Nonlinear Mixed-effects Modeling Of Branch Growth For Korean Pine Plantation

This article takes planted Korean pine forest with different ages, site condition and density in Meng jia gang forest located in Heilongjiang province as the research object. In order to build the growth model of branch diameter and branch length of Korean pine,60sample trees were collected and analysed based on the stem and branch analysis technique from12plots in Korean pine plantations in Mengjiagang Forest Farm.The growth characteristics of branch from single sample tree, different size in same stand and in different stand were analysed. The results show that the growth curve of branch diameter and branch length for individual tree shows "S" shape, diameter increment of branches decrease gradually with increasing branch age, the annual increment of branch length decrease gradually with increasing branch age after they reached the maximum at the beginning. As for the same stand, the cumulative growth of branches from bigger trees was bigger than branch from smaller trees, however, the cumulative growth of branches differed in different stands, the branches of the younger trees had the higher cumulative growth rate.Growth models of branch diameter and branch length were developed from attributes of branches including DBH, age and DINC. After testing many combinations of potential independent variables, as well as their transformation that added to the basic model, the following three-variable equations were found to be the best model for estimating branch diameter (BD) and branch length (BL) of Korean pine trees. The proc nlmixed procedure of SAS software was adopted to develop the nonlinear mixed models of branch diameter and branch length with consideration of individual tree and plot effect. The evaluation statistics such as Akaike information criterion (AIC)、Bayesian information criterion(BIC)、-2Log Likelihood and Likelihood ratio test (LRT) were used to compare the predicting precisions of the models. The results showed that when considering plot effect the models of branch diameter and branch length growth had the best performance with α1、α3and β3、β5as random parameters respectively. With consideration of tree effect, the models of branch growth model had the best performance, with α2、α3and β3、β5as random parameters respectively. The nonlinear mixed model not only showed the mean variation of branch growth model, but also showed the differences among the individuals. No matter considering plot effect or tree effect, the nonlinear mixed models provided better model fitting than original model, moreover, the precision of nonlinear mixed model when considering tree effect was better than considering plot effect.The growth models of branch diameter and branch length can be applied to the simulation of the dynamics of live crown development, the prediction tree growth and estimation of the Korean pine fruit production.