落叶松人工林单木生长模型的研究
|
摘要
本研究以孟家岗林场落叶松人工林为研究对象,采用1994-1999年和2004-2009两期5块复测样地数据,通过分析单木胸高断面积生长量与单木各调查因子之间的关系,选择自身相对胸径(RD)和有效冠表面积(ECSA)作为竞争因子,采用多元逐步回归技术建立了形式简洁、预估良好并便于生产应用的落叶松人工林单木胸高断面积与距离无关的生长模型。同时,本文应用该地区2007-2008年19块固定样地中95株解析木数据,根据经验方程选择单木树高曲线的基本模型,应用选定的模型对不同立地条件下的落叶松人工林进行树高曲线拟合,用再参数化的方法确定参数与各个林分调查因子之间的关系,从而最终建立单木树高曲线模型。另外,本研究还应用Logistic方程建立了落叶松人工林单木枯损率模型。
经过研究表明,落叶松人工林单木有效冠高(HEC)与树高(H)的正相关性最大,与冠长率呈负相关的关系；有效冠表面积(ECSA)与单木胸径(D)、有效冠高(HEC)及有效冠长(ECL)呈幂函数关系,有效冠表面积(ECSA)与有效冠长(ECL)的正相关性最大,同时与胸径(D)呈正比的关系,与有效冠高(HEC)呈反比；本文将有效冠表面积作为竞争因子,用多元逐步回归的方法建立落叶松人工林胸高断面积与距离无关的单木生长模型,同时与未引入有效冠表面积的生长模型进行比较,发现在引入有效冠表面积做为竞争因子的单木生长模型比未引入有效冠表面积的模型的复相关系数提高了3.2%,模型的精度提高0.03%,说明有效冠表面积对于单木的生长具有一定影响,将其作为单木竞争指标可以提高单木模型的拟合效果。
本文选择了Richards理论模型作为落叶松人工林单木树高曲线基本模型,同时发现参数与林分的地位级指数(SCI)成线性关系,而与年龄和密度的关系并不明显,最终建立的树高曲线方程为：H=(12.38025+0.74079SCI)(1-e-0.05D)0.66529+1.3,这个模型的优点是：当0 本研究所构造的单木生长模型,客观地反映了孟家岗林场落叶松人工林单木生长动态,可较好的模拟单木的生长过程,为该地区落叶松人工林的集约经营和生产决策提供了重要依据,具有一定理论和实践的价值。
The data used to develop individual model for Larix olgensis plantation were collected from 5 periodic permanent sample plots of 5-year periodic from 1994 to 1999 and 2004-2009 in Mengjiagang Forest, Based on analyzing relationship between diameter basal area increment of individual trees with tree surveying factors and choosing tree relative diameter(RD) and the effective crown surface area(ECSA) as competitive index, the growth models for distance-independent individual trees of Larix olgensis plantation, that have simple form, good predicting precision, and easily applicable, were developed using stepwise regression method.In this paper, the individual tree height curve of Larix olgensis in different site conditions was fitted with the model which was chosen according to experienced models, with the data of 95 analysis trees in 19 permanent plots of 2007-2008. The relationship between parameter and surveying stand factors was obtained and then the individual tree height curve model was established finally with the method of re-parameterization. Besides, the individual tree mortality probability model for Larix olgensis plantation had been developed based on Logistic equation.
The research results showed that the individual height of effective crown (HEC) of Larix olgensis plantation had the greatest positive correlation with height (H), and negative correlation with crown ratio (CR). The effective crown surface area(ECSA) had power function with individual diameter(D)、HEC and effective crown length(ECL). ECSA had the greatest positive correlation with effective crown length (ECL), positive proportional relationship with D, negative with HEC. Then employing ECSA as a competitive index, distance-independent individual growth model of basal area of Larix olgensis plantation was set up by multiple stepwise regressions. Then, the comparison of non-ECSA and ECSA individual growth model was made. The results showed that the multiple correlation coefficients were improved 3.2% and the accuracy of model was improved 0.03% after introducing ECSA. Therefore, the effective crown surface area (ECSA), which has influence on individual growth, can enhance the fitting effect of individual models as individual competition index.
