蒙古栎林单木生长模型系研究
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摘要
单木生长收获模型是天然林经营的重要工具。本文以蒙古栎林为对象，基于汪清林业局195块固定样地两期复测数据，建立了蒙古栎天然林的与距离无关的单木生长模型系，包括单木直径生长量模型、树高曲线模型、枯死模型和林分进界生长模型。
（1）通过分析蒙古栎林单木直径生长量与期初胸径、竞争和立地条件的关系，找出影响林木生长量的主要因子，并采用逐步回归技术建立了形式简洁、统计可靠并便于生产应用的蒙古栎林与距离无关的单木生长模型。研究结果表明，影响蒙古栎单木直径生长量的最主要因素是林木直径大小（D），其次是竞争指标，而立地条件对其影响不大。
（2）通过对比普通树高曲线和标准树高曲线的拟合结果发现，一般普通树高曲线的R2在0.65左右，而标准树高曲线的R2在0.73-0.91之间，可见增加了树木和林分因子的标准树高曲线，其精度有大幅提高。建立了蒙古栎单木标准树高曲线模型，模型自变量包括胸径、林分每公顷株数、林分每公顷断面积、优势木平均高。
（3）采用二分类的Logistic回归方法建立了蒙古栎林的单木枯死模型，结果表明起初胸径、竞争指数、林分密度都是显著影响树木枯死的因子，林木的直径是影响林木枯死的重要因子，直径越小，枯死概率越大。2检验的结果以及ROC曲线显示，使用logistic回归可以有效地反映树木的枯死情况，所建模型较合理。
（4）采用两阶段条件法建立了蒙古栎林分进界生长模型，首先使用二分类的logistic回归方法建立进界概率模型，模型的自变量包括海拔、地位级指数、林分每公顷断面积、林分每公顷株数，2检验的结果以及ROC曲线显示，该模型都具有较好的解释性和预测性。其次使用普通线性逐步回归建立了蒙古栎林的进界株数模型，检验的结果表明所建模型较合理。
（5）采用似乎不相关联立估计方法，建立了蒙古栎林直径生长量模型和枯死模型联立方程组，进行联合估计，保证了模型的相容性和参数估计的无偏性。对模型的精度及模型参数的稳定性进行了检验，该模型可以用于直径生长和枯死预估。
Individual tree growth models are of imporance for natural forest management. The dataused to develop individual model for Mongolian oak forest was collected from195re-measured permanent sample plots with10-year period from1997to2007in WangqingForest Bureau of northeast China. Growth model system was developed which inludedindividual diameter growth model, height-diameter model, mortality model, and recruitmentmodel.
(1) Based on analyzing the relationship between diameter increment of individual treeswith tree size, competitive status, and site condition and the major independent variables,individual tree growth model of Mongolian oak forest was developed using stepwise regressionmethod. The model was characterized by simple form, good predicting precision, and easyapplication. Main variables which had influence on diameter increment of individual trees weretree size and competition index. The site condition was not related with diameter increment.
(2) Fitting results of local and general height-diameter models were compared. R2valueswere around0.65and between0.73-0.91for local and general height-diameter models,repectively. This result indicated that the general height-diameter models had higher precision.So optimal generalized height-diameter model was developed，and the independed variblesinclude diameter, the number of trees per hectare, stand basal area per hectare, average heightof dominant trees.
(3) The mortality model for Mongolian oak was developed using binary logistic model,and results indicated that the diameter, competition index and stand density had significanteffects on tree mortality. As diameter decreases, the mortality probability increases.Chisquare-Test results and ROC curve showed that the binary logistic can generate rationalprediction.
(4) Two-stage estimate was used for recruitment model of Mongolian oak. Firstly, therecruitment probability model was developed using binary logistic model, and the independedvaribles include elevation，site class index，stand basal area per hectare, the number of trees perhectare. Chisquare-Test results and ROC curve show that the model has good explanatory andpredictability. Secondly, the number of recruitment trees were estimated using the ordinarylinear stepwise regression method, and results indicated that the model can generate rationalprediction.
(5) The simultaneous equations of individual diameter growth model and mortality modelfor Mongolian oak were developed using seemingly unrelated regression, so the parameterestimation of the group of correlated equations was unbiased and the equations werecompatible. Results indicated that the estimated values of the diameter growth and mortalityare accurate.
