Study on single tree survival model of mixed stands of Larix olgensis, Abies nephrolepis and Picea jazoensis based on mixed effect model and survival analysis method
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摘要:目的 准确预测林木的生存和枯损是森林生长收获模型系统中十分重要的组成部分。构建基于混合效应模型和生存分析方法相结合的林木生存模型，能够提高林木枯损模型的精度。方法 以吉林省汪清林业局20块落叶松云冷杉林样地数据为例，基于生存分析方法中常用的6个时间参数分布回归模型（指数分布、Weibull分布、对数正态分布、对数Logistic分布、Gompertz分布及Gamma分布），把林分因子和立地因子作为协变量加入到模型中去，构建林木生存模型。并在此基础上考虑样地的随机效应，并与传统模型的模拟效果进行比较。结果 研究结果表明，随着单木初始胸径的增加，其枯损的风险降低，生存率提高；随着单木大于对象木断面积值的增加，其枯损的风险增加，生存率降低；随着林分密度的增加，林木枯损的概率增加，生存率降低；立地因子对林木的生存没有显著影响；6个参数分布回归模型中，Weibull分布的模拟精度最高。与固定效应模型相比，Weibull分布模型在考虑样地水平随机效应后，模型的模拟精度获得明显的提高，并且达到极显著程度。结论 在森林经营中，要提高林木的生存率，需采取科学合理的经营方法和经营时间，避免使林分的密度过大。Abstract:Objective Accurate prediction of tree mortality is a very important part of forest growth and yield model system. Constructing a tree survival model based on mixed effect model and survival analysis method can improve the precision of tree mortality model.Method Taking the data of 20 sample plots of mixed stands of Larix olgensis, Abies nephrolepis and Picea jazoensis in Wangqing Forestry Bureau of Jilin Province, northeastern China as the example, the tree mortality and survival model was constructed based on 6 parameter distribution models of survival analysis method (exponential distribution, Weibull distribution, log-normal distribution, log-Logistic distribution, Gompertz distribution, Gamma distribution), stand factor and site factor were added into the model as covariates. The sample plot’s random effect was considered and compared with the simulation effect of the traditional model.Result With the increase of initial DBH, the risk of tree mortality decreased and the survival rate increased; with the increase of BAL, the risk of mortality increased and the survival rate decreased; with the increase of stand density per hectare, the probability of tree mortality increased and the survival rate decreased; the good-fitness of Weibull distribution model was the best; compared with the fixed effect model, the simulation accuracy of Weibull distribution model was greatly improved after considering the sample plot’s random effect, and reached a very significant degree.Conclusion In forest management, if we want to improve the survival rate of trees, we should adopt scientific and reasonable management methods and management time to avoid excessive stand density.
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《北京林业大学学报》（原名《北京林学院学报》）创刊于1979年，由教育部主管、北京林业大学主办，国内外公开发行。历任主编分别为我国6位著名林学家汪振儒、沈国舫、关毓秀、王九龄、贺庆棠、尹伟伦。
《北京林业大学学报》是中文核心期刊、中国科技核心期刊、中国科学引文数据库统计源期刊、中国科技论文统计源期刊。荣获第二届国家期刊奖提名奖、第三届国家期刊奖百种重点期刊、中国精品科技期刊、中国高校精品科技期刊、中国国际影响力优秀学术期刊、“中国科技论文在线优秀期刊”一等奖等。
连续收录《北京林业大学学报》的著名检索期刊和数据库有：美国《化学文摘》（CA）、俄罗斯《文摘杂志》（AJ）、英国国际农业与生物学数据库（CABI）、英国《动物学记录》（ZR）、中国科学引文数据库（CSCD）、中国科技论文统计与引文分析数据库（CSTPCD）、《中国学术期刊文摘》《中国生物学文摘》、中国林业科技文献数据库等。
《北京林业大学学报》是中国最有代表性的林业科学期刊之一，主要刊登代表中国林业科学研究前沿创新水平的稿件。期刊定位为“立足中国，面向世界”的全国性林业科学期刊。面向国内外作者广泛征稿，对校内外稿件的质量要求一视同仁。
为保持学科特色，《北京林业大学学报》重点报道以林木遗传育种学、森林培育学、森林经理学、森林生态学、树木生理学、森林土壤学、森林植物学、森林保护学、自然保护区学、园林植物与观赏园艺、风景园林、水土保持与荒漠化防治、森林工程、木材科学与技术、林产化学加工工程、其他学科在林学上的应用等方面的论文。
《北京林业大学学报》现拥有以北京林业大学、中国林业科学研究院、中国科学院、国内其他综合性大学、农林院校、工科院校以及国外有关科研机构和大学等单位的研究人员为主的作者队伍。近年来随着期刊学术水平和影响因子的不断提高，投稿量显著增加，其中校外作者的投稿量占总收稿量的2/3左右。在此，我们对所有给《北京林业大学学报》赐稿的作者表示衷心的感谢!
