Objective This study c aimed to examine the effects of forest fire disturbance on the height–diameter relationship of naturally regenerated Betula platyphylla saplings in the Greater Khingan Mountains. By incorporating stand structure and soil nutrient characteristics, a more precise multi-factor model is developedwas developed to provide theoretical support for post-fire forest management in this area.

Method TA total of 1 465 Betula platyphylla saplings were surveyed across 24 permanent plots in Panggu Forest Farm, Tahe Forestry Bureau, Greater Khingan Mountains, covering areas burned in 1996, 2010, and 2019 as well as unburned controls. The adjust the coefficient of determination (R_\rma^2 ), mean absolute error (MAE), and root mean square error (RMSE) were used to select the optimal height-diameter basic model. A dummy variable representing fire disturbance status was then incorporated, and stand and soil factors were introduced into the base model via reparameterization to construct a generalized nonlinear model. To address the imbalance in sample size between burned and unburned plots, a stratified sampling strategy was adopted for 3-fold cross-validation to ensure consistent proportions of plot types across folds, thereby evaluating model generalization.

Result (1) The Gompertz model was identified as the optimal base model with R_\rma^2 , RMSE, and MAE of 0.683 9, 1.03 m, and 0.78 m, respectively. (2) The generalized nonlinear model incorporating fire disturbance, Shannon diversity index of tree species, and soil total phosphorus significantly improved prediction accuracy, increasing R_\rma^2 by approximately 4.1%, and reducing RMSE and MAE by approximately 4.9% and 6.4%, respectively. (3) The nonlinear mixed-effects model further improved R_\rma^2 to 0.730 6, with RMSE and MAE decreasing to 0.95 m and 0.71 m, respectively. (4) Both the Shannon diversity index and soil total phosphorus were negatively correlated with sapling height growth.. However, fire disturbance significantly attenuated their inhibitory effects. For saplings with a DBH of 5 cm, predicted height in burned areas (6.44 m) was 4.7% higher than that in unburned areas (6.15 m).

Conclusion Our findings indicate that fire disturbance promotes Betula platyphylla sapling height growth by alleviating stand competition and soil phosphorus limitation. The mixed-effects model developed in this study effectively captured plot-level heterogeneity, providing a reliable tool for predicting natural regeneration following fire disturbance.