Study On The Number And Size Of Branches For Larix Olgensis Plantations

In this study,the generalized linear mixed model was used to study the distribution of the number and size of first-order branch for planted Larix olgensis trees.The modeling data were based on 596 first-order branches of 49 branch analysis trees selected from 7 permanent sample plots in Larix olgensis plantation from Mengjiagang forest farm,Jiamusi city,Heilongjiang Province.Poisson model,Normal model,Beta model were introduced to develop the optimal basic model of branch quantity,maximum branch diameter,other branch diameter with the PROC GLIMMIX procedure of SAS.Considering the different tree effects,the generalized linear mixed model of number of first-order branch per 0.5 m.maximum branch diameter per 0.5 m,relative branch diameter per 0.5 m was developed on the selected optimal basic model.AIC,BIC,-2Log likelihood and LRT test were selected to compare the goodness-of-fit statistics of the models.Firstly,the results showed that all of the convergence mixed models with the combination of random coefficients fitted better than the basic model.Finally,the one with three random coefficients(including DINC,LnRDINC,RDINC)was selected as the optimal mixed model to describe the distribution of number of first-order branch per 0.5 m for planted Larix olgensis trees.In this model,the parameter values for LnRDINC and CL were positive;the ones for DINC,RDINC2,HT/DBH,DBH were negative.Moreover,there was a peak value for the number of first-order branch per 0.5 m.The fitting result of model showed that the coefficient of determination(Rn2)was 0.669 and the mean absolute error was 2.250 and the root mean square error was 3.012.Secondly,the results showed that all of the convergence mixed models with the combination of random coefficients fitted better than the basic model.Finally,the one with three random coefficients(including Int,LnRDINC,RDINC2)was selected as the optimal mixed model to describe the distribution of maximum branch diameter per 0.5 m for planted Larix olgensis trees.In this model,the parameter values for CL,HCB,LnRDINC were positive;the ones for HT/DBH,RDINC2 were negative.Moreover,there was a peak value for maximum branch diameter per 0.5 m.The fitting result of model showed that the coefficient of determination(Rn2)was 0.917 and the mean absolute error was 1.779 and the root mean square error was 2.258.Thirdly,the results showed that all of the convergence mixed models with the combination of random coefficients fitted better than the basic model.Finally,the one with three random coefficients(including NB,Rank)was selected as the optimal mixed model to describe the relative branch diameter per 0.5 m for planted Larix olgensis trees.In this model,the parameter values for NB were positive;the ones for Rank were negative.Moreover,there was a peak value for the relative branch diameter per 0.5 m.The fitting result of model showed that the coefficient of determination(Rn2)was 0.582 and the mean absolute error was 0.097 and the root mean square error was 0.121.All in all,not only could the mixed model describe the mean trend of the distribution of the branch number and size,but also it reflected the differences between sample trees.It was shown that the generalized linear mixed model could improve the simulation accuracy of the model.As a result,the optimal mixed model would be suitable for predicting the number and diameter of first-order branch and will provide theoretic basis to modeling crown architecture and three-dimension visualization for Larix olgensis plantation.