[Tree height-diameter modeling of Larix olgensis plantations based on generalized additive mixed models]

Based on data from 71 permanent plots established in the Maoershan Experimental Forest Farm of Northeast Forestry University and the Shengli Experimental Forest Farm in Harbin City, we developed three types of height-diameter models for Larix olgensis plantations. A generalized additive model (GAM) included only the main effects of either the stand density index (SDI) or the site index (SI). A generalized additive mixed model (GAMM) incorporated the interaction between SDI and SI. A varying-coefficient generalized additive mixed model (VC-GAMM) adjusted the slope by the logarithm of diameter at breast height (logD). Model selection was based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Model performance was evaluated using the adjusted coefficient of determination (R_adj2 ), root mean square error percentage (RMSE), and mean absolute error percentage (MAE). The effects of stand density, site conditions, and their interaction on individual-tree height-diameter curves of L. olgensis plantations were quantified to provide a theoretical basis for sustainable plantation management. The results showed that the VC-GAMM was the optimal height-diameter model, with a R_adj2 value of 0.733, representing an improvement of 9.6%-13.6% over the GAM models and 0.14% over the GAMM model, while its RMSE and MAE were 12.4% and 9.7%, respectively, which were the lowest among all kinds of models. Marginal effect analysis showed that under extremely poor site conditions (standardized site index SI_s=-1.89), a one-standard-deviation increase in the standardized stand density index (SDI_s) increased tree height by only 0.34 m, whereas under excellent site conditions (SI_s=+2.15), tree height increased by 0.78 m, corresponding to 1.9% difference in relative height gain. The maximum tree height occurred in regions characterized by moderate SDI_s and relatively high SI_s. The interaction between stand density and site conditions was strongest at the small-diameter stage (25th percentile of DBH), where the relative variation in tree height was 5% higher than that at the medium- and large-diameter stages. There was a significant interaction between stand density and site conditions, and their combined explanatory power for tree height variation exceeded that of either factor alone. Increasing stand density promoted height growth under favorable site conditions. Under poor site conditions, high stand density intensified competition and suppressed height growth, with tree height being more sensitive to this interaction during the early developmental stages of the stand.