基于非线性混合效应模型的东北红松树高-胸径关系  

Relationship between tree height and DBH of Pinus koraiensis in northeastern China based on nonlinear mixed effects model

作　　者：李欣宇 叶尔江·拜克吐尔汉 王娟[3] 张新娜[1] 张春雨[1] 赵秀海[1] Li Xinyu;Yeerjiang Baiketuerhan;Wang Juan;Zhang Xinna;Zhang Chunyu;Zhao Xiuhai(Research Center of Forest Management Engineering of National Forestry and Grassland Administration,Beijing Forestry University,Beijing 100083,China;College of Forestry and Landscape Architecture,Xinjiang Agricultural University,Key Laboratory of Xinjiang Uygur Autonomous Region for Forest Ecology and Industrial Technology in Arid Zone,Urumqi 830052,Xinjiang,China;School of Ecology and Nature Conservation,Beijing Forestry University,Beijing 100083,China)

机构地区：[1]北京林业大学国家林业和草原局森林经营工程技术研究中心,北京100083 [2]新疆农业大学林学与风景园林学院,新疆干旱区林业生态与产业技术重点实验室,新疆乌鲁木齐830052 [3]北京林业大学生态与自然保护学院,北京100083

出　　处：《北京林业大学学报》2025年第3期38-48,共11页Journal of Beijing Forestry University

基　　金：国家重点研发计划(2023YFF1304004-06)。

摘　　要：【目的】构建红松非线性混合效应树高-胸径模型,并对比分析不同抽样方法和不同抽样数量对模型预测精度的影响,为研究红松的生长发育规律提供理论依据。【方法】基于吉林省蛟河地区与黑龙江省凉水地区两块样地合计4 441组红松数据,将数据随机分为建模数据(80%)和检验数据(20%)。对常见的15个树高-胸径模型进行拟合,筛选效果最佳的模型作为基础模型,并将胸高断面积、优势木平均高和林分平均胸径加入基础模型,构建最优广义模型。同时,引入样方水平的随机效应,分别构建基础混合效应模型和广义混合效应模型,并评价两个固定效应模型与两个混合效应模型的拟合能力和预测精度。使用检验数据验证模型预测精度,采用固定效应模型的平均水平预测(FPA)、混合模型的总体平均响应预测(MPA)和主体响应预测(MPS)3种预测类型进行比较。此外,对混合模型在随机抽取、抽胸径最大、抽胸径最小和抽取平均木(胸径接近平均值的样本)4种抽样方案下的预测精度和样本数量关系进行分析。【结果】(1)Prodan模型为最优基础模型(R2、RMSE、MAE分别为0.841、3.335 m、2.492 m),加入林分平均胸径、优势木平均高和胸高断面积的广义模型预测精度更高(R2、RMSE、MAE分别为0.914、2.449 m、1.816 m)。引入样方随机效应后,模型的精度显著提升(基础混合效应模型R2、RMSE、MAE分别为0.961、1.652 m、1.231 m,广义混合效应模型R2、RMSE、MAE分别为0.958、1.719 m、1.288 m)。(2)通过检验数据验证模型精度,结果表明模型预测精度均表现为MPA>FPA>MPS,广义模型预测精度总体优于基础模型。(3)4种抽样方案中,抽取平均木的抽样方法表现最佳,当抽取8株时,预测能力最优;在实际应用中,考虑人工成本与经济成本,抽取5株平均木测量树高以估计随机参数的方法亦合理可行。【结论】将林分因子和样方效应引�[Objective]This paper aims to construct a nonlinear mixed-effects model for the tree height-DBH relationship of Pinus koraiensis,compare the prediction accuracy of various sampling methods and sample sizes,and provide a theoretical basis for understanding the growth patterns of Pinus koraiensis.[Method]This study used 4441 sets of data from two sample plots in Jiaohe,Jilin Province,and Liangshui,Heilongjiang Province of northeastern China.The data were randomly divided into two parts,with 80%used for modeling and 20%for validation.Fifteen common tree height-DBH models were fitted,and the best-performing model was selected as the base model.Variables such as basal area,dominant height,and quadratic mean diameter were added to the base model to construct the optimal generalized model.Random effects at the plot level were also considered,resulting in the construction of a base mixed-effects model and a generalized mixed-effects model.The fitting ability and prediction accuracy of two fixed-effects models and two nonlinear mixed-effects models were evaluated.We validated the model prediction accuracy using validation data,compared three prediction types:fixed effects model average prediction(FPA),mixed model overall mean response prediction(MPA),and subject response prediction(MPS).Additionally,we analyzed the prediction accuracy and relationship between sample size and four sampling schemes for the mixed model:random sampling,the largest DBH sampling,the smallest DBH sampling,and average tree sampling(samples with DBH close to the average value).[Result](1)The optimal base model was the Prodan model(R2,RMSE,MAE were 0.841,3.335 m,2.492 m,respectively).The generalized model incorporating quadratic mean,dominant height,and basal area had the highest prediction accuracy(R2,RMSE,MAE were 0.914,2.449 m,1.816 m,respectively).Introducing plot-level random effects significantly improved model accuracy;the base mixed-effects model had R2,RMSE,MAE of 0.961,1.652 m,1.231 m,respectively,and the generalized mixed-effects model h

关 键 词：红松 树高-胸径模型 广义模型 非线性混合效应模型 抽样设计 

分 类 号：S757[农业科学—森林经理学]