),教授。
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.
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