In this study, the Richards theoretical model was chosen as the basic model for individual height curve model of Larix olgensis plantation, a linear relationship between the parameters and stand site class index (SCI) was found, however unobvious with age and density. Finally, the individual height curve model was built as follows: H= (12.38025+0.74079SCI)(1-e-0.05D)0.66529+1.3The advantage of this mode1 was that D could be equaled to zero when H was less than 1.3, conforming to the biological characteristic of tree growth. Besides, the diameter of trees was significantly related to mortality from the individual tree mortality probability model. As diameter decrease, the mortality probability of individual increased.
The individual tree growth models developed in this study can actually reflect the tree increment of Larix olgensis plantation of Mengjiagang Forest, and it could imitate the growth process of individual tree well. Furthermore, it will provide detail information of tree increment to intensive the forest management and decision-making for Larix olgensis plantation. Therefore, this research had the theoretic foundation and practical values.
经过研究表明,落叶松人工林单木有效冠高(HEC)与树高(H)的正相关性最大,与冠长率呈负相关的关系；有效冠表面积(ECSA)与单木胸径(D)、有效冠高(HEC)及有效冠长(ECL)呈幂函数关系,有效冠表面积(ECSA)与有效冠长(ECL)的正相关性最大,同时与胸径(D)呈正比的关系,与有效冠高(HEC)呈反比；本文将有效冠表面积作为竞争因子,用多元逐步回归的方法建立落叶松人工林胸高断面积与距离无关的单木生长模型,同时与未引入有效冠表面积的生长模型进行比较,发现在引入有效冠表面积做为竞争因子的单木生长模型比未引入有效冠表面积的模型的复相关系数提高了3.2%,模型的精度提高0.03%,说明有效冠表面积对于单木的生长具有一定影响,将其作为单木竞争指标可以提高单木模型的拟合效果。
本文选择了Richards理论模型作为落叶松人工林单木树高曲线基本模型,同时发现参数与林分的地位级指数(SCI)成线性关系,而与年龄和密度的关系并不明显,最终建立的树高曲线方程为：H=(12.38025+0.74079SCI)(1-e-0.05D)0.66529+1.3,这个模型的优点是：当0
The data used to develop individual model for Larix olgensis plantation were collected from 5 periodic permanent sample plots of 5-year periodic from 1994 to 1999 and 2004-2009 in Mengjiagang Forest, Based on analyzing relationship between diameter basal area increment of individual trees with tree surveying factors and choosing tree relative diameter(RD) and the effective crown surface area(ECSA) as competitive index, the growth models for distance-independent individual trees of Larix olgensis plantation, that have simple form, good predicting precision, and easily applicable, were developed using stepwise regression method.In this paper, the individual tree height curve of Larix olgensis in different site conditions was fitted with the model which was chosen according to experienced models, with the data of 95 analysis trees in 19 permanent plots of 2007-2008. The relationship between parameter and surveying stand factors was obtained and then the individual tree height curve model was established finally with the method of re-parameterization. Besides, the individual tree mortality probability model for Larix olgensis plantation had been developed based on Logistic equation.
The research results showed that the individual height of effective crown (HEC) of Larix olgensis plantation had the greatest positive correlation with height (H), and negative correlation with crown ratio (CR). The effective crown surface area(ECSA) had power function with individual diameter(D)、HEC and effective crown length(ECL). ECSA had the greatest positive correlation with effective crown length (ECL), positive proportional relationship with D, negative with HEC. Then employing ECSA as a competitive index, distance-independent individual growth model of basal area of Larix olgensis plantation was set up by multiple stepwise regressions. Then, the comparison of non-ECSA and ECSA individual growth model was made. The results showed that the multiple correlation coefficients were improved 3.2% and the accuracy of model was improved 0.03% after introducing ECSA. Therefore, the effective crown surface area (ECSA), which has influence on individual growth, can enhance the fitting effect of individual models as individual competition index.
