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Key message The non-linear seemingly unrelated regression mixed-effects model (NSURMEM) and generalized additive model (GAM) were applied for the first time in crown width (CW) additive models of larch (Larix gmelinii Rupr.), birch (Betula platyphylla Suk.), and poplar (Populus davidiana Dode). The crown radii in four directions (CR) exhibited different growth trends and responded differently to tree size and competition variables. In the absence of calibration, GAM was more accurate than NSURMEM for CR and CW predictions. Context Crown radii in four directions (CR) and crown width (CW) are fundamental indicators used to describe tree crowns. The complexity of the CR growth in four directions of different tree species in natural forests is often ignored. There is logical additivity among CR and CW that is also often overlooked. Furthermore, the existing methods applied to CW additive models have some drawbacks. Aims We aim to: (i) evaluate the utility of two new methods in developing CW additive models for larch (Larix gmelinii Rupr.), birch (Betula platyphylla Suk.), and poplar (Populus davidiana Dode) in natural secondary forests of Northeastern China; and (ii) explore the growth patterns of CR in four directions to gain important ecological insights. Methods The non-linear seemingly unrelated regression mixed-effects model (NSURMEM) and generalized additive model (GAM) were used to develop CW additive models and to explore crown growth patterns. The predictive ability of the additive models was evaluated using leave-one-plot-out cross-validation (LOOCV). Results At a fair level without calibration, GAM provided slightly better results than NSURMEM. The response of the four CR to tree size and competition variables is different and may be non-uniform due to complex stand conditions and tree growth strategies. Conclusion The newly provided methods applied to additive models are available for external datasets. GAM is recommended in the absence of calibration. This study has important implications for the understanding of natural forest dynamics and decision-making for critical stand management.