基于非线性混合模型的东北兴安落叶松树高和直径生长模拟

以黑龙江省带岭林业局大青川林场80株人工兴安落叶松解析木数据为例,采用Richards生长模型作为基础模型,利用S-PLUS软件中的NLME过程,分别拟合非线性树高和直径生长模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的精度进行比较分析。结果表明:当对树高-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好;当对直径-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好。把相关性结构包括一阶自回归结构AR(1)、一阶移动平均结构MA(1)及一阶自回归与移动平均结构ARMA(1,1)]加入到树高和直径最优混合模型中,一阶自回归结构AR(1)显著提高了树高混合模型的拟合精度,一阶移动平均结构MA(1)显著提高了直径混合模型的拟合精度。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。因此,混合模型在应用上不但能反映树高和直径的平均预测趋势,还能用方差协方差结构和误差相关性结构校正随机参数来反映个体之间的差异。

Height and Diameter Growth Modeling of Dahurian Larch Based on Nonlinear Mixed Model in Northeastern China

With the stem analysis data based on 80 sample trees from dahurian larch (Larix gmelinii Rupr.) plantations located in Daqingchuan Forestry Center of Dailing Forest Bureau in Heilongjiang Province, the Richards growth model was selected to model the height/age and diameter/age relationships of dahurian larch using NLME procedure of S-PLUS. Evaluation statistics, such as AIC, BIC, Log Likelihood and likelihood ratio test were used for precision analyzing and comparing of different models. The results indicated that Richards model with parameters b₁ and b₃ as mixed effects showed the best performance for both height-age relationships and diameter-age relationships. Correlation structures including first-order autoregressive correlation structure AR(1), moving average correlation structure MA(1) and autoregressive-moving average correlation structure were incorporated into the optimal height and diameter mixed models. AR(1) significantly improved the precision of mixed height model and MA(1) significantly improved the precision of mixed diameter model. Model validation showed that the mixed model with calibration of random parameters could improve the precision of prediction. Therefore, the application of the mixed model showed not only the mean trends of height and diameter prediction, but also the individual difference by calibrating random parameters using variance-covariance structure and correlation structure.