摘要
森林是人类巨大的自然资源,具有多种功能。然而我国森林质量低下,迫切需要其提高生产力。天然林作为森林资源的主体,研究其生长规律,通过异龄林生长模型对其生长动态进行预测,并据此制定合理的经营方案,是当今林业研究的重大课题。本文在充分总结分析森林生长模型建模方法的基础上,以长白山云冷杉混交林为对象,利用大量皆伐样地样木数据和固定样地长期复测数据,建立了异龄林的生长动态模型预测体系,得到的主要结论有：
(1)以年龄为自变量的胸径、树高和材积生长方程都以Gompertz方程精度最高,根据森林数量成熟龄推算,红松、冷杉、云杉、椴树、色木和枫桦的胸径分别达到36.2cm、44.4cm、42.2cm、59.4cm、25.8cm、48.9cm即可采伐；普通树高曲线的R2在0.74左右,而标准树高曲线的R2在0.86-0.91之间,表明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。普通的一元材积方程精度最差；二元材积方程的精度最高；推导的一元材积方程精度居中。在胸径和树高都测量时,可使用本文建立的二元材积方程分别三个树种计算材积；在只测量了胸径时,则使用推导的一元材积方程分别树种计算材积。
(2)本研究综合考虑竞争因子(胸径、大于对象木的断面积、相对胸径、林分每公顷断面积、林分每公顷株数、林分密度因子)、林分属性因子(阔叶树断面积比重、树种本身的断面积比重、采伐强度)和立地因子(海拔、坡度、坡向、腐殖质厚度、土壤厚度)建立长白山云冷杉混交林中三个优势树种冷杉、云杉和红松的直径生长模型,结果表明,直径生长模型中应引入林分属性因子。其中采伐强度,不仅作为调节密度的指标,也通过影响周围环境影响林分的直径生长。此外,本文使用二分类的logistic回归,建立了冷杉、云杉和红松的枯损模型,结果表明,使用logistic回归可以有效地反映树木的枯损情况,所建模型均较合理。
(3)Weibull分布用来拟合天然异龄林的典型反J型直径结构效果最好,负指数相对于p和weibull分布效果较差。三种分布中,负指数的参数随时间变化有明显规律。本研究使用回归方法模拟负指数的参数变化,得到了直径结构的预测模型,该模型可以用来预测10年内的直径结构和断面积结构。此外,通过研究q值的变化规律发现,在未干扰林分中,q值随时间呈递减；在有采伐的样地中,采伐后q值增加,随后又开始下降。
(4)基于固定样地复测数据,使用多分类logistic回归模型建立不分树种,以及分别冷杉、云杉、红松和其他树种组的矩阵模型,结果表明所有模型均具有较好的预测性和解释性。此外,本文以局4样地为例对未来50年的生长动态进行预测,结果表明,采伐周期为10年,采伐强度为10%为最优的采伐方案。
本研究的主要创新点有如下三个方面：(1)本研究以长白山云冷杉混交林为例,基于大量样木和固定样地复测数据,首次系统地建立了异龄林的生长动态模型预测体系。(2)本研究首次在国内的异龄林直径生长模型中引入采伐强度这一变量。(3)本研究首次在国内使用多分类logistic回归求解矩阵模型中的转移概率。
进一步的研究可在以年龄为自变量的胸径、树高和材积生长模型,以及各种材积方程中,增加竞争因子等变量,以提高模型精度；可对合理的树种组划分深入研究,并尝试使用树高和直径的关系或者过去的生长量作为立地因子；建立与距离有关的生长模型；在用矩阵模型预测时,可以综合森林的多种目标,建立林分经营的多目标规划模型；使用新的方法如误差度量模型、混合效应模型等。
Forests are significant natural resources for human beings, and they have a variety of functions. However, the quality of Chinese forest is very low; thus, an urgent need is to increase their productivity. As natural forest is the dominant part of forest, its growth pattern and growth dynamic should be modelled, so as to make suitable management plan accordingly. This is a big project for Chinese forestry. In this dissertation, I took spruce-fir forest in Changbai Mountains as the object, used large dataset including clear-cutting plots, and numerous permanent re-measured plots, to develop a system of growth models for uneven-aged forest. Main conclusions are as following:
(1) The Gompertz function is optimal for fitting diameter, height, and volume growth models, which taking age as the independent variable. According to the quantitative mature age, Korean pine, fir, spruce, tilia, acer, and Korean birch should be cut while their diameter reach 36.2cm,44.4cm,42.2cm, 59.4cm,25.8cm and 48.9cm. R2 of local height-diameter models are around 0.74, while it is between 0.86-0.91 for general height-diameter models. This result indicates that the general height-diameter models have higher precision. Among different types of volume functions, the single entry volume equations have the lowest precision, general volume equations which using diameter and height as the independent variables have the highest precision, the one entry volume function deduced from general volume equations and height-diameter models have the medium precision. Therefore, when height data was available, general equations should be used, otherwise, the deduced one entry volume equations should be chosen.
