Construction Of General Equations For Primary Branches Attribute Factors Of Three Typical Coniferous Tree Species

Canopy structure is the basis of tree growth and development,and they play an important role in stand dynamics and productivity,such as forest fire sensitivity,local microclimate,wood quality,etc.Canopy structural characteristics lie in the number,size and position of branches.The growth of primary branches is the most important especially,and its length and spatial arrangement play a dominant role in the shape of the tree.Although some studies have quantified the branching attribute factor of individual conifer species,there have been no studies comparing the differences in canopy branching attribute factor of temperate conifer species.Previous studies have modeled each conifer species separately,and have not attempted to predict each attribute factor of primary branches for different conifer species by establishing a universal equation.Therefore,this paper starts from the actual demand of establishing the universal branch attribute factor equation,Based on the data of primary branches of three typical conifers（Pinus koraiensis,Larix olgensis,Pinus sylvestris var.Mongolica）in Mengjiagang Forest farm,Heilongjiang Province.The differences of primary branches attribute factor of different species were examined.In order to provide theoretical basis for further analysis of growth potential of branches and reasonable determination of stand density,the research was carried out from three research angles:base diameter of branches（Base diameter,BD）,length of branches（Branch length,BL）and angle of branches（Branch angel,BA）.The main conclusions are as follows:（1）The base diameter and length of primary branches of the same tree species vary significantly under different tree classes.The higher the tree class,the greater the base diameter and length.Based on the same rank of trees,Larix olgensis is significantly different from the other two species in terms of base diameter and branch length.It was found that the characteristics of Pinus koraiensis and Pinus sylvestris var.mongolica were similar,and there was no significant difference in base diameter of primary branches between them.Although there was a significant difference in the length of first branch between Pinus koraiensis and Pinus sylvestris var.mongolica,the significance was less than that of Larix olgensis.From the analysis results of branching angle,it can be seen that the distribution interval of average branching angle of all species is similar,and the branching angle of primary branches of all species presents an overall upward trend along with the increase of trunk branching depth,while the crown base presents a downward trend.（2）The results of dummy variable model show that the estimation results of all parameters are stable,and the estimated values of parameters are significantly non-0,which indicates that the use of dummy variables to distinguish conifer species is effective.The results of the mixed effects model show that the evaluation indexes such as the adjustment coefficient of the mixed effects model with tree species as random effects are better than those of the re-parameterized basic model.These evaluation indexes indicate that the introduction of random parameters improves the prediction accuracy of the model.In addition,the test results of the mixed effects model show that the test results of the model containing random effects are better than those of the re-parameterized basic model,and the test results of the re-parameterized basic model are better than those of the model containing fixed effects,which is consistent with the fitting conclusion,indicating that the prediction accuracy of the model has been improved after adding random effects.The above results indicate that it is feasible to introduce tree species as qualitative variables and random effects to establish the general equation of branch attribute factors,which is a useful attempt to simplify the modeling work of branch size.（3）The²₍（6（95））of the primary branch base diameter prediction model based on dummy variable model method and nonlinear mixed effects model reaches 0.6167 and 0.6036,and the RMSE are 0.4475 and 0.4377.The²₍（6（95））of the length prediction model reaches 0.6794 and0.6712,and the RMSE are 0.5207 and 0.5153 respectively.The prediction effect of dummy variable model is better than that of nonlinear mixed effects model.However,according to the fitting process of the model,The appropriate branch attribute prediction model should be selected according to the sample size and fitting process when predicting the base diameter and length of branches.（4）According to the fitting effect of each model,the optimal model was selected to simulate the curve of attribute factors of each branch of different tree species.From the results reflected in the model,tree species differences can significantly affect the size of the first branch.Based on the same stand and tree conditions,the size values of the primary branch base diameter and length of the three species were sorted as Pinus sylvestris var.mongolica>Pinus koraiensis>Larix olgensis.Based on the survey data of Mengjiagang forest farm,this study examined the differences of primary branch attribute factors for different tree species.We established a universal model for predicting base diameter and branch length of primary branches for three conifer species.Appropriate models were selected to predict the size of primary branches of different tree species.This simplifies the modeling of branch size and provides a reference for the establishment of a wide range of branch attribute factor prediction models.