Objective This study sought to identify the most suitable nonlinear growth model for describing height and ground diameter growth in one-year-old Quercus mongolica seedlings, and to develop a nonlinear mixed-effects model that partitions variation at provenance and individual levels, and to characterise the seedling growth rhythm and growth differences among provenances of Q. mongolica.

Method We used 757 one-year-old seedlings from nine provenances across Liaoning, Jilin and Heilongjiang provinces. Height and ground diameter were measured every 30 days during the growing season (20 June to 20 November 2025), giving six repeated observations per seedling. Three growth functions—Logistic, Gompertz and von Bertalanffy—were fitted to the data. The best basic model was selected by minimising root mean square error (RMSE) and mean absolute error (MAE). We then constructed a nonlinear mixed-effects model, treating the asymptotic parameter a as random and parameters b and k as fixed. Parameters were estimated using restricted maximum likelihood (REML). Likelihood-ratio tests were used to compare different random-effect structures, and model performance was evaluated using the coefficient of determination (R²), RMSE and MAE.

Result (1) The Logistic model achieved the lowest RMSE across all provenances (3.152–7.965 cm), MAE of 2.459–6.077 cm; for ground diameter, RMSE was 0.549–0.977 mm and MAE was 0.439–0.731 mm. (2) The basic Logistic model, which ignored the hierarchical data structure, exhibited poor fit: R² ranged from 0.312 to 0.510 for height and from 0.453 to 0.594 for diameter. After incorporating provenance and individual nested random effects, the mixed-effects model performed substantially better: R² increased to 0.611–0.852 for height and 0.685–0.868 for diameter. On average, R² rose by about 0.356 for height and 0.257 for diameter, RMSE decreased by about 34% for height and 33% for diameter, and MAE decreased by about 39% for height and 36% for diameter. (3) Variance component decomposition revealed that most of the variation in asymptotic height came from individuals (variance component 22.09, 39.48% of total variation), followed by provenances (14.59, 26.07%). Similarly for ground diameter, individual variation contributed 0.55 (44.16%) and provenance variation 0.34 (27.70%). (4) Growth potential differed significantly among provenances. The Fushun, Jinzhou and Longjiang provenances had higher theoretical maximum height (a values: 30.779, 30.038 and 29.346 cm, respectively), while the Chaihe and Yehe provenances had lower values (20.359 and 19.786 cm). For ground diameter, Longjiang had the highest theoretical maximum (5.037 mm) and Gaizhou the lowest (3.245 mm). Seedling growth followed a “height-first, diameter-later” rhythm: all nine provenances reached their peak height growth rate earlier than their peak diameter growth rate.

Conclusion The Logistic model is a broadly suitable choice for modelling height and ground diameter growth in one-year-old Q. mongolica seedlings. By incorporating provenance and individual nested random effects, the nonlinear mixed-effects model greatly improved fitting accuracy and effectively captured the hierarchical variation in seedling growth traits. These findings provide a scientific basis and quantitative tools for cultivating high-quality seedlings, optimising nursery management, and evaluating germplasm resources at an early stage.