(2)The competition group (including diameter, basal area in larger trees, relative diameter, basal area per ha, trees per ha, stand density index), stand attribute group (including basal area ratio of broadleaves species, basal area ration of the species itself, cutting intensity), and site index (including elevation, slope, aspect, humus depth, soil depth) were used as the candidate independent variables to develop individual diameter growth model for fir, spruce, and pine in spruce-fir forest in Changbai Mountains. Results indicated that stand attribute variables are very important in the model, and the cutting intensity may influence the diameter growth despite varying stand density. The mortality models for fir, spruce, and pine were developed using binary logistic model, and results indicated that the binary logistic can generate rational prediction.
(3) Weibull function, beta function, and negative-exponential function were compared for fitting diameter distribution in uneven-aged forest. Results show that the weibull function is the best, while negative-exponential function is the worst. But the parameters of negative-exponential function are decreasing along time apparently. The ordinary linear regression was used to simulate the parameters variation, so as to develop diameter dynamic model. This model can be used to predict the diameter distribution and basal area in 10 years. Additionally, the variations of q value show that it will decrease in undisturbed stand, while increase after cutting.
(4)Based on long-term permanent re-measure data, multinomial logistic models were used to develop matrix model for all species, fir, spruce, Korean pine, and other species group. Results indicated that this multinomial logistic method is very good, and can generate precise prediction. Using the matrix model developed to predict the dynamic for plot 4, as an example, and 13 different cutting scenarios were tested. From the dynamic of 50 years, I can make the conclusion that the optimal cutting strategy is to cut at 10% intensity with 10 years cutting cycle.
The main innovation of this thesis are the three following aspect:(1) The models of uneven-aged forest was first developed systematiclly by using large sample trees and permanent re-measure plots data in spruce-fir forest in Changbai Mountains. (2) It is the first time in China to include cutting intensity as an independent variable in diameter growth models. (3) Multinomial logistic models were first be used in China to calculate the transition probability in matrix models.
Further study could include competition variables into diameter-age, height-age, volume-age, volume-diameter, and volume-diameter & height functions. Better method for grouping species need be studied. As for the site index, height-diameter models and using past diameter increment could be tested. Spatial growth model is another new subject. The matrix models in this dissertation were only used to predict timber and size biodiversity, and it could be connected with more objectives. New methods such like error covariance model and mixed-effect models should be used to get higher precision.
引文
1.安慧,上官周平.密度对刺槐幼苗生物量及异速生长模式的影响[J].林业科学,2008,44(3)：151-155
2.柴一新.天然白桦林的特点与经营[J].东北林业大学学报,2000,28(5)：31-34
3.常敏.基于实测数据和经验模型的单木可视化研究[D].北京林业大学硕士论文,2005
4.曹新孙.森林采伐[M].北京：中国林业出版社.1990.
5.陈昌雄,曹祖宁,杨英恩等.天然针阔混交林立地质量的主要影响因子研究[J].福建林学院学报,2003,23(4)：343-347
6.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
7.陈信旺.杉木人工林最优经营密度模型的研究[J].林业勘察设计,2006,(1)：7-10
8.陈章水.杨树二元立木材积表的编制[J].林业科学研究.1989,2(1)：78-83
9.邓成,吕勇等.林分生长和收获模型整体化思路探讨[J].林业调查规划,2008,33(4)：7-9
10.邓红兵,王庆礼.红松、长白落叶松树高生长模型的研究及应用[J].辽宁林业科技.1997(5)：23-27
11.邓红兵,郝占庆,王庆礼,姜萍.红松单木高生长模型的研究[J].生态学杂志.1999,18(3)：19-22
12.丁贵杰.马尾松人工林标准树高曲线模型的研究[J].浙江林学院学报,1997,14(3)：225-230
13.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,1999a,12(2)160～164
14.杜纪山.落叶松林木枯损模型[J].林业科学,1999b,35(2)：45-49
15.段爱国,张建国,童书振.6种生长方程在杉木人工林林分直径结构上的应用[J].林业科学研究,2003,16(4)：423～429
16.范万圣,孔淑庆.对林分密度与密度指标的初步评价[J].山西水土保持科技,1994,(4)：34-36
17.房长有,段有,杨龙等.朝阳地区杨树二元立木材积表的编制[J].辽宁林业科技.2001,(4)：5-8
18.葛宏立.异龄林立地质量评价的数量指标探讨[D].北京林业大学硕士论文,1993
19.葛宏立,孟宪宇,唐小明.应用于森林资源连续清查的生长模型系统[J].林业科学研究,2004,17(4)：413-419.
20.葛宏立,项小强,何时珍等.年龄隐含的生长模型在森林资源连续清查中的应用[J].林业科学研究,1997,10(4)：420-424.
