基于非线性混合模型的油松天然林树高曲线研究

Height-diameter Models of Pinus tabuliformis Based on Nonlinear Mixed Models

树高和胸径作为重要的林分因子,二者的异速生长关系是林分生长与收获预估的基础。以北京市古石峪61块油松(Pinus tabuliformis)天然林样地为研究对象,样地按郁闭度CD≥0.6(类型Ⅰ)、0.5≤CD<0.6(类型Ⅱ)、0.4≤CD<0.5(类型Ⅲ)、0.3≤CD<0.4(类型Ⅳ)和CD<0.3(类型Ⅴ)划分5个等级类型,采用非线性混合模型方法,从26种常用树高曲线中选择拟合精度最高的作为基础模型,以类型和样地作为随机效应,分别基于单水平和嵌套二水平,考虑异方差构建最优的油松天然林树高曲线。采用AIC、BIC和负2倍的对数似然值对不同模型的精度进行比较,并用平均绝对误差、剩余均方根误差和调整后的决定系数对模型进行检验。结果表明,混合参数个数不同,模型预测精度不同;考虑异方差结构的嵌套2水平非线性混合模型预测精度高,调整后的决定系数达0.924 4,剩余均方根误差为0.842 1,可以准确地反映油松树高与胸径的关系,但与以样地作为随机效应的单水平样模型的差异不显著。

Tree height and diameter at breast height are two important forest factors.The allometric growth between two factors is the basis for the forecast of stand growth and harvest.In this study,61 plots of Pinus tabuliformis stands in Gushiyu Village,Beijing were used as research objects,each plot was divided into five classes by stand canopy density（CD）：CD≥0.6（TypeⅠ）,0.5≤CD0.6（TypeⅡ）,0.4≤CD0.5（TypeⅢ）,0.3≤CD0.4（TypeⅣ）,and CD0.3（TypeⅤ）.The best model from 26 height curve functions was selected to model the height-diameter relationships of P.tabuliformis with one level（type or plot effect）and nested two-level（nested effects of type and plot）nonlinear mixed effects（NLME）models.Then the best model which had the lowest AIC,BICand-2Log likelihood was chosen.Evaluation statistics,such as absolute mean residual（AMR）,root mean square error（RMSE）,and adjusted coefficient of determination（adj-R2）were used for precision analysis and comparison of different models.The results showed that there were different prediction accuracies of NLME models with different mixed parameters.The nested two-level NLME model considering heteroscedasticity structure possessed with predictable accuracy,with the high adjusted determination coefficient of 0.924 4and root mean square error of 0.842 1.The nested two-level NLME model would be allowed for estimating accuracy the height-diameter relationships of P.tabuliformis,but there were no significant differences between the nested two-level NLMEmodel and the one level（plots）NLME model.