In this study, the Richards theoretical model was chosen as the basic model for individual height curve model of Larix olgensis plantation, a linear relationship between the parameters and stand site class index (SCI) was found, however unobvious with age and density. Finally, the individual height curve model was built as follows: H= (12.38025+0.74079SCI)(1-e-0.05D)0.66529+1.3The advantage of this mode1 was that D could be equaled to zero when H was less than 1.3, conforming to the biological characteristic of tree growth. Besides, the diameter of trees was significantly related to mortality from the individual tree mortality probability model. As diameter decrease, the mortality probability of individual increased.
The individual tree growth models developed in this study can actually reflect the tree increment of Larix olgensis plantation of Mengjiagang Forest, and it could imitate the growth process of individual tree well. Furthermore, it will provide detail information of tree increment to intensive the forest management and decision-making for Larix olgensis plantation. Therefore, this research had the theoretic foundation and practical values.
引文
[1]Davis. L. S. and K. N. Johnson. Forest management New York: Megara-Hill Book Company.1987.
[2]李希菲等.大岗山实验局杉木人工林可变密度收获表的编制[J].林业科学研究,1998,1(4)：382-389.
[3]Daniels, R.F.1976. Simple competition indices and their correlation with annual loblolly pine growth[J]. Forest Sci.22:454-456.
[4]Monserud R A, Sterba H.A basal area increment model for individual trees growing in Even and uneven-aged forest stands in Austria [J]. For Ecol Manage,1996, 1(80):57-80.
[5]Wykoff W R, Crookston N L, and Stage A R. User's guide to the stand prognosis model. USDA For Serv, GTR INT-133,1982.
[6]Wykoff W R. Supplement to the User's guide for the stand prognosis model-Verrion5.0 [J] USDA For. Serv. Gen. Tech. Rep.1986.36p.
[7]卢军.长白山地区天然混交林单木生长模型的研究[J].哈尔滨：东北林业大学,2004.
[8]邵国凡.红松人工林单木生长模型的研究[J].东北林业大学学报,1985,13(3)：38-45.
[9]励龙昌.以潜能函数建立单木生长模型[J].东北林业大学学报,1990,18(4)：22-28.
[10]关玉秀,张守攻.竞争指标的分类及评价[J].北京林业大学学报,1992,14(4)：1-7.
[11]韩兴吉.林分生长和产量的数学模型(综述)[J].北京林业大学学报,1986,8(3)：85-98.
[12]黄家荣.马尾松人工林单木竞争指标及生长模型研究[J].林业科技,2001,26(3)：1-4.
[13]江希钿,邱学清,黄健儿.马尾松人工林单木生长模型的研究[J].华东森林经理,1992,3(6)：19-21.
[14]黄家荣,万兆溟.马尾松人工林与距离有关的单木模型研究[J].山地农业生物学报,2000,19(1)：10-15.
[15]陈辉,刘玉宝,廖正花.厚朴人工纯林种内竞争及单木生长模型的研究[J].经济林研究,1997,15(2)：11-13.
[16]吕理兴.栓皮栎天然林种内竞争关系及单木生长模型的研究[J].林业勘察设计,1998,(2)：14-19.
[17]邱学清.杉木简单竞争指数及单木生长模型的研究[J].福建林学院学报,1994,14(3)：195-200.
[18]黄家荣,杨世逸,温佐吾.马尾松人工林单木胸径生长模型研究[J].贵州农学院学报,1994,13(1)：12-16.
[19]陈东来,刘丽华,张景兰.林分密度的新指标-冠积指数[J].东北林业大学学报,2003,31(5)：15-17.
[20]王迪生,宋新民.一个新的单木竞争指标-相对有效冠幅比[J].林业科学研究,1994,7(3)：337-341.
[21]闫明准.帽儿山地区天然次生林单木生长模型的研究[D].哈尔滨：东北林业大学,2009.
[22]孟宪宇,张弘.闽北杉木人工林单木模型[J].北京林业大学学报,1996,18(2)：1-8.
[23]王孝安,段仁燕,王明利.太白红杉单木胸径生长模型的研究[J].武汉植物学研究,2005,23(2)：157-162.
[24]马友平,马友金等.日本落叶松人工林单山生长模型的研究[J].湖北民族学院学报,2002,6(2)：15-17.
