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作 者 ：李婉婷;姜立春;万道印

期 刊 ：植物研究 2014年 34卷 03期 页码：343-348

关键词：树高—胸径模型；混合效应；样地效应；

Keywords:height-diameter model, mixed effects, plot effect, Larix gmelinii,

摘 要 ：以黑龙江省带岭林业局大青川林场和永翠林场的兴安落叶松人工林为研究对象，基于41块样地调查数据和Richards模型，构建了含有林分变量的树高与胸径关系模型。利用混合效应模型方法拟合常规Richards模型y_ij=(β₁+b_i1)(1-e^{-(β₂+b_i2)x_ij})^(β₃+b_i3)+ε_ij和含有林分变量的模型y_ij=(β₁+b_i1)(D_q)^(β₂+b_i2)(1-e^{-(β₃+b_i3)(N(β₄+b_i4))x_ij})+ε_ij。结果表明：当对Richards混合效应模型拟合时，引入随机参数b₁、b₂时模型拟合最好; 当对含有林分变量的Richards混合效应模型拟合时，引入随机参数b₂、b₄时模型拟合最好。模型检验表明：当随机抽取独立样本时，混合模型误差小于固定效应模型。如果随机抽取4个样本校正时，混合模型的误差和均方根误差降低71.8%和42.1%。

Abstract:The sample data was from dahurian larch (Larix gmelinii（Rupr.）Rupr.) plantations located in Daqingchuan and Yongcui Forest Farms, Dailing Forest Bureau in Heilongjiang Province. Height-diameter model with stand variables was developed based on sample data from 41 plots and Richards’s model. A mixed-effect modeling approach was applied in fitting Richards’s model y_ij=(β₁+b_i1)(1-e^{-(β₂+b_i2)x_ij})^(β₃+b_i3)+ε_ij and the same model with stand variables y_ij=(β₁+b_i1)(D_q)^(β₂+b_i2)(1-e^{-(β₃+b_i3)(N(β₄+b_i4))x_ij})+ε_ij. Results showed that Richards model with inclusion of random parameters b₁, b₂ was the best when fitting mixed-effects model of Richards; Inclusion of random parameters b₂, b₄ was the best when fitting Richards model with stand variables. Model validation indicated that mixed model showed lower error than fixed-effects model when randomly selected independent samples. However, using calibration with randomly selected four trees, mixed model reduced the bias and RMSE of the prediction by almost 71.8% and 42.1%, respectively.

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