Height-diameter models of regenerated saplings of Larix gmelinii based on dummy variable and quantile regression

Based on data collected from 2054 saplings of Larix gmelinii forest in 55 fixed plots in 2018-2019 in Cuigang Forestry Station, Daxing'anling area, we classified the stand density index (SDI) into four classes, i.e., Class Ⅰ (SDI₁<1863 plants·hm^-2), Class Ⅱ (1863 plants·hm^-2≤SDI₂<2155 plants·hm^-2), Class Ⅲ (2155 plants·hm^-2≤SDI₃<2459 plants·hm^-2) and Class Ⅳ (SDI₄≥2459 plants·hm^-2) by using the quartile method. We constructed a dummy variable model and quantile regression model for the height-breast diameter of saplings of L. gmelinii with dummy variable method introduced SDI. The results showed that among the five selected representative non-linear tree height curve models, the Richards model fitted the best, with R_a², RMSE and MAE of 0.7637, 0.8250 m and 0.5696 m. The dummy variable model including the SDI constructed based on the Richards model showed a 1.3% increase in R_a² compared with the base model, while RMSE, MAE, and AIC decreased by 2.1%, 1.5%, and 11.2%, respectively. When the quantile τ was 0.5, R_a² of quantile regression model was the maximum, and RMSE, MAE, AIC was the minimum, being 0.7612, 0.8294 m, 0.5657 m, and -767.19, respectively. Compared with SDI₁, sapling height in SDI₂-SDI₄ was increased by 5.6%, 5.6%, and 11.3%, suggesting reasonable that regulation of stand density was conducive to increase the height growth of saplings in regeneration.