[25]江希钿.柳杉单木直径生长及形状指数模型[J].福建林学院学报,1995,15(3)267-271.
[26]吕勇,汪新良,张晓蕾.杉木人工林单木竞争生长模型的研究[J].林业资源管理,1999,(3)：60-62.
[27]刘兆刚,李凤日,于金成.落叶松人工林单木模型的研究[J].植物研究,2003,23(2)：237-244.
[28]张惠光.福建柏单木生长模型的研究[J].中南林业调查规划,2006,25(3)：14.
[29]王文斗,李凤日,那冬晨等.辽东栎单木生长模型的研究[J].林业科技,2005,30(2)：11-13.
[30]吴巩胜,王政权.水曲柳落叶松人工林混交林中树木个体生长的竞争效应模型[J].应用生态学报,2000,11(5)：646-650.
[31]杜纪山.用二类调查样地建立落叶松单木直径生长模型[J].林业科学研究,1999,12(2)：160-164.
[32]杜纪山.林木生长和收获预估模型的研究动态[J].世界林业研究,1999,12(4)：19-22.
[33]Chulz H. Harding S. Vitality analysis of Scots pines using a multivariate approach. Forest Ecology and Management [J].186, (1-3):73-84.
[34]Buchman R G, Pederson S P, Walter N R.A tree survival model with application to species of the Great Lakes region [J]. Can J For Res,1983,13:601-608.
[35]Kohonen, T. Associative Memory: A System Theory Approach. Springer, New York.1977.
[36]孟宪宇主编.测树学(第二版).中国林业出版社,1995,286-287.
[37]洪伟,吴承祯.闽北杉木人工林密度效应新模型[J].浙江林学院学报,1996,13(1)：15-20.
[38]李凤日.林木直径分布的研究.林业译丛,1986,12-18.
[39]李凤日.兴安落叶松天然林直径分布及产量预测模型的研究[J].东北林业大学学报,1987,15(4)：8-16.
[40]蒋伊尹,李凤日.兴安落叶松天然林生长与收获的研究[J].林业科学,1989,25(5)：477-482.
[41]惠刚盈.林分直径结构模型的研究.林业科学研究[J],1995,7(3)：136-141.
[42]江希钿,林文清,陈兆算等.柳杉人工林单木材积生长模型的研究[J].福建林学院学报,1995,15(4)：380-385.
[43]吴承祯,洪伟.杉木人工林直径结构模型的研究[J].福建林学院学报,1998,18(2)：110-113.
[44]吴承祯,洪伟.林分直径结构新模型研究[J].西南林学院学报,1999,19(2)：90-95.
[45]吴承祯,洪伟.杉木数量经营学引论[M].北京：中国林业出版社,2000：158-191.
[46]Newham R M, Smith J H G Development and testing of stand models for Douglas-fir and lodgepole pine [J]. Forest Chron,1964,40:492-502.
[47]Lemmon P.E. and F.X. Schumacher. Stocking density around ponderosa pine trees. Forest Sci.1962.8(4).
[48]Stage A R. An expression for the effect of Aspect, slope, and habitat type on tree growth. Forest Sci. 1976.22(4):457-460.
[49]黄家荣.马尾松人工林生长的人工神经网络研究模型[D].北京：北京林业大学.2005.
[50]孟宪宇,邱水文.长白落叶松直径分布收获模型的研究[J].北京林业大学学报,1991,13(4)：9-16.
[51]白云庆,郝文康.测树学[M].哈尔滨：东北林业大学出版社,1986.
[52]刘艳艳.樟子松人工林树冠结构的研究[D].哈尔滨：东北林业大学,2005.
[53]Sprinz P T, Burkhart H E. Relationships between tree crowns, stems, and stand characteristics in unthinned loblolly pine plantations [J]. Can. J. For. Res,1987,17:534-538.
[54]高洪亮,贾炜玮.落叶松人工林地位指数级导向曲线模型的研究[J],林业科技情报,2009,41(1)：20-22.
[55]李凤日,王治富.落叶松人工林有效冠动态研究(有效冠的确定)[J],东北林业大学学报,1996,1(1)：1-8.