21.龚直文.长白山退化云冷杉林演替动态及恢复研究[D].北京林业大学博士论文.2009
22.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)：1-8
23.郭正刚,吴秉礼.灰色系统理论在林分蓄积量预测中的应用[J].甘肃农业大学学报,1999,34(2)：171-174
24.郭跃东.庞泉沟保护区天然华北落叶松林单木生长过程研究[J].山西林业科技.2009,38(2)：6-9
25.贺思慧.邻体竞争指数模型的改进及其在Ⅱ龄级华北落叶松营林中的应用[J].山西林业科技,1996(4)：11-14.
26.洪伟,吴承祯,闫淑君.广义Schumacher模型的改进及其应用[J].应用生态学报,2004,15(2)：241-244
27.胡晓龙.林分枯损模型的研究[J].林业科学研究,1996,9(5)：525-529
28.胡晓龙.长白落叶松林分断面积生长模型的研究[J].林业科学研究,2003,16(4)：449-452
29.胡晓龙,孙树德,王艳青.直径生长潜力模型的研究[J].辽宁林业科技,2002,(4)：4-5,28
30.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
31.黄家荣,孟宪宇,关毓秀.马尾松人工林单木生长神经网络模型研究[J].山地农业生物学报,2004,23(5)：386～391
32.江希钿,邱学清.杉木简单竞争指数及生长模型的研究[J].福建林学院学报,1994,14(3)：195-200
33.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
34.金星姬,贾炜玮,李凤日.基于BP人工神经网络的兴安落叶松天然林全林分生长模型的研究[J].植物研究,2008,28(3)：370-374,384
35.景向欣.樟子松人工林单木动态生长三维可视化模型的研究[D].东北林业大学硕士论文,2007
36.康晓梅,刘盛,陈建伟等.人工林林木竞争数量指标的对比研究[J].吉林林业科技.2002,31(6)：11-14
37.亢新刚,胡文力,董景林等.过伐林区检查法经营针阔混交林林分结构动态[J].北京林业大学学报,2003,25(6)：1-5
38.亢新刚,赵俊卉,刘燕.长白山云冷杉针阔混交过伐林优化结构研究[J].林业资源管理.2008,(3)：57-62.
39.赖巧玲,胥辉,杨为民.非参数估计在构造树高曲线中的应用[J].北京林业大学学报.2006,28(4)：77-81
40.雷加富.中国森林资源[M].北京：中国林业出版社,2005.
41.雷向东,常敏,陆元昌等.长白落叶松单木生长可视化系统设计与实现[J].计算机工程与应用,2006,17：180-183
42.雷相东,李永慈,向玮.基于混合模型的单木断面积生长模型[J].林业科学,2009,45(1)：74-80
43.雷相东,李希菲.混交林生长模型研究进展[J].北京林业大学学报.2003,25(3)：105-110
44.李春明.混合效应模型在森林生长模型中的应用[J].林业科学.2009,45(4)：131-138
45.李法胜.针叶混交异龄林最优收获调整问题的研究[D].北京林业大学硕士论文.1990
46.李凤日.落叶松人工林林分动态模拟系统的研究[D].北京林业大学博士论文.1994.
47.李永慈.林分生长收获模型的参数估计研究[D].北京林业大学博士论文.2004
48.林辉,彭长辉.人工神经网络在森林资源管理中的应用[J].世界林业研究,2002,15(3)：22-31
49.林通.木荷一元材积表和地径材积表的研制[J].福建林业科技.2007,34(2)：97-101
50.刘平.美国森林植被模拟系统FVS在北京地区人工林上的应用研究[D].北京林业大学博士论文,2007
51.刘平,马履一等.油松人工林单木树高生长模型研究[J].林业资源管理,2008a,(5)：50-56
52.刘平,马履一,贾黎明等.油松林木枯损率模型研究[J].林业资源管理,2008b,(2)：51-56
53.刘平,马履一等.油松中幼人工林单木胸径生长模型研究[J].沈阳农业大学学报,2009,40(2)：197-201
54.刘杏娥,王小青,江泽慧等.初植密度对小黑杨人工林生长和材质的影响以及材质评价模型的建立[J].北京林业大学学报,2007,29(6)：161-166
55.刘永霞.北京山地油松生长过程数量化模拟[D].北京林业大学博士论文.2007
56.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
57.卢军.长白山地区天然混交林单木生长模型的研究[D].东北林业大学硕士论文.2005
58.吕康梅.长白山过伐林区云冷杉针阔混交林最优林分结构和最优生长动态的研究[D].北京林业大学硕士论文,2006
59.吕勇.杉木人工林生长率模型的研究[J].林业科学,2002,38(1)：146-149
60.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
