第49卷第5期 林 业 科学 Vol.49,No.5 2013年5月 SCIENTIA SILVAE SINICAE May,2013 doi:10.11707/j.1001-7488.20130515 树木位置空间模式建模与预测* 金星姬李凤日'贾炜玮 张连军2 (1.:东北林业大学林学院哈尔滨150040：2.美国纽约州立大学环境科学和林业学院锯拉丘兹NY13210) 摘要：传统的林分生长与收获模型不能为林分和生态系统管理提供准确的空间信息。采用3种配对势函数的 Gibbs点过程模型对美国东北部50块云冷杉样地里树木的空间分布模式进行模拟。该Gibbs模型能够较好地模拟 这50块样地中的82%~84%，但其对完全随机分布和规则分布的样地模拟比对聚集分布的样地模拟效果要好。 使用常用的林分变量如林分密度、公顷断面积、林分平均胸径、平均树高、平均冠幅和冠长建立经验回归模型对 Gbbs模型的2个参数进行预测。结果表明这些回归模型对81%的样地可以得到满意的模拟效果，其中，100%的 完全随机分布样地、71%的规则分布样地和56%的聚集分布样地模拟效果较好。选择3块样地对树木的模拟空间 位置和实际观测位置的相似性进行对比和说明。 关键词：空间点模式；空间点过程：Gibbs模型；Ripley's K--function;马尔可夫链Monte Carlo(MCMC); Metropolis算法；Takacs-Fiksel方法 中图分类号：S711 文献标识码：A 文章编号：1001-7488(2013)05-0110-11 Modeling and Predicting Spatial Patterns of Trees Jin Xingji'Li Fengri'Jia Weiwei'Zhang Lianjun' (1.School of Forestry,Northeast Forestry University Harbin 150040; 2.College of Environmental Science and Forestry.State University of New York (SUNY-ESF)Syracuse,NY13210,USA) Abstract:Traditional forest growth and yield models have been criticized for their inability to provide precise spatial information for forest and ecosystem management.In this study the spatial patterns of trees within 50 spruce-fir plots in the Northeast,USA were modeled by a Gibbs point process model with three pair potential functions.In general,82%-84% of these 50 plots were modeled well by the Gibbs model.However,the complete spatial random CSR)and regular spatial patterns were modeled better than the clustered plots.Further,empirical regression models were developed to predict the two parameters of the Gibbs model using the available stand variables as predictors such as stand density,basal area, mean tree diameter,mean tree height,mean crown length,and mean crown width.The simulation results showed that 81%of the 50 plots were satisfactorily predicted by the empirical regression models.Among them,100%of the CSR plots,71%of the regular plots,and 56%of the clustered plots were predicted well by the empirical regression models. Three example plots were selected to illustrate the similarity between simulated tree locations and observed ones. Key words:spatial point pattern;spatial point process;Gibbs model;Ripley's K-function;Markov Chain Monte Carlo (MCMC);Metropolis algorithm;Takacs-Fiksel method chance success of different species or individuals over 1 Introduction time.The spatial distributions of trees strongly affect Spatial patterns of tree locations in a forest stand competition between neighboring trees,size variability reflect the complex historical and environmental mosaic and distribution,growth and mortality,and crown imposed by initial establishment patterns, structure Kuuluvainen et al.,1987;Kenkel,1988; microenvironment differences,climatic factors, Miller et al.,1989;Hara,1992;Moeur,1993; competing vegetation,management activities,and the Rouvinen et al.,1997;Dovciak et al.,2001 ) Received date:2012-08-06;Revised date:2012-10-12 Foundation project:Supported by the Scientifie Research Funds for Forestry Publie Welfare of China(201004026);Ministry of Education "Overseas Experts and Scholars"project. Corresponding author:Li Fengri. 万方数据第49卷第5期 2 0 1 3年5月 林 业 科 学 SCIENTIA SILVAE SINICAE VoL 49．No．5 May，2 0 1 3 doi：10．11707／j．1001-7488．20130515 树木位置空间模式建模与预测 金星姬1 李凤日1 贾炜玮1 张连军2 (1．东北林业大学林学院哈尔滨150040；2．美国纽约州立大学环境科学和林业学院锡拉丘兹NYl3210) 摘 要： 传统的林分生长与收获模型不能为林分和生态系统管理提供准确的空间信息。采用3种配对势函数的 Gibbs点过程模型对美国东北部50块云冷杉样地里树木的空间分布模式进行模拟。该Gibbs模型能够较好地模拟 这50块样地中的82％一84％，但其对完全随机分布和规则分布的样地模拟比对聚集分布的样地模拟效果要好。 使用常用的林分变量如林分密度、公顷断面积、林分平均胸径、平均树高、平均冠幅和冠长建立经验回归模型对 Gibbs模型的2个参数进行预测。结果表明这些回归模型对81％的样地可以得到满意的模拟效果，其中，100％的 完全随机分布样地、7t％的规则分布样地和56％的聚集分布样地模拟效果较好。选择3块样地对树木的模拟空间 位置和实际观测位置的相似性进行对比和说明。 关键词： 空间点模式；空间点过程；Gibbs模型；Ripley’S K—function；马尔可夫链Monte Carlo(MCMC)； Metropolis算法；Takacs．Fiksel方法 中图分类号：$711 文献标识码：A 文章编号：1001—7488(2013)05—0110—11 Modeling and Predicting Spatial Patterns of Trees Jin Xingji Li Fengri 1 Jia Weiwei Zhang Lianjun2 (1．School of Forestry，Northeast Forestry University Harbin 150040； 2．College ofEnvironmental Science and Forestry，State University ofNew York(SUNY-ESF)Syracuse，NYl3210，USA) Abstract：Traditional forest growth and yield models have been criticized for their inability to provide precise spatial information for forest and ecosystem management．In this study the spatial patterns of trees within 50 spruce·fir plots in the Northeast，USA were modeled by a Gibbs point process model with three pair potential functions．In general，82％一84％ of these 50 plots were modeled well by the Gibbs model．However，the complete spatial random(CSR)and regular spatial patterns were modeled better than the clustered plots．Further，empirical regression models were developed to predict the two parameters of the Gibbs model using the available stand variables as predictors such as stand density，basal area， mean tree diameter，mean tree height，mean crown length，and mean crown width．The simulation resuhs showed that 8l％of the 50 plots were satisfactorily predicted by the empirical regression models．Among them．100％of the CSR plots，7 1％of the regular plots，and 56％of the clustered plots were predicted well by the empirical regression models． Three example plots were selected to illustrate the similarity between simulated tree locations and observed ones． Key words： spatial point pattern；spatial point process；Gibbs model；Ripley’S K—function；Markov Chain Monte Carlo (MCMC)；Metropolis algorithm；Takacs—Fiksel method 1 Introduction Spatial patterns of tree locations in a forest stand reflect the complex historical and environmental mosaic imposed by initial establishment patterns， microenvironment differences， climatic factors， competing vegetation，management activities，and the chance success Of difierent species or individuals over time．The spatial distributions of trees strongly affect competition between neighboring trees，size variability and distribution，growth and mortality，and crown structure(Kuuluvainen et a1．，1987；Kenkel，1988； Miller et a1．，1989；Hara，1992；Moeur，1993； Rouvinen et a1．，1997；Dovciak et a1．，2001)． Received date：2012一08—06；Revised date：2012—10—12， Foundation project：Supported by the Scientific Research Funds for Forestry Public Welfare of China(201004026)；Ministry of Education“Overseas Expels and Scholars”project． $Corresponding author：Li Fen96． 万方数据