[56]刘兆刚,郭承亮,袁志强等.落叶松人工林树冠形状的预估[J].东北林业大学学报,1996,24(6)：14-19.
[57]惠刚盈,盛炜彤,Gadow K V.等.杉木人工林收获模型系统的研究[J].林业科学研究,1994,7(4)：353-358.
[58]刘平,马履一,贾黎明等.油松人工林单木树高生长模型研究[J],林业资源管理,2008,10(5)：50-55.
[59]孙圆,王万江.江苏省杨树树高曲线模型的研制[J].应用研究,2005,19(5)：31-34.
[60]吕勇.林木树高曲线模型研究[J].中南林学院学报,1997,17(4)：86-89.
[61]杜纪山.落叶松林木枯损模型[J].林业科学,1999,35(2)：4549.
[62]Clutter J L, Jones E P J. Prediction of growth after thinning in old-field slash pine plantations. USDA for Seri, Res Pap,1980.
[63]Bailey R L, Borders B E, Ware K D, Jones E.P, A compatible model relating slash pine plantation survival to density, age, site index, and type and intensity of thinning. Forest Sci.1985,31(1):180-189.
[64]Lee Y. Predicting mortality for even-aged stand of lodge pole pine. For Chiron,1971,47:29-32.
[65]Moore J A, Hamilton D A, Yao X, et al. Bedrock type significantly affects individual tree mortality for various conifers in the North West U.S.A. [J].Can. J. For. Res.2004,34(1):31-42.
[66]Monserud R A, Sterba H. Modeling individual tree mortality for Austrian forest species [J]. For. Ecol. Manage.,1999,113 (2):109-123.
[67]李凤日.落叶松人工林林分动态模拟系统的研究[D].北京：北京林业大学.1994.
[68]Glove G R, Hool J N. A basal area ratio predictor of loblolly pine plantation mortality. Forest Sci.1979, 25(2):275-282.
[69]Lowell K E, Mitchell R J. Stand growth projection: simultaneous estimation of growth and mortality using a single probabilistic function. Can J For Res,1987,17:1466-1470.
[70]Ryan K C, Peterson D L, Reinhardt E D. Modeling long-term fire-caused mortality of Douglas-fir[J]. Forest Sci.1988,34(1):190-199.
[71]Buchman R G, Pederson S P, Walters N R. A tree survival model with application to species of the Great Lakes region. Can J For Res,1983,13:601-608.
[72]王明亮,李希菲.非线性树高曲线模型的研究[J],林业科学研究,2000,13(1)：75-79.
[2]李希菲等.大岗山实验局杉木人工林可变密度收获表的编制[J].林业科学研究,1998,1(4)：382-389.
[3]Daniels, R.F.1976. Simple competition indices and their correlation with annual loblolly pine growth[J]. Forest Sci.22:454-456.
[4]Monserud R A, Sterba H.A basal area increment model for individual trees growing in Even and uneven-aged forest stands in Austria [J]. For Ecol Manage,1996, 1(80):57-80.
[5]Wykoff W R, Crookston N L, and Stage A R. User's guide to the stand prognosis model. USDA For Serv, GTR INT-133,1982.
[6]Wykoff W R. Supplement to the User's guide for the stand prognosis model-Verrion5.0 [J] USDA For. Serv. Gen. Tech. Rep.1986.36p.
[7]卢军.长白山地区天然混交林单木生长模型的研究[J].哈尔滨：东北林业大学,2004.
[8]邵国凡.红松人工林单木生长模型的研究[J].东北林业大学学报,1985,13(3)：38-45.
[9]励龙昌.以潜能函数建立单木生长模型[J].东北林业大学学报,1990,18(4)：22-28.
[10]关玉秀,张守攻.竞争指标的分类及评价[J].北京林业大学学报,1992,14(4)：1-7.
[11]韩兴吉.林分生长和产量的数学模型(综述)[J].北京林业大学学报,1986,8(3)：85-98.
[12]黄家荣.马尾松人工林单木竞争指标及生长模型研究[J].林业科技,2001,26(3)：1-4.
[13]江希钿,邱学清,黄健儿.马尾松人工林单木生长模型的研究[J].华东森林经理,1992,3(6)：19-21.
