应用非线性混合模型建立白桦枝长与枝径关系

Relationship between Betula platyphyllum Branch Length and Branch Diameter Using Nonlinear Mixed Model

为了探究枝条生长的动态变化规律,以张家口永定河上游地区为研究区,在研究区设置4个100 m×100 m的固定样地,每个样地采集生长良好的白桦样木4株,共计采集16株天然白桦3 576个枝条数据。在白桦枝长的广义非线性模型的基础上构建样木效应混合模型、枝级效应混合模型和样木枝级嵌套混合模型,采用赤池信息准则(BIC)、贝叶斯信息准则(AIC)、对数似然值(LL)和似然比检验(LRT)等指标比较各模型的拟合效果。结果表明:样木和分枝等级两水平混合效应模型明显优于广义基础模型、样木效应模型和枝级效应模型;当b0、b2、b3作为样木随机参数,b1、b3作为分枝等级随机参数时,两水平混合模型拟合最优,决定系数(R2)和均方根误差分别为0.870 4、11.461 3。因此,考虑样木和分枝等级嵌套两层次的混合模型预测精度均高于广义非线性模型、样木随机效应模型和分枝等级随机效应模型,更好地模拟冀西北白桦的枝长与枝径关系。

To investigate the dynamic changes in branch growth, this study was conducted in the upstream area of Yongding River, Zhangjiakou, and four fixed plots measuring 100 m×100 m were established. In each plot, four birch ( Betula platyphylla Suk.) trees were selected, resulting in a total collection of 16 trees and 3 576 branch data. From the generalized nonlinear model of birch branch length, mixed models were constructed to account for tree-level effects, branch-level effects, and nested tree-branch effects. The fitting performance of each model was compared using criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood (LL), and likelihood ratio test (LRT). The two-level mixed effects model considering both tree and branch levels outperformed the generalized base model, tree effect model, and branch effect model. When b 0, b 2 , and b 3 were treated as random parameters for tree level, and b 1 and b 3 as random parameters for branch level, the two-level mixed effect model demonstrated the best fit with a coefficient of determination ( R 2) of 0.870 4 and a root mean square error (RMSE) of 11.461 3. Therefore, the mixed model incorporating the nested hierarchy of tree and branch levels exhibited higher predictive accuracy than the generalized nonlinear model, tree random effect model, and branch random effect model, providing a better simulation of the branch length-diameter relationship in birch trees in northwest Hebei.