61.马丰丰.基于FVS的背景地区侧柏单木模型优化及应用[D].北京林业大学硕士论文.2008
62.马丰丰,贾黎明.林分生长和收获模型研究进展[J].世界林业研究,2008,21(3)：21-27
63.马建路,宣立峰,刘德君.用优势树全高和胸径的关系评价红松林的立地质量[J].东北林业大学学报,1995,23(2)：20-27
64.马履一,王希群.生长空间竞争指数及其在油松、侧柏种内竞争中的应用研究[J].生态科学,2006.25(5)：385～389
65.马翔宇,段文英,崔金刚.白桦人工林单木生长的人工神经网络模型研究[J].森林工程,2009,25(3)：30-33,38
66.孟宪宇.测树学·第三版[M].中国林业出版社.2006
67.孟宪宇,葛宏立.云杉异龄林立地质量评价的数量指标探讨[J].北京林业大学学报,1996,17(1)：1-9
68.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
69.宁金魁,郑小贤,高甲荣,等.干扰指数在密云县侧柏水源涵养林中的应用[J].北京林业大学学报,2003,25(6)：15-19
70.覃林,陈平留,刘健.闽北异龄林生长矩阵模型研究[J].生物数学学报,1999,14(3)：332-337
71.曲智林,胡海清.森林种群径阶转移模型中转移概率的估算方法[J].应用生态学报,2006,17(12)：2307～2310
72.曲智林,曲松,唐翠.基于矩阵模型的森林动态模拟与经营[J].东北林业大学学报,35(6)：28-30
73.任瑞娟,亢新刚,杨华.天然林单木生长模型研究概况[J].西北林学院学报.2008a,23(6)：203～206
74.任瑞娟,杨华,亢新刚,张艳红.单木竞争指数的研究应用概况[J].现代林业研究,2008b,2(1)：68-72
75.阮敬.SAS统计分析从入门到精通[M].北京：人民邮电出版社.2009.4
76.邵国凡,赵士洞,舒噶特.森林动态经营——兼论红松林的优化经营[M].中国林业出版社.1995
77.孙晓梅,李凤日等.长白落叶松人工林生长模型的研究[J].林业科学研究,1998,11(3)：306～312
78.孙圆,王万江.江苏省杨树树高曲线模型的研制[J].林业科技开发,2005,19(5)：31-34
79.唐守正.广西大青山马尾松泉林整体生长模型及其应用[J].林业科学研究.1991a,4(增刊)：8-13
80.唐守正,杜纪山.利用树冠竞争因子确定同龄间伐林分的断面积生长过程[J].林业科学,1999b,35(6)：35-41
81.唐守正,郎奎建,李永慈,等.ForStat2.0统计之林教程[M].北京：中国林业科学研究院资源信息研究所,2006：271-276
82.唐守正,李勇.生物数学模型的统计学基础[M].科学出版社,2002
83.唐守正,李希菲,孟昭和.林分生长模型研究的进展[J].林业科学研究.1993,6(6)：672-679
84.田有圳,黄金桃,林照授等.凹叶厚朴一元立木材积方程的研究[J].浙江林学院学报.2002,19(3)：255-258
85.王飞,代力民,邵国凡等.非线性状态方程模拟异龄林径阶动态——以长白山阔叶红松林为例[J].生态学杂志.2004,23(5)：101-105.
86.王飞.阔叶红松林结构调整的研究与应用[D].沈阳农业大学硕士论文.2005a
87.王飞,邵国凡,代力民等.矩阵模型在森林择伐经营中的应用[J].生态学杂志.2005b,24(6)：681-684.
88.王明亮,唐守正.标准树高曲线的研制[J].林业科学研究,1997,10(3)：259-264
89.王卫,肖锐,卢军.白河林业局单木枯损模型研究[J].林业科技情报,2008,40(2)：24-25,27
90.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
91.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
92.翁国庆.异龄林生长与收获模型[J].林业勘察设计,1996a,(1)：5-12.
93.翁国庆.林分动态生长模型的研究[J].林业贷源营理,1996b,(4)：25-28
94.向玮,吕勇,邱林.湖南黄丰桥林场杉木树高曲线模拟研制[J].中南林业调查规划.2007,26(1)：16-18
95.向玮,雷相东,刘刚等.近天然落叶松云冷杉林单木枯损模型研究[J].北京林业大学学报,2008,30(6)：90-98
96.谢哲根.长白山林区云冷杉为主的混交异龄林生长动态分析及最优择伐序列[D].北京林业大学硕士论文.1991
97.胥辉,全宏波,王斌.思茅松标准树高曲线的研究[J].西南林学院学报,2000,20(2)：74-77
98.徐悦,陈昌华,蒋之富,等.天然赤松胸径与树高相关模型的研究[J].林业调查规划,2008,33(3)：56-58
99.薛俊杰,白景萍,郭晋平,等.邻体干扰模型的改进[J].山西农业大学学报,1999,19(2)：17-18.