[14]黄家荣,万兆溟.马尾松人工林与距离有关的单木模型研究[J].山地农业生物学报,2000,19(1)：10-15.
[15]陈辉,刘玉宝,廖正花.厚朴人工纯林种内竞争及单木生长模型的研究[J].经济林研究,1997,15(2)：11-13.
[16]吕理兴.栓皮栎天然林种内竞争关系及单木生长模型的研究[J].林业勘察设计,1998,(2)：14-19.
[17]邱学清.杉木简单竞争指数及单木生长模型的研究[J].福建林学院学报,1994,14(3)：195-200.
[18]黄家荣,杨世逸,温佐吾.马尾松人工林单木胸径生长模型研究[J].贵州农学院学报,1994,13(1)：12-16.
[19]陈东来,刘丽华,张景兰.林分密度的新指标-冠积指数[J].东北林业大学学报,2003,31(5)：15-17.
[20]王迪生,宋新民.一个新的单木竞争指标-相对有效冠幅比[J].林业科学研究,1994,7(3)：337-341.
[21]闫明准.帽儿山地区天然次生林单木生长模型的研究[D].哈尔滨：东北林业大学,2009.
[22]孟宪宇,张弘.闽北杉木人工林单木模型[J].北京林业大学学报,1996,18(2)：1-8.
[23]王孝安,段仁燕,王明利.太白红杉单木胸径生长模型的研究[J].武汉植物学研究,2005,23(2)：157-162.
[24]马友平,马友金等.日本落叶松人工林单山生长模型的研究[J].湖北民族学院学报,2002,6(2)：15-17.
[25]江希钿.柳杉单木直径生长及形状指数模型[J].福建林学院学报,1995,15(3)267-271.
[26]吕勇,汪新良,张晓蕾.杉木人工林单木竞争生长模型的研究[J].林业资源管理,1999,(3)：60-62.
[27]刘兆刚,李凤日,于金成.落叶松人工林单木模型的研究[J].植物研究,2003,23(2)：237-244.
[28]张惠光.福建柏单木生长模型的研究[J].中南林业调查规划,2006,25(3)：14.
[29]王文斗,李凤日,那冬晨等.辽东栎单木生长模型的研究[J].林业科技,2005,30(2)：11-13.
[30]吴巩胜,王政权.水曲柳落叶松人工林混交林中树木个体生长的竞争效应模型[J].应用生态学报,2000,11(5)：646-650.
[31]杜纪山.用二类调查样地建立落叶松单木直径生长模型[J].林业科学研究,1999,12(2)：160-164.
[32]杜纪山.林木生长和收获预估模型的研究动态[J].世界林业研究,1999,12(4)：19-22.
[33]Chulz H. Harding S. Vitality analysis of Scots pines using a multivariate approach. Forest Ecology and Management [J].186, (1-3):73-84.
[34]Buchman R G, Pederson S P, Walter N R.A tree survival model with application to species of the Great Lakes region [J]. Can J For Res,1983,13:601-608.
[35]Kohonen, T. Associative Memory: A System Theory Approach. Springer, New York.1977.
[36]孟宪宇主编.测树学(第二版).中国林业出版社,1995,286-287.
[37]洪伟,吴承祯.闽北杉木人工林密度效应新模型[J].浙江林学院学报,1996,13(1)：15-20.
[38]李凤日.林木直径分布的研究.林业译丛,1986,12-18.
[39]李凤日.兴安落叶松天然林直径分布及产量预测模型的研究[J].东北林业大学学报,1987,15(4)：8-16.
[40]蒋伊尹,李凤日.兴安落叶松天然林生长与收获的研究[J].林业科学,1989,25(5)：477-482.
[41]惠刚盈.林分直径结构模型的研究.林业科学研究[J],1995,7(3)：136-141.
[42]江希钿,林文清,陈兆算等.柳杉人工林单木材积生长模型的研究[J].福建林学院学报,1995,15(4)：380-385.
[43]吴承祯,洪伟.杉木人工林直径结构模型的研究[J].福建林学院学报,1998,18(2)：110-113.