（1）通过分析蒙古栎林单木直径生长量与期初胸径、竞争和立地条件的关系，找出影响林木生长量的主要因子，并采用逐步回归技术建立了形式简洁、统计可靠并便于生产应用的蒙古栎林与距离无关的单木生长模型。研究结果表明，影响蒙古栎单木直径生长量的最主要因素是林木直径大小（D），其次是竞争指标，而立地条件对其影响不大。
（2）通过对比普通树高曲线和标准树高曲线的拟合结果发现，一般普通树高曲线的R2在0.65左右，而标准树高曲线的R2在0.73-0.91之间，可见增加了树木和林分因子的标准树高曲线，其精度有大幅提高。建立了蒙古栎单木标准树高曲线模型，模型自变量包括胸径、林分每公顷株数、林分每公顷断面积、优势木平均高。
（3）采用二分类的Logistic回归方法建立了蒙古栎林的单木枯死模型，结果表明起初胸径、竞争指数、林分密度都是显著影响树木枯死的因子，林木的直径是影响林木枯死的重要因子，直径越小，枯死概率越大。2检验的结果以及ROC曲线显示，使用logistic回归可以有效地反映树木的枯死情况，所建模型较合理。
（4）采用两阶段条件法建立了蒙古栎林分进界生长模型，首先使用二分类的logistic回归方法建立进界概率模型，模型的自变量包括海拔、地位级指数、林分每公顷断面积、林分每公顷株数，2检验的结果以及ROC曲线显示，该模型都具有较好的解释性和预测性。其次使用普通线性逐步回归建立了蒙古栎林的进界株数模型，检验的结果表明所建模型较合理。
（5）采用似乎不相关联立估计方法，建立了蒙古栎林直径生长量模型和枯死模型联立方程组，进行联合估计，保证了模型的相容性和参数估计的无偏性。对模型的精度及模型参数的稳定性进行了检验，该模型可以用于直径生长和枯死预估。
Individual tree growth models are of imporance for natural forest management. The dataused to develop individual model for Mongolian oak forest was collected from195re-measured permanent sample plots with10-year period from1997to2007in WangqingForest Bureau of northeast China. Growth model system was developed which inludedindividual diameter growth model, height-diameter model, mortality model, and recruitmentmodel.
(1) Based on analyzing the relationship between diameter increment of individual treeswith tree size, competitive status, and site condition and the major independent variables,individual tree growth model of Mongolian oak forest was developed using stepwise regressionmethod. The model was characterized by simple form, good predicting precision, and easyapplication. Main variables which had influence on diameter increment of individual trees weretree size and competition index. The site condition was not related with diameter increment.
(2) Fitting results of local and general height-diameter models were compared. R2valueswere around0.65and between0.73-0.91for local and general height-diameter models,repectively. This result indicated that the general height-diameter models had higher precision.So optimal generalized height-diameter model was developed，and the independed variblesinclude diameter, the number of trees per hectare, stand basal area per hectare, average heightof dominant trees.
(3) The mortality model for Mongolian oak was developed using binary logistic model,and results indicated that the diameter, competition index and stand density had significanteffects on tree mortality. As diameter decreases, the mortality probability increases.Chisquare-Test results and ROC curve showed that the binary logistic can generate rationalprediction.
(4) Two-stage estimate was used for recruitment model of Mongolian oak. Firstly, therecruitment probability model was developed using binary logistic model, and the independedvaribles include elevation，site class index，stand basal area per hectare, the number of trees perhectare. Chisquare-Test results and ROC curve show that the model has good explanatory andpredictability. Secondly, the number of recruitment trees were estimated using the ordinarylinear stepwise regression method, and results indicated that the model can generate rationalprediction.
(5) The simultaneous equations of individual diameter growth model and mortality modelfor Mongolian oak were developed using seemingly unrelated regression, so the parameterestimation of the group of correlated equations was unbiased and the equations werecompatible. Results indicated that the estimated values of the diameter growth and mortalityare accurate.
引文
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杜纪山．用二类调查样地建立落叶松单木直径生长模型．林业科学研究，1999，12(2)：160-164
杜纪山．落叶松林木枯死模型．林业科学，1999，35(2)：45-49
丁贵杰．马尾松人工林标准树高曲线模型的研究．浙江林学院学报，1997，14(3)：225-230
樊后保．应用生命表对蒙古栎种群的年龄结构的研究．福建林学院学报，1992，12（1）：50-56
樊后保，王义弘，臧润国．蒙古栎种群空间分布格局及其动态的研究．福建林学院学报，1994，14(2)：100-103
龚直文．长白山退化云冷杉林演替动态及恢复研究．北京林业大学博士论文，2009.
胡晓龙．林分枯死模型的研究．林业科学研究，1996，9(5)：525-529
雷相东．东北过伐林区几种典型森林类型的物种和林分结构多样性及采伐的影响研究．北京林业大学博士论文，2000
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