【摘要】 【目的】构建冬奥核心区华北落叶松和白桦单木冠幅预测模型，对比不同模型的优缺点，给出模型选择建议，为获取更多的单木和林分参数提供支撑，为华北落叶松和白桦科学经营决策提供理论依据。【方法】以冬奥核心区4 537株华北落叶松和2 603株白桦为研究对象，首先，选取10种常用冠幅-胸径模型作为备选模型分别拟合华北落叶松和白桦数据，从中选出AIC和BIC最小的模型作为基础模型；然后，在基础模型中进一步添加与冠幅相关系数大的变量作为协变量构建修正模型；最后，在修正模型基础上分别构建华北落叶松和白桦冠幅的非线性最小二乘模型、单水平非线性混合效应模型、加性模型和组级贝叶斯模型。【结果】4种华北落叶松冠幅模型中，加性模型的预测精度最高（R²＿mean=0.704 3,RMSE＿mean=0.512 7）,4种白桦冠幅模型中，非线性混合效应模型的预测精度最高（R²＿mean=0.664 3,RMSE＿mean=0.794 4）。在变量方面，华北落叶松和白桦冠幅均随其胸径递增，华北落叶松冠幅随其树高缓慢递增、枝下高递减，白桦冠幅随其冠长率先减小后增大，并受林分密度影响波动较大，当林分密度为600～800 hm^-2时，白桦冠幅随林分密度递减，此时应进行适当补植；当林分密度为800～1 000 hm^-2时，白桦冠幅随林分密度递增，并在1 000 hm^-2时出现拐点，如果经营目的是为了环境保护，可将林分密度控制在1 000 hm^-2左右；当林分密度为1 000～1 200 hm^-2时，白桦冠幅随林分密度递减，此时可对林分进行抚育间伐调整林分密度。【结论】冬奥核心区华北落叶松冠幅受胸径、树高和枝下高影响较大，白桦冠幅受胸径、冠长率和林分密度影响较大。无论是预测华北落叶松还是白桦冠幅，组级贝叶斯模型、加性模型和非线性混合效应模型效果均优于非线性最小二乘模型，在仅添加样地随机效应的情况下，首选加性模型和非线性混合效应模型，其次选择组级贝叶斯模型，但考虑到训练组级贝叶斯模型时间长、对表达式敏感等因素，可用别的模型替代时建议不使用组级贝叶斯模型。更多还原

【Abstract】 【Objective】This study was implemented to construct a high-accuracy model of single-wood crowns of Larix principis-rupprechtii and Betula platyphylla in the core area of the Winter Olympics, and to compare the advantages and disadvantages of different models to provide theoretical supports for scientific management decisions.【Method】We took 4 537 L. principis-rupprechtii trees and 2 603 B. platyphylla trees in the core area of the Winter Olympics as the research objects. Firstly, we fitted our data with 10 commonly used crown diameter models, and then selected the best performance model as the basic model for L. principis-rupprechtii and B. platyphylla, respectively. Secondly, other variables were further added as covariates to construct an improved model based on the basic model. Finally, on the basis of the improved model, the nonlinear least squares model, single-level mixed effects model, generalized additive model and group-level Bayesian model of L. principis-rupprechtii and B. platyphylla were constructed, respectively.【Result】Among the 4 L. principis-rupprechtii crown models, the additive model had the highest prediction accuracy（R²＿mean=0.704 3,RMSE＿mean=0.512 7）, and the mixed effect model among the 4 B. platyphylla crown models had the highest prediction accuracy（R²＿mean =0.664 3,RMSE＿mean =0.794 4）. In terms of variables, the crown width of L. principis-rupprechtii and B. platyphylla both increased with the growth of the diameter at breast height. However, the crown width of L. principis-rupprechtii slowly increased with the height of the tree, and decreased with the height to crown base. The B. platyphylla crown width first decreased and then increased with the crown length ratio increasing, on the other hand, the B. platyphylla crown width fluctuated greatly under the change of stand density. When the stand density ranged from 600 to 800 hm^-2, the B. platyphylla crown width decreased with larger stand density, and appropriate replanting should be carried out at this time. When the stand density was in the range of 800 to 1 000 hm^-2, the B. platyphylla crown width increased with larger stand density, and an inflection point of stand density to crown curve appeared at 1 000 hm^-2. Therefore, if the management purpose was to protect the environment, the stand density could be controlled at 1 000 hm^-2. When the stand density was in the range of 1 000 to 1 200 hm^-2, the B. platyphylla crown width decreased with larger stand density. At this time, the forest should be tended and thinned to adjust its stand density.【Conclusion】The crown width of L. principis-rupprechtii in the core area of the Winter Olympics was greatly affected by the diameter at breast height, tree height and height to crown base, while the crown width of B. platyphylla was greatly affected by the diameter at breast height, crown length ratio and stand density. All in all, the performances of the group-level Bayesian model, additive model, and nonlinear mixed-effect model were better than those of the nonlinear least squares model, regardless of whether it was used to predict the crown width of L. principis-rupprechtii or B. platyphylla. When only the random effect of sample plot was added, generalized additive model and the nonlinear mixed effects model should be used first, followed by group-level Bayesian models. However, because of group-level Bayesian model’s lengthy training period and sensitivity to expressions, it was recommended that it should not be developed when another model could be used instead.更多还原