基于混合效应的长白落叶松一级枝条基径预估模型

Prediction model of base diameter of primary branch for Larix olgensis based on mixed effects

【目的】利用非线性混合效应建模方法构建龄组-单木两水平长白落叶松一级枝条基径模型,为探索不同龄组下枝条基径的生长特点及差异提供理论依据。【方法】对4个基础模型进行改进,通过调整系数(Radj2),均方根误差(RMSE)选择备选模型,在此基础上构建长白落叶松枝条基径非线性混合效应模型。利用独立数据验证模型拟合结果,用平均绝对误差(MAE)、平均相对误差绝对值(MRAE)评价模型预测能力。并对基础模型与混合模型的预测值进行比较,利用龄组水平的随机参数模拟各龄组枝条基径的分布。【结果】以改进后的Gompertz方程为基础模型,当龄组随机效应作用于参数b、单木随机效应同时作用于参数b、c、d上,随机效应的方差协方差结构为广义正定矩阵,异方差结构为幂函数时,模型的拟合效果最优。混合模型的Radj^2有所提升,RMSE、MAE和MRAE都明显降低。最终模型的Radj^2、RMSE、MAE和MRAE分别为0.6998、4.7684 mm、3.7058 mm和0.3916 mm。混合模型的预测值可体现单木间的差异,枝条基径的分布范围随着龄组的增大逐渐增大,各龄组的枝径生长均有差异。【结论】考虑龄组与单木水平所构建的枝条基径混合效应模型能提高模型的预测精度。利用龄组水平的随机效应参数模拟枝条基径的生长可以反映其规律和差异,也符合树木生理学意义。因此基于龄组与单木两水平所构建的混合效应模型可对不同年龄长白落叶松一级枝枝条基径的生长进行合理的预测。

[Objective]This paper aims to establish an age group-individual tree two-level primary branch diameter model for Larix olgensis using the nonlinear mixed effect model approach,and provide theoretical basis for the research on the characteristics and differences of branch diameter growth in different age groups.[Method]Out of four improved basic models,one was selected as the basic model after referring to the adjusting coefficient(Radj2)and root mean square error(RMSE).Nonlinear mixed-effect model of the branch diameter was constructed based on the selected model.Independent data were used to verify the model fitting results,while mean absolute error(MAE)and mean relative absolute error(MRAE)were used to evaluate the model prediction ability.The prediction values of the basic model and the mixed model were compared.Simulation of the branch diameter distribution in each age group was done using the random parameters from age group level.[Result]Based on the improved Gompertz equation,the model performed the best when the age group random effects acted on parameter b,the individual tree random effects acted on parameters b,c and d at the same time,the variance-covariance structure of the random effects was generalized positive definite matrix,and the heteroscedasticity structure was power function.The adjustment coefficient(Radj^2)of the mixed model was improved,and RMSE,MAE and MRAE were all significantly reduced.The values of the adjustment coefficient,RMSE,MAE and MRAE of the final model were 0.6998,4.7684 mm,3.7058 mm and 0.3916 mm,respectively.The predicted values of the mixed model reflected the differences between individual trees.The distribution range of branch diameter was found increasing with the increase of age groups,and the branch diameter growth showed difference between the age groups.[Conclusion]The accuracy of the mixed effect model of branch diameter can be improved by incorporating the random effects of age groups and individual trees into the model.Simulation of the branch diameter growth using the random effect parameters in the age group level can reasonably reflect their growth patterns and differences,and also conform to the significance of the tree physiology.Therefore,the mixed effect model based on age group and individual tree level can reasonably predict the growth of primary branch diameter of Larix olgensis at different ages.