100.薛毅和陈丽萍.统计建模与R软件[M].清华大学出版社,2007
101.闫明准.帽儿山地区天然次生林单木生长模型的研究[D].东北林业大学硕士论文.2009
102.闫明准,刘兆刚.帽儿山地区次生林椴树单木胸高断面积生长模型的研究[J].森林工程,2009,25(2)：1-4,21
103.杨龙,殷有,房长有等.辽宁朝阳地区杨树二元材积表与一元材积表的比较[J].沈阳农业大学学报.2002,33(1)：51-52
104.姚东和,吕勇.基于人工神经网络的杉木竞争生长模型研究[J].中南林学院学报.2001,21(1)：17-20
105.殷传杰.异龄林动态系统与经营模型的研究——兼天山中东部林区天山云冷杉林的应用[D].北京林业大学硕士论文.1988
106.喻泓,杨晓晖,慈龙骏.内蒙古呼伦贝尔沙地不同樟子松林竞争强度的比较[J].应用生态学报,2009,20(2)：250-255
107.曾伟生.异龄林的生长动态与最优经营[D].北京林业大学硕士论文.1990
108.曾伟生.国家森林资源连续清查中的材积估计问题探讨[J].中南林业调查规划.2007,26(2)：1-4
109.曾种,雷相东,刘宪钊等.落叶松云冷杉林单木树高曲线的研究[J].林业科学研究2009,22
(2)：182～189
110.张成程.落叶松人工林空间结构优化经营及可视化模拟的研究[D].东北林业大学硕士论文,2009
111.张成程,李凤日,赵颖慧.落叶松人工林空间结构优化的探讨[J].植物研究,2008,28(5)：632-636&640
112.张会儒.落叶松云冷杉林生长模拟及生态采伐更新技术体系研究[D].中国林业院博士论文,2006
113.张贵,李伟.广义Schumacher方程及其应用[J].中南林学院学报.1999,19(2)：39-42
114.张少昂.兴安落叶松天然林林分生长模型和可变密度收获表的研究[J].东北林业大学学报.1986,14(3)：17-26
115.张思玉,郑世群.笔架山常绿阔叶林优势树种群内种间竞争的数量研究[J].林业科学,2001,37(1)：185-188
116.张伟东,伊柏峰.森林资源动态管理系统中人工林进界木株数模型研究[J].华东森林经理,2003,17(1)：56-58
117.张向忠,倪志云,张瑞文等.落叶松人工林二元材积模型的研究[J].河北农业大学学报.1996,19(1)：100-101
118.张彦东,王庆成,谷艳华.水曲柳落叶松人工幼龄混交林生长与种间竞争关系[J].东北林业大学学报,1999,27(2)：6-9.
119.张跃西.邻体干扰模型的改进及其在营林中的应用[J].植物生态学与地植物学学报,1993,17(4)：352-357.
120.张志云,欧阳勋志,蔡学林.林分立木材积估计的新方法[J].江西农业大学学报.1999,21(1)：99-102
121.章时运.灰色系统理论预测森林生长量方法的初探[J].林业资源管理,1997(6)：58-60
122.赵俊卉,亢新刚,刘燕.长白山主要针叶树种最优树高曲线研究[J].北京林业大学学报,2009a,31(4)：13-18.
123.赵俊卉,亢新刚,张慧东,刘燕.长白山主要针叶树种胸径和树高变异系数与竞争因子的关系[J].应用生态学报,2009b,(8)：1832-1837.
124.赵晓云.柳杉单立木生长模型拟合的初步研究[J].四川林业科技,2004,25(1)：55-58
125.郑鹏,李金铭,赖晓燕等.主成分分析法与逐步聚类法在树种分类中的应用[J].福建电脑,2006,(2)：20-21
126.郑嵘,肖淑萍,杨小纯等.峡江县人工湿地松中幼龄林进界胸径预估模型[J].江西林业科技,2004,(2)：15-16
127.郑小贤.信州落叶松人工林生长模型及其系统收获表的研究[J].林业科学,1997,33(1)：42-47
128.郑跃军.最优化与最优控制在异龄林收获调整中的应用[D].北京林业大学硕士论文.1987
129.朱慧,洪伟,吴承祯.闽东柳杉人工林经营密度与生长关系的研究[J].江西农业大学学报,2004,26(1)：51-55.
130.朱永红,翁国庆.热带雨林生长与收获预估简介[J].林业资源管理,2000(6)：14-17
131.邹春静.沙地云杉种内、种间竞争的研究[J].植物生态学报,1998,22(3)：269,274.
132.邹得棉.马尾松天然林立地质量评价[J].福建林业科技,2001,28(1)：76-78
133. Adame P, Hynynen J, Canellas I, et al.2008.Individual-tree diameter growth model for rebollo oak (Quercus pyrenaica Willd.) coppices[J]. Forest Ecology and Management,1990.255:1011-1022.
134. Adame P, Rio M D, Canellas I. A mixed nonlinear height-diameter model for Pyrenean oak (Quercus pyrenaica Willd.) [J]. Forest ecology and management.2008,256:88-98
135. Alenius, V., Ho"kka", H., Salminen, H., Evaluating Estimation Methods for Logistic Regression in Modeling Individual-tree Mortality, Modelling Forest Systems[R]. CABI, London,2003. pp. 225-236.