《北京林业大学学报》自2015年起由原来的双月刊改为单月刊，大16开本，每月月底出版。每期定价50元。各地邮局发行，邮发代号：82−304。国内统一刊号：CN 11−1932/S。如当地邮局订阅不便或错过征订时间，也可直接汇款向本刊编辑部订阅。
地址：北京市海淀区清华东路35号《北京林业大学学报》编辑部
邮编：100083 发行电话：010−62338397 联系人：刘大林
发行电子信箱：liudalin@bjfu.edu.cn
网址：http://j.bjfu.edu.cn，http://journal.bjfu.edu.cn
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图 1 落叶松云冷杉林林木生存曲线趋势
Figure 1. Survival curve trend of mixed stands of Larix olgensis, Abies nephrolepis and Picea jazoensis
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图 2 301样地不同初始胸径的林木生存曲线趋势
Figure 2. Survival curve trend of trees with different initial DBH in sample plot 301
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图 3 不同初值密度对胸径10 cm林木生存率的影响
Figure 3. Effect of differential initial densities on tree survival rate of 10 cm DBH
表 1 样地基本情况表
Table 1 Basic characteristics of sample plots
样地号
Sample plot No.面积/hm2
Area/ha海拔
Elevation/m坡向
Aspect坡度
Slope/(°)间伐强度
Thinning
intensity/%平均胸径
Mean DBH/
cm林分密度/
(株·hm−2)
Plant number per hectare/
(plant·ha−1)公顷断面积/
(m2·hm−2)
Basal area
per hectare/
(m2·ha−1)树种组成
Species
composition301 0.077 5 760 东北 Northeast 10 40 14.9 955 16.83 6L3PJ1PK 302 0.077 5 760 东北 Northeast 10 0 14.7 1 572 26.69 5L4PJ1K 303 0.130 0 760 东北 Northeast 10 30 14.3 1 098 17.64 4L4PJ1PK1K 304 0.097 5 760 东北 Northeast 10 20 15.9 883 17.56 7L2PJ1K 305 0.200 0 780 西 West 18 30 15.1 1 158 20.64 6L2PJ2K 306 0.200 0 780 东北 Northeast 7 0 13.7 2 008 29.42 7L2PJ1K 307 0.200 0 780 西 West 18 20 15.0 1 153 20.50 9L1K 308 0.200 0 780 东北 Northeast 10 40 15.8 846 16.39 9L1K + PJ 309 0.250 0 660 西北 Northwest 6 0 15.6 1 189 22.86 6L2PJ1PK1K 310 0.250 0 670 西北 Northwest 10 30 16.2 860 17.74 5L3PJ1PK1K 311 0.250 0 670 西北 Northwest 6 20 17.2 833 19.39 6L2PJ1K 312 0.250 0 680 西北 Northwest 10 40 15.5 914 17.30 5L2PJ2K1PK 315 0.112 5 660 北 North 7 0 13.6 1 694 24.44 6L2PJ1PK 316 0.100 0 645 北 North 7 20 14.9 1 127 19.66 6L2K1PJ1PK 317 0.100 0 615 东北 Northeast 7 20 13.5 1 286 18.65 7L2PJ1K 318 0.112 5 610 东北 Northeast 7 40 14.4 919 15.03 7L2PJ1K 319 0.100 0 605 东北 Northeast 9 30 15.2 820 14.84 10L + PK 320 0.100 0 600 东北 Northeast 9 0 13.7 1 670 24.41 6L3PJ1K 注：L. 长白落叶松； PJ. 云杉；PK. 红松；K. 包括水曲柳、白桦、椴树和枫桦等。Notes：L indicates Larix olgensis; PJ indicates Picea jazoensis; PK indicates Pinus koraiensis; K includes Fraxinus mandshurica, Betula platyphylla, Tilia tuan, Butula costata, etc. 
