Distribution And Model Construction Of Branch Attribute Factors Of Larix Olgensis

The vertical and horizontal distribution of primary branch constitutes the basic form of tree crown,which determines the number and location of leaves,thus directly affects the material exchange ability between trees and environment,and affects the acquisition and accumulation of organic matter in trees.Therefore,studying the distribution of branch factors is the basis of studying the spatial structure of tree crown and analyzing the degree of absorption and transformation of natural materials.Larix olgensis is one of the most important timber species in Northeast China.In this paper,the distribution of branch diameter,branch length,branch angle and branch number of Larix olgensis at different ages were analyzed.The significance of the difference was judged by variance analysis,and the age group and individual tree two-level nonlinear mixed effect model was established for the significant factors（branch diameter,branch length）.The predicted values of the basic model and the mixed model were compared,and the distribution of branch diameter and branch length of each age group was simulated by using the random parameters of the age group level.Independent data were used to verify the model fitting results.The results show that:1.At any age,the distribution range of branch diameter and length increased with the increase of DBH and tree height.The branch angles were evenly distributed between 20°and 90°with no significant difference.At middle and mature stages,the diameter and length of branch base increased gradually with the increase of branch depth,and decreased after reaching the maximum,gradually increased at the young age and near maturity.At the young,near-mature and mature stages,the closer to the lower part of the tree trunk,the greater the branch angle.In the middle age,it gradually decreases with the increase of branch depth and the decreasing range is small.The number of branches increased first and then decreased with the increase of relative branch depth.In the azimuth distribution,the number of branches is more in the south direction.There were significant differences in diameter and length of branches among different age groups,but no significant differences in branch angle and number.2.The mixed effect model of branch diameter:taking the branch depth and DBH as independent variables,the improved Gompertz equation was selected as the optimal basic model,and the model adjustment coefficient(²_adj)was 0.5979,the root mean square error（RMSE）was 5.5188.The model performed the best when the age group random effects acted on parameter b,the individual tree random effects acted on parameters b,c and d at the same time,the variance-covariance structure of the random effects was generalized positive definite matrix,and the heteroscedasticity structure was power function.The²_adj of the mixed model was improved,and RMSE were all significantly reduced.The values of the²_adj,RMSE of the final model were 0.6998,4.7684.3.The mixed effect model of branch length:taking branch depth and DBH as independent variables,Logistic equation as the optimal basic model,and the model²_adj was 0.6389,RMSE was 0.4580.The model performed the best when the age group random effects acted on parameter a,the individual tree random effects acted on parameters b,c and d at the same time,the variance-covariance structure of the random effects was generalized positive definite matrix,and the model without heteroscedasticity structure.The fitting index was significantly reduced and the fitting effect was improved.Compared with the fixed model,The mean absolute error（MAE）and mean absolute relative error（MRAE）of the model with random effect are significantly reduced,indicating that the mixed effect model can significantly improve the prediction accuracy of the model.Using different levels of random parameters to simulate the distribution of branch diameter and length can reflect its laws and differences.Therefore,the mixed effect model based on age group and single tree two levels can reasonably predict the growth of basal diameter and length of primary branches of Larix olgensis at different ages.