Crown width model for planted Korean pine in eastern Liaoning mountains based on mixed effect linear quantile

Abstract

Crown width is a critical variable in reflecting the individual tree growth status and in developing forest growth and yield models. With the crown width base model as reference, we developed the crown width quantile regression models for different quantiles (0.50, 0.90, 0.93, 0.95, 0.96, 0.99) based on the data of 2763 Korean pines in 66 permanent plots from the 10-55 years old plantations in Dabiangou forest farm, mountainous areas of eastern Liaoning Province. We used the reparameterization method by introducing the single tree competition index (Rd) and used the dummy variable method by introducing stand density and forest layer variables. We then selected optimal quantile of maximum crown width in the stand by comparing our model developed routine to the traditional methods. The final crown width linear mixed effect quantile regression model was developed based on the optimal quantile at the plot level. The influence of each variable on crown width was analyzed to reflect the difference of crown width among individual trees in the stand. The models with different stand densities and forest layers had significant difference based on F statistical test: the Ra2 of the model increased by 0.0104, the root mean square error decreased by 0.0115 and the mean square error reduction was 7.4%, after the variables of forest layer, forest density, and competition being incorporated into the basic model. The developed quantile regression model performed better than that of the ordinary least square method in simulating the maximum crown width of a single tree in the forest stand. The selected best quantile of the quantile regression model for the upper forest layer and lower forest layer was 0.96 and 0.93, respectively. The linear quantile regression model with the mixed effect was superior to the traditional quantile regression model in Akaike, Bayesion and HQ information criterion and other evaluation para-meters, the standard error for the parameters of estimates was significantly reduced, and the introduced mixed effect well explained differences among different plots. For the upper forest layer and lower forest layer, the maximum crown width decreased with increasing stand density, increased with increasing relative diameters. The influence of stand density on the crown width of the lower forest layer was greater than that of the upper forest layer. The crown width would increase first and then decrease with the increases of DBH when the stand density was large enough. The mixed effect of the quantile regression model developed here could significantly improve the fitting stability of the model. The sustainable development of Korean pine plantation in the mountainous area of eastern Liaoning Pro-vince should be realized by adjusting stand density and moderate tending and thinning in the future.