【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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