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表 2 各种参数分布的模型类型
Table 2 Model types of various parameter distribution
模型类型
Model type概率密度函数
Probability density function生存函数
Survival function风险函数
Hazard function指数分布 Exponential distribution (Exponential) f(t)=λe−λt S(t)=e−λt h(t)=λ 威布尔分布 Weibull distribution (Weibull) f(t)=mλ(λt)m−1e−(λt)m S(t)=e−(λt)m h(t)=mλ(λt)m−1 对数正态分布 Log-normal distribution (log-normal) f(t)=1√2πmte−1/2[(lgt−λ)/m]2 S(t)=1−Φ(lgt−λm) h(t)=1√2πmte−1/2[(lgt−λ)/m]21−Φ(lgt−λm) 对数Logistic分布 Log-Logistic distribution (log-Logistic) f(t)=(mλ)(tλ)m−1[1+(tλ)m]2 S(t)=[1+(tλ)m]−1 h(t)=(mλ)(tλ)m−11+(tλ)m Gompertz分布 Gompertz distribution (Gompertz) f(t)=λexp(mt)exp[λm(1−emt)] S(t)=exp[λm(1−emt)] h(t)=λemt Gamma分布 Gamma distribution (Gamma) f(t)=λ(λt)m−1e−λtΓ(m) S(t)=1−∫t0tm−1e−uΓ(m)du h[t]=λ(λt)m−1e−λtΓ(m){1−F[t;T∼Γ(m)]} 注：t、u为时间变量，λ为尺度参数，m为形状参数。下同。Notes: t and u are time variables, λ is scale parameter, m is shape parameter. The same below.
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表 3 6个参数分布模型模拟结果
Table 3 Simulation results of six parameter distribution models
参数 Parameter Exponential log-normal log-Logistic Gompertz Gamma Weibull
(固定效应Fixed effect)Weibull
(随机效应Random effect)β0 4.396 3
(0.159 6) ***4.168 3
(0.159 2) ***4.053 2
(0.147 0) ***4.626 7
(0.167 6) ***4.232 1
(0.149 7) ***4.218 5
(0.139 5) ***3.690 2
(0.386 5) ***β1 0.051 2
(0.007 5) ***0.045 4
(0.006 9) ***0.044 8
(0.006 6) ***0.052 4
(0.007 6) ***0.046 0
(0.006 8) ***0.045 1
(0.006 6) ***0.067 7
(0.010 7) ***β2 −0.102 9
(0.020 9) ***−0.140 9
(0.021 0) ***−0.1239
(0.019 5) ***−0.108 9
(0.021 1) ***−0.118 7
(0.020 2) ***−0.094 3
(0.018 1) ***−0.039 6
(0.011 5) *β3 −0.000 6
(0.000 06) ***−0.000 6
(0.000 1) ***−0.000 6
(0.000 1) ***−0.000 7
(0.000 1) ***−0.000 6
(0.000 1) ***−0.000 6
(0.000 06) ***−0.000 4
(0.000 1) *m 1.168 8
(0.029 1)1.352 7
(0.032 7)0.018 5
(0.003 8)0.508 5
(0.103 3)1.377 3
(0.029 6)1.197 4
(0.029 7)AIC 12 973.7 12 943.4 12 947.5 12 952.3 12 952.0 12 939.1 12 697.1 BIC 12 998.3 12 974.2 12 978.3 12 983.7 12 988.9 12 969.9 12 702.9 −2logL 12 965.7 12 933.4 12 937.5 12 942.3 12 940.0 12 929.1 12 685.1 Waldχ2 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 注：β0为截距值，β1为单木初始胸径值，β2为大于对象木断面积值，β3为林分密度值；*为P < 0.05；**为P < 0.01；***为P < 0.001，括号内的数值为参数的标准差。Notes: β0 is intercept value, β1 is initial DBH of single tree, β2 is basal area larger than the object tree, β3 is value of stand density;
* means P < 0.05; ** means P < 0.01; *** means P < 0.001, values in brackets are SD of parameters.
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