136. Atta-Boateng J, Moser JW. A method for classifying commercial tree species of an uneven-aged mixed species tropical forest for growth and yield model construction [J]. Forest Ecology and Management,1998,104:89-99
137. Bertelink H H. A growth model for mixed forest stands. Forest Ecology and Management, 2000,134:29-43
138. Biging GS, Dobbertin M. Evaluation of competition indices in individual tree growth models[J]. Forest Science,1995,41 (2):360-377
139. Boltz F, Carter DR. Multinomial logit estimation of matrix growth model for tropical dry forest of eastern Bolivia[J]. Canadian Journal of Forest Research,2006,36:2623-2632
140. Bravo-Oviedo A, Sterba H, del Ri'o M, Bravo F. Competition-induced mortality for Mediterranean Pinus pinaster Ait. and P. sylvestris L[J]. Forest Ecology and Management,2006,222:88-98.
141. Buongiorno J, Michie BR. A matrix model of uneven-aged forest management [J]. Forest Science. 1980.26(4):609-625.
142. Buongiomo J, Peyron JL, et al. Growth and management of mixed-species, uneven-aged forests in the French Jura:implications for economic returns and tree diversity [J]. Forest Science,1995, 41(3):397-429.
143. Bruce D, Wensel L C. Modeling forest growth approaches, definitions and problems in proceeding of IUFRO conference:forest growth modeling and prediction [R]. USDA Forest Service General Technical Report NC-120. Minneapolis, Minnesota,1987:1-8.
144. Calama Rafael and Montero Gregorio. Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain[J]. Canadian Journal of Forest Research,2004,34:150-163
145. Curtis R,郝敏,郝文康.美国东部异龄林的培育和经营异龄林的生长和收获[J].国外林业,1990(4)：13-16.
146. Dolph KL. Prediction of periodic basal area increment for young-growth mixed conifers in the Sierra Nevada [R]. United States Department of Agriculture Forest Service Pacific Southwest Forest and Range Experiment Statlon,1988.Research Paper PSW-190.
147. Dorado F C, Die'guez-Aranda U, Anta M B et al. A generalized height-diameter model including random components for radiata pine plantations in northwestern Spain [J]. Forest Ecology and Management,2006,229:202-213
148. Eid T, Tuhus E. Models for individual tree mortality in Norway [J]. Forest Ecology and Management.2001.154,69-84.
149. Favrichon V. Modeling the dynamics and species composition of a tropical mixed-species uneven2aged natural forest:effects of alternative cutting regimes[J]. Forest Science,1998,44 (1): 113～124.
150. Hostin P J, Titus S J. Indirect site productivity models for white spruce in Alberta's boreal mixedwood forest[J]. Forestry Chronicle,1996,72 (1):73-79
151. Huang SM. Diameter and height growth models[D]. Ph.D. Thesis in University of Alberta,1992.
152. Huang SM, Titus S J. An index of site productivity for uneven-aged or mixed-species sands[J]. Canadian Journal of Forest Research,1993,23:558-562
153. Huang SM. An aged-independent individual tree height prediction model for boreal spruce-aspen stands in Alberta[J]. Canadian Journal of Forest Research,1994,24:1295-1301
154. Huang SM, Titus SJ. Estimating a system of nonlinear simultaneous individual tree models for white spruce in boreal mixed-species stands[J]. Canadian Journal of Forest Research,1999,29: 1805-1811
155. Huang SM. Reality, Models and Parameter Estimation-The Forestry Scenario[M]. Edmonton: Amaro, A., Sesimbra,2002,243-250.
156. Huang SM, Meng SX, Yang YQ. Using nonlinear mixed model technique to determine the optimal tree height prediction model for black spruce[J]. Modern Applied Science,2009,3(4):3-18
157. Hubert. Sustainable forest management[M]. Springer,2006
158. Jogiste, K. Productivity of mixed stands of Norway spruce and birch affected by population dynamics:a model analysis[J]. Ecological Modelling,1998.106 (1),77-91.
159. Jonsson B. Thinning response function for single trees of Pinus sylvestris L and Picea abies (L) Karst[J]. Scandinavian Journal of Forest Research,1995,10:353～369.
160. Jorge C. Miguel E., Antonio V. Projection of height and diameter growth and estimation of future volume yield in a silvopastoral trial[J]. Forest Ecology and Management,1999,123:275-285
161. Kariuki M. Modelling the impacts of various thinning intensities on tree growth and survival in a mixed species eucalypt forest in central Gippsland, Victoria, Australia[J]. Forest Ecology and Management.2008. doi:10.1016/j.foreco.2008.07.035.
162. Kiernan D H., Bevilacqua E, Nyland R D. Individual-tree diameter growth model for sugar maple trees in uneven-aged northern hardwood stands under selection system[J]. Forest Ecology and Management,2008.256:1579-1586.
163.Kimmins, J.P. Modeling the sustainability of forest production and yield for a changing and uncertain future[J]. Forestry Chronicle,1990.66,271-280.
164. Kimmins, J.P. Scientific foundations for the simulation of ecosystem function and management in FORCYTE-11[R]. Northwest region, Forestry Canada,1993. Information Report NOR-X-328, p. 88.
