Efficient prediction model for crown ratio of Larix olgensis plantations based on nonlinear mixed-effects model

Liu Shuaidong, Miao Zheng, Hao Yuanshuo, Dong Lihu

Journal of Nanjing Forestry University (Natural Sciences Edition) ›› 2026, Vol. 50 ›› Issue (5) : 152-160.

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Journal of Nanjing Forestry University (Natural Sciences Edition) ›› 2026, Vol. 50 ›› Issue (5) : 152-160. DOI: 10.12302/j.issn.1000-2006.202509032

Efficient prediction model for crown ratio of Larix olgensis plantations based on nonlinear mixed-effects model

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Abstract

【Objective】Crown ratio (CR) is a vital indicator of tree vigor and a fundamental parameter for stand growth prediction. However, high-precision CR prediction models specifically for Larix olgensis plantations remain scarce, and the key driving factors are not yet fully understood. Furthermore, existing models often rely on variables such as total tree height and height to crown base, which are costly and difficult to measure. Therefore, this study aimed to develop a nonlinear mixed-effects (NLME) crown ratio model for L. olgensis plantations using easily obtainable variables and to determine an efficient calibration strategy for prediction to support precision forest management. 【Method】The study utilized observation data from 463 sample plots of L. olgensis in the Dongjingcheng Forestry Bureau, Linkou Forestry Bureau, and Mengjiagang Forest Farm in Heilongjiang Province. A Richards function was selected as the basic model. Stepwise regression was employed to incorporate stand mean dominant height, stand basal area per hectare, and a distance-dependent competition index (Ic5) as covariates to construct the NLME model. Leave-one-out cross-validation and random sampling calibration schemes were employed to analyze the effects of different calibration sample sizes (ranging from 1 to 20 trees) on model prediction accuracy. 【Result】The developed NLME model demonstrated good goodness-of-fit, with an adjusted coefficient of determination (${\mathit{R}}_{\mathrm{a}}^{2}$) of 0.705 4, a root mean square error (RMSE) of 0.086 9, and an Akaike information criterion (AIC) of -17 147.76. Parameter estimates indicated that CR was negatively correlated with stand mean dominant height and stand basal area per hectare, but positively correlated with competition index (Ic5). Sampling calibration significantly improved prediction accuracy; however, the marginal gain in accuracy diminished markedly when the sample size exceeded five trees. 【Conclusion】The NLME model developed in this study effectively quantifies the multifactorial effects of site quality, stand density, and competition on the CR of Larix olgensis without relying on height-related measurements. A calibration sample size of five trees per plot is recommended as the optimal strategy. These findings provide a reliable method and practical tool for achieving low-cost, high-accuracy CR predictions in L. olgensis plantations in Heilongjiang Province.

Key words

crown ratio / Larix olgensis / nonlinear mixed-effects model / sampling calibration

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Liu Shuaidong , Miao Zheng , Hao Yuanshuo , et al. Efficient prediction model for crown ratio of Larix olgensis plantations based on nonlinear mixed-effects model[J]. Journal of Nanjing Forestry University (Natural Sciences Edition). 2026, 50(5): 152-160 https://doi.org/10.12302/j.issn.1000-2006.202509032

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