[44]吴承祯,洪伟.林分直径结构新模型研究[J].西南林学院学报,1999,19(2)：90-95.
[45]吴承祯,洪伟.杉木数量经营学引论[M].北京：中国林业出版社,2000：158-191.
[46]Newham R M, Smith J H G Development and testing of stand models for Douglas-fir and lodgepole pine [J]. Forest Chron,1964,40:492-502.
[47]Lemmon P.E. and F.X. Schumacher. Stocking density around ponderosa pine trees. Forest Sci.1962.8(4).
[48]Stage A R. An expression for the effect of Aspect, slope, and habitat type on tree growth. Forest Sci. 1976.22(4):457-460.
[49]黄家荣.马尾松人工林生长的人工神经网络研究模型[D].北京：北京林业大学.2005.
[50]孟宪宇,邱水文.长白落叶松直径分布收获模型的研究[J].北京林业大学学报,1991,13(4)：9-16.
[51]白云庆,郝文康.测树学[M].哈尔滨：东北林业大学出版社,1986.
[52]刘艳艳.樟子松人工林树冠结构的研究[D].哈尔滨：东北林业大学,2005.
[53]Sprinz P T, Burkhart H E. Relationships between tree crowns, stems, and stand characteristics in unthinned loblolly pine plantations [J]. Can. J. For. Res,1987,17:534-538.
[54]高洪亮,贾炜玮.落叶松人工林地位指数级导向曲线模型的研究[J],林业科技情报,2009,41(1)：20-22.
[55]李凤日,王治富.落叶松人工林有效冠动态研究(有效冠的确定)[J],东北林业大学学报,1996,1(1)：1-8.
[56]刘兆刚,郭承亮,袁志强等.落叶松人工林树冠形状的预估[J].东北林业大学学报,1996,24(6)：14-19.
[57]惠刚盈,盛炜彤,Gadow K V.等.杉木人工林收获模型系统的研究[J].林业科学研究,1994,7(4)：353-358.
[58]刘平,马履一,贾黎明等.油松人工林单木树高生长模型研究[J],林业资源管理,2008,10(5)：50-55.
[59]孙圆,王万江.江苏省杨树树高曲线模型的研制[J].应用研究,2005,19(5)：31-34.
[60]吕勇.林木树高曲线模型研究[J].中南林学院学报,1997,17(4)：86-89.
[61]杜纪山.落叶松林木枯损模型[J].林业科学,1999,35(2)：4549.
[62]Clutter J L, Jones E P J. Prediction of growth after thinning in old-field slash pine plantations. USDA for Seri, Res Pap,1980.
[63]Bailey R L, Borders B E, Ware K D, Jones E.P, A compatible model relating slash pine plantation survival to density, age, site index, and type and intensity of thinning. Forest Sci.1985,31(1):180-189.
[64]Lee Y. Predicting mortality for even-aged stand of lodge pole pine. For Chiron,1971,47:29-32.
[65]Moore J A, Hamilton D A, Yao X, et al. Bedrock type significantly affects individual tree mortality for various conifers in the North West U.S.A. [J].Can. J. For. Res.2004,34(1):31-42.
[66]Monserud R A, Sterba H. Modeling individual tree mortality for Austrian forest species [J]. For. Ecol. Manage.,1999,113 (2):109-123.
[67]李凤日.落叶松人工林林分动态模拟系统的研究[D].北京：北京林业大学.1994.
[68]Glove G R, Hool J N. A basal area ratio predictor of loblolly pine plantation mortality. Forest Sci.1979, 25(2):275-282.
[69]Lowell K E, Mitchell R J. Stand growth projection: simultaneous estimation of growth and mortality using a single probabilistic function. Can J For Res,1987,17:1466-1470.
[70]Ryan K C, Peterson D L, Reinhardt E D. Modeling long-term fire-caused mortality of Douglas-fir[J]. Forest Sci.1988,34(1):190-199.
[71]Buchman R G, Pederson S P, Walters N R. A tree survival model with application to species of the Great Lakes region. Can J For Res,1983,13:601-608.
[72]王明亮,李希菲.非线性树高曲线模型的研究[J],林业科学研究,2000,13(1)：75-79.