165.Korol, R.L., Running, S.W., Milner, K.S. Incorporating intertree competition into an ecosystem model[J]. Canadian Journal of Forest Research.1994.25,413-424.
166. Korol, R.L., Milner, K.S., Running, S.W., Testing a mechanistic model for predicting stand and tree growth[J]. Forest Science.1996.42,139-153.
167. Kristian K. Height growth patterns of Scots pine and Norway spruce in the coastal areas of western Finland[J]. Forest Ecology and Management,2000,135:205-216
168. Landsberg JJ. Physiological Ecology of Forest Production[C]. Academic Press, Sydney, Australia. 1986.
169. Lexer(?)d NL. Growth and yield models for uneven-sized forest stands in Finland[J]. Forest Ecology and Management,2005,206:91-108
170. Lin C R, Buongiorno J, Vasievich M. A multi-species, density-dependent matrix growth model to predict tree diversity and income in northern hardwood[J]. Ecological Modelling,1996,91 193-211
171. Liu J, Burkhart H E, Amateis R L. Projecting crown measures for loblolly pine trees using a generalized thinning response function [J]. Forest Science,1995,41 (1):43～53.
172. Lu HC, Buongiorno J. Long and short-term effects of alternative cutting regimes on economic returns and ecological diversity in mixed-species stands [J]. Forest Ecology and Management.1993. 58,173-192.
173. Lu J, Li FR. Individual Tree Growth Models for Natural Mixed Forests in Changbai Mountains, Northeast China[J]. Journal of Korean Forestry Society,2007,96(2):160～169
174. Maltamo M. Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand[J]. Silva Fennica,1997,31 (1):53-65
175. Mohren, G.M.L., Burkhart, H.E., Jansen, J.J. Contrasts between biologically-based process models and management-oriented growth and yield models[J]. Forest Ecology and Management.1994,69, 1-5.
176. Monserud RA, Sterba H. A basal area increment model for individual trees growing in even and uneven aged forest stands in Austria[J]. Forest Ecology and Management,1996,80:57-80
177. Monserud RA, Sterba H. Modelling individual tree mortality for Austrian forest species[J].1999. Forest Ecology and Management,113,109-123.
178. Moravie MA, Durand M, Houllier F. Ecological meaning and predictive ability of social status,vigour and competition indices in a tropical rain forest (India) [J]. Forest Ecology and Management,1999,117:221-240
179. Namaalwa J, Eid T, Sankhayan P. A multi-species density-dependent matrix growth model for the dry woodlands of Uganda[J]. Forest Ecology and Management,2005,213:312-327
180. Nicholas NS, Gregoire TG,& Zedaker SM. The reliability of tree crown position classification[J]. Canadian Journal of Forest Research,1991,21:698-701.
181. Nicolas P, Avner BH, Yann G. Modelling diameter class distribution with a second-order matrix model[J]. Forest Ecology and Management.2003,180:389-400
182. Nunifu K T. Calibrating t he mixedwood growth model (MGM) for Lodgepole Pine (Pinus contorta) and associated species in Alererta[D]. University of Alberata,2003.
183. Ostaff WS, Carvell KL, Wiant H V. Comparative site index of eight hardwood species on the West Virginia University Forest[R]. West Virginia University Forestry Notes,1982,9:18-20
184. Payandeh B, Wang Y. Variable stocking version of Plonskips yield tables formulated[J]. Forestry Chronicle,1996a,72 (2):181-184
185. Payandeh B, Wang Y. Variable stocking yield functions for the boreal mixed wood in Ontario[J]. Forestry Chronicle,1996b,72 (4):416-419
186. Perez D. Growth and volume equations developed from stem analysis for Tectona grandis in costa rica[J]. Journal of tropical forest science.2008,20(1):66-75
187. Peng CH, Liu JX, Dang QL, et al. TRIPLEX:a generic hybrid model for predicting forest growth and carbon and nitrogen dynamics[J]. Ecological Modelling.2002,153:109-130
188. Pienaar L V, Rheney J W. Modeling stand level growth and yield response to silvicultural treatments[J]. Forest Science,1995,41 (3):629～638.
189. Porte A., Bartelink H.H. Modelling mixed forest growth:a review of models for forest management[J]. Ecological Modelling,2002,150:141-188
190. Pukkala T, La"hde E, Laiho O. Growth and yield models for uneven-sized forest stands in Finland[J]. Forest Ecology and Management.2009,258:207-216
191. Quang V C. Prediction of annual diameter growth and survival for individual trees from periodic measurements [J]. Forest Science,2000,46 (1):127-134.
192. Reynolds, M.R., Burk, T.E. and Huang, W. Goodness-of-fit tests and model selection procedures for diameter distribution models[J]. Forest Science,1988,34:373-399
193. Roberts S D, Harrington C A. Individual tree growth response to variable-density thinning in coastal Pacific Northwest forests[J]. Forest Ecology and Management,2008.255:2771-2781.
