Construction of general equations for the primary branch sizes of three typical coniferous tree species

Taking the data of trunk resolution and branch resolution of three typical coniferous species (Pinus koraiensis, Larix olgensis, Pinus sylvestris var. mongolica) in Mengjiagang forest farm in Heilongjiang province as an example, the models suitable for the base diameter and branch length of the primary branches were constructed by the dummy variable model method and the nonlinear mixed effect model method. The growth characteristics and differences of the branch base diameter and branch length of different tree species were explored and the branch modeling work was simplified.

In order to improve the predictive ability of the models, the dummy variable models of branch base diameter and branch length with tree species as the dummy variables were constructed based on the re-parameterized model. The nonlinear mixed effect models of branch base diameter and branch length with tree species as the random effect were constructed. Then, using four indicators ( $R_{\text{adj}}^{\text{2}}$, RMSE, AIC, BIC), the predictive ability of the models was evaluated. Finally, according to the evaluation results, the growth differences of three tree species were analyzed based on the model with a better fitting effect.

1) The base diameter and length of the primary branches of the same tree species were significantly different under different grades. The higher the tree grade, the greater the base diameter and length. Based on the same grade of wood, Larix olgensis was significantly different from the other two tree species in terms of branch diameter and base length. 2) The $R_{\text{adj}}^{\text{2}}$ value of the base diameter prediction model for the primary branches based on the dummy variable model method and the nonlinear mixed effect model method reached 0.616 7 and 0.603 6, respectively. The $R_{\text{adj}}^{\text{2}}$ value of the length prediction model for the primary branches based on the dummy variable model method and the nonlinear mixed effect model method reached 0.679 4 and 0.671 2, respectively. The prediction effects of the dummy variable models were better than the nonlinear mixed effect models. However, according to the fitting process of the models, the suitable branch attribute prediction model should be selected according to the sample size when predicting the base diameter and length of primary branches. 3) According to the fitting results of the dummy variable models, there were differences in the base diameter and length of the primary branches of the three tree species, and the range of variation was different. From the perspective of tree species, the order of the base diameter and length of the primary branches of the three tree species was Pinus sylvestris var. mongolica > Pinus koraiensis > Larix olgensis.

Both the dummy variable models and the nonlinear mixed effect models are useful attempts to simplify the modeling of branch size.