基于非线性混合效应模型的云南松林树高曲线  

Tree height curves of Pinus yunnanensis forest based on nonlinear mixed effects model

作　　者：冯源 李贵祥 和丽萍 毕波 覃阳平 王发平 胡滨显 尹久明 Feng Yuan;Li Guixiang;He Liping;Bi Bo;Qin Yangping;Wang Faping;Hu Binxian;Yin Jiuming(Yunnan Academy of Forestry and Grassland,Kunming 650201,Yunnan,China;Yunnan Key Laboratory of Biodiversity of Gaoligong Mountain,Kunming 650201,Yunnan,China;Gaoligong Mountain Forest Ecosystem Observation and Research Station of Yunnan Province,Kunming 650201,Yunnan,China;Southwest Survey and Planning Institute,National Forestry and Grassland Administration,Kunming 650031,Yunnan,China;Chuxiong City State-Owned Forest Farm Jiuguan Management and Protection Station,Chuxiong 675099,Yunnan,China)

机构地区：[1]云南省林业和草原科学院,云南昆明650201 [2]云南省高黎贡山生物多样性重点实验室,云南昆明650201 [3]高黎贡山森林生态系统云南省野外科学观测研究站,云南昆明650201 [4]国家林业和草原局西南调查规划院,云南昆明650031 [5]楚雄市国有林场旧关管护站,云南楚雄675099

出　　处：《北京林业大学学报》2025年第3期49-60,共12页Journal of Beijing Forestry University

基　　金：云南省基础研究专项重大项目(202303AC100009);云南省林草局科技创新补助项目(K202222026)。

摘　　要：【目的】云南松林是云南省最重要的森林类型之一。构建云南松林树高曲线的非线性混合效应模型,对促进滇中地区乃至云南省云南松林科学经营及森林质量精准提升具有重要意义。【方法】基于云南省楚雄市旧关林场9块典型云南松林样地调查数据,选取12个基础模型拟合树高-胸径关系,筛选出最优模型作为基础模型。将树种组作为哑变量纳入模型,同时考虑林分变量的影响,并将样地作为随机效应,构建云南松林树高-胸径非线性混合效应模型。采用留一交叉验证对模型拟合效果进行检验。【结果】12个基础模型中,Schumacher模型表现最佳,被选为基础模型。在林分变量中,优势木平均高(Hd)和大于对象木断面积(BAL)与树高相关性显著,且具有生物学意义,因此被用于建立树高-胸径广义非线性模型。Hd与树高呈显著正相关,而BAL与树高呈负相关。最终建立的非线性混合效应模型能解释树高74%的变异,均方根误差为1.57 m。交叉验证结果表明,模型不存在过拟合现象,且残差无明显异方差。【结论】与传统基础模型相比,加入Hd和BAL的云南松林树高-胸径非线性混合效应模型能更准确地描述云南松林树高与胸径的关系。在森林经营实践中,可通过适地适树、调整林分密度和优化林分结构等措施降低林木个体竞争,从而促进林木树高生长。本研究为滇中地区云南松林树高曲线模拟研究提供方法借鉴及技术支持,对森林资源管理和生态保护具有重要的科学和实践价值。[Objective]Pinus yunnanensis forest is one of the most important forest types in Yunnan Province of southwestern China.The application of a nonlinear mixed effects model to simulate tree height curves of Pinus yunnanensis forests is important for advancing both scientific management and accurately assessing forest quality,not only in central Yunnan Province but also across the entire Yunnan Province.[Method]Based on the survey data of 9 sample plots from typical Pinus yunnanensis forests in Jiuguan Forest Farm,Chuxiong City of Yunnan Province,12 basic models were applied to establish the relationship between tree height and DBH,and the optimal model was selected as the basic model subsequently.The species group was then used as a dummy variable,and the stand variables and random effect of sample plots were incorporated into the model,yielding a nonlinear mixed effects model of tree height-DBH in Pinus yunnanensis forests;and model fit was evaluated using leave-one-out cross-validation.[Result]The Schumacher model was found to be the best of 12 basic models.Among many stand variables,the average top height(Hd)and sum of basal area larger than the subject tree(BAL)exhibited strong correlations with tree height and had biological significance;thus,both variables were chosen for constructing the generalized nonlinear model of tree height-DBH.Hd displayed a significant positive correlation with tree height,while BAL showed a negative correlation with tree height.The final nonlinear mixed effects model of Pinus yunnanensis forests accounted for 74%of the variation in tree height,with an RMSE value of 1.57 m.The results of cross-validation showed that the model was not overfitted and the residuals did not show obvious heteroscedasticity.[Conclusion]In contrast to basic models established through traditional methods,this study integrated the average top height and the sum of basal area larger than the subject tree into the nonlinear mixed effects model of Pinus yunnanensis forests,which can better describe the relationsh

关 键 词：云南松 树高曲线 非线性混合效应模型 立地质量 林木竞争 

分 类 号：S758[农业科学—森林经理学]