194. Sanchez-Gonzalez M, Canellas I and Montero G. Generalized height-diameter and crown diameter prediction models for cork oak forests in Spain[J]. Sistemasy Recursos Forestales,2007,16(1): 76-88
195. Schroder J, Soalleiro RR, Alonso GV. An age-independent basal area increment model for maritime pine trees in northwester Spain[J]. Forest Ecology and Management,2002.157:55-64.
196. Sharma M and Parton J. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach[J]. Forest ecology and management,2007,249:187-198
197. Shifley SR, Fan Z, Kabrick JM, Jensen RG. Oak mortality risk factors and mortality estimation [J]. Forest Ecology and Management,2006,229,16-26.
198. Shi HJ. Local Analysis of Tree Competition and Growth[D]. State of University of New York College of Environmental Science and Forestry Syracuse,2003.
199. Solomon D S, Herman D A, Leak W B. FIBER 3.0:An eco logical growth model for Northeaster forest types[R]. USDA For Serv, Gen Tech Rep N E2204,1995:24.
200. Somers GL, Nepal SK. Linking individual-tree and stand-level growth models[J]. Forest Ecology and Management.1994,69:233-243
201. Stage AR, Ledermann. TEffects of competitor spacing in a new class of individual-tree indices of competition semi-distance-independent indices computed for Bitterlich versus fixed-area plots[J]. Canadian Journal of Forest Research,2008.38:890-898.
202. Sterba H, Blab A, Katzensteiner K. Adapting an individual tree growth model for Norway spruce (Picea abies L. Karst.) in pure and mixed species stands[J]. Forest ecology and management, 2002.159:101-110.
203. Temesgen, H.& Gadow, K. V. Generalized height-diameter models-an application for major tree species in complex stands of interior British Columbia[J]. European Journal of Forest Research, 2004,123,45-51.
204. Thomas N L. Modeling individual tree growth from data with highly irregular measurement intervals [J]. Forest Science,2006,52 (2):198-208.
205. Trasobares A, Tome M, Miinac J. Growth and yield model for Pinus halepensis Mill. in Catalonia, north-east Spain[J]. Forest ecology and management,2004a,203:49-62.
206. Trasobares A, Pukkala T. Using past growth to improve individual-tree diameter growth models for uneven-aged mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia, north-east Spain[J]. Annals of Forest Science,2004b,61:409-417
207. Usher M B. A matrix approach to the management of renewable resources with special reference to selection forests[J].Journal of applied ecology,1966,3:355-367
208. Uzoh F C C., Oliver W W. Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model[J]. Forest ecology and management,2008,256:438-445.
209. Uzoh F C C., Oliver W W. Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models[J]. Forest ecology and management,2006.221:147-154.
210. Vanclay JK. Modelling Forest Growth and Yield:Applications to Mixed Tropical Forests[M]. CAB International, Wallingford UK,1994
211. Vanclay JK. Assessing site productivity in tropical moist forests:a review[J]. Forest ecology and management,1992a.54:257-287.
212. Vanclay, JK. Modelling regeneration and recruitment in a tropical rainforest[J]. Canadian Journal of Forest Research,1992b,22:1235-1248
213. Wang GG. Is height of dominant trees at a reference diameter an adequate measure of site quality? [J]. Forest Ecology and Management,1998,112:49-54
214. Wimberly M C, Bare B B. Distance-dependent and distance-independent models of Douglas-fir and western hemlock basal area growth following silvicultural treatment[J]. Forest Ecology and Management,1996.89:1-11.
215. Wykoff W R. A Basal Area Increment Model for Individual Conifers in the Northern Rocky Mountains[J]. Forest Science.1990,136,4:1077-1104.
216. Yang YQ. Mortality models for major boreal mixedwood species in Alberta[D]. University of Alberta,2002.
217. Yang YQ, Titus SJ, Huang SM. Modeling individual tree mortality for white spruce in Alberta[J]. Ecological Modelling,2003,163,209-222.
218. Yue CF, Kohnle U, Hein S. Combining Tree-and Stand-Level Models:A New Approach to Growth Prediction[J]. Forest Science.2008,54(5):553-566
219. Zhang LJ, Bi HQ, et al. Modeling spatial variation in tree diameter-height relationships[J]. Forest Ecology and Management,2004,189:317-329
220. Zhao DH, Borders B, Wilson M. A density-dependent matrix model for bottomland hardwood stands in the Lower Mississippi Alluvial Valley[J]. Ecological Modelling,2005,184:381-395
221. Zhao DH, Borders B, Wilson M. Individual-tree diameter growth and mortality models for bottomland mixed-species hardwood stands in the lower Mississippi alluvial valley[J]. Forest ecology and management,2004.199:307-322.
222. Zhou M. Managing resources for multiple purposes Markov models of southern mixed loblolly pine-hardwood forests[D]. Ph.D. Thesis in University of Wisconsin-Madison.2005.