基于GLMM的人工林红松二级枝条分布数量模拟

【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、lnR_(DINC)(R_(DINC)为着枝深度)、R_(DINC)~2和C_L(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,lnR_(DINC)、CL和DBH(胸径)前的系数为正值,R_(DINC)~2、H_(DR)(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R~2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。

Modelling the vertical variation in the number of second order branches of Pinus koraiensis plantation trees through GLMM

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 treelevel 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 lnRDIC,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 fixedeffect model since they delineated both the mean trend of vertical variation in number of second-order branches and treespecific deviation from the mean trend.