基于非线性混合模型的落叶松木材管胞长度模拟

以黑龙江省七台河市林业局金沙林场9 株人工落叶松6 825 对早、晚材管胞长度样品数据为例,选择6 个常用方程进行非线性回归分析,把拟合精度最高的Richards 模型作为早、晚材管胞长度基础模型y = β1 [1 - exp( - β2 x)]β3 + ε。基于Richards 模型,利用非线性混合模型技术构建落叶松早、晚材管胞长度混合效应模型yij = (β1 + b1i ){1 - exp[ - (β2 + b2i )t]}β3 + b3i + εij 。结果表明:当对早材管胞长度进行拟合时,b1i 、b2i 、b3i同时作为随机参数时早材管胞长度模型拟合最好;当对晚材管胞长度进行拟合时,b1i 、b2i 、b3i 同时作为随机参数时晚材管胞长度模型拟合最好;一阶自回归模型AR(1)能够较好地表达树木内误差相关性;同时考虑随机效应和时间序列相关性结构能够提高落叶松早、晚材管胞长度混合模型的预测精度。 

Modeling wood tracheid length based on nonlinear mixed model for dahurian larch

The sample data was based on 6 825 pairs of earlywood and latewood tracheid length samples of 9 trees from dahurian larch (Larix gmelinii Rupr.) plantations located in Qitaihe Forest Bureau in Heilongjiang Province, northeastern China. Six functions were selected using nonlinear regression analysis. The Richards model y=β1[1-exp(-β2x)]β3+ε was selected to model earlywood and latewood tracheid length based on goodness-of-fit statistics. Nonlinear mixed-effects modeling approach was used to build mixed-effects models of earlywood and latewood tracheid length based on Richards model yij=(β1+b1i){1-exp[-(β2+b2i)t]}β3+b3i+εij. The results showed that Richards model with parameters b1i,b2i,b3i as random effects showed the best performance for both earlywood and latewood tracheid length. Time series correlation structures AR(1) describe error correlation within tree well. Prediction precision of earlywood and latewood tracheid length mixed models could be improved through considering both random effects and time series correlation structures.