林业科学  2016, Vol. 52 Issue (9): 95-102 PDF
DOI: 10.11707/j.1001-7488.20160911
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#### 文章信息

Cui Lingjun, Zhang Xiongqing, Duan Aiguo, Zhang Jianguo

A Hierarchical Bayesian Model to Predict Maximum-Size Density Line for Chinese Fir Plantation in Southern China

Scientia Silvae Sinicae, 2016, 52(9): 95-102.
DOI: 10.11707/j.1001-7488.20160911

### 作者相关文章

1. 中国林业科学研究院林业研究所 国家林业局林木培育重点实验室 北京 100091;
2. 南京林业大学南方现代林业协同创新中心 南京 210037

A Hierarchical Bayesian Model to Predict Maximum-Size Density Line for Chinese Fir Plantation in Southern China
Cui Lingjun1,2, Zhang Xiongqing1,2, Duan Aiguo1,2, Zhang Jianguo1,2
1. Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration Research Institute of Forestry, CAF Beijing 100091 ;
2. Collaborative Innovation Center of Sustainable Forestry in Southern China, Nanjing Forestry University Nanjing 210037
Abstract: 【Objective】 Self-thinning line is an important curve for describing the tree death in a certain stand. The objective of this study was to provide a new idea for exploring self-thinning law using hierarchical Bayesian method based on the Chinese fir (Cunninghamia lanceolata) data with different initial densities in Fujian Province. 【Method】 Firstly, the maximum-size density equation was established according to the relationship between stand quadratic mean diameter and number of trees per hectare. For analyzing the effect of initial density on maximum-size density line, we introduced the hierarchical Bayesian models: 1) random effect on the intercept; 2) random effect on the slope; 3) random effects on the intercept and slope. 【Result】 The results showed that the hierarchical Bayesian models (R2=0.867 8) were better than non-hierarchical Bayesian model (R2=0.859 3). The random effects of initial density were not significant neither on the intercept (σ02=0.008,SD=0.029) nor on the slope (σ12=0.003,SD=0.016). In addition, the uncertainty of model predictions was mostly due to within-subject variability. 【Conclusion】 Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables on maximum-size density line, which gave us the posterior distribution of parameters of maximum-size density line. The research of maximum-size density line could be benefit from the use of hierarchical Bayesian method and helpful for managing Chinese fir plantations.
Key words: hierarchical Bayesian method     Chinese fir plantation     maximum-size density line     initial planting density

1 试验地概况及数据整理

2 研究方法 2.1 最大密度线方程

Reineke(1933)根据林分平方平均直径(Q)和每公顷株数(N)的关系，提出最大密度线方程：

 (1)

Reineke(1933)方程中，认为b是一个常数，为-1.605。之后，Yoda等(1963)在此方程理论基础上，提出了植物平均生物量和密度的关系，并得到了著名的3/2法则。White(1981)认为树木的生物量和材积有着非常密切的关系，因此，在林业上一般将平均生物量用平均材积(V)代替，得到以下方程：

 (2)

2.2 贝叶斯理论

 (3)

 (4)

 (5)

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 (7)
2.3 分层贝叶斯

 (8)
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 (10)

2.4 先验分布

3 模型评价

 (11)

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4 结果与分析

 图 1 杉木最大密度线的截距和斜率的后验概率分布(M2) Fig.1 Posterior density curves of maximum-size density curve of Chinese fir for model M2
 图 2 杉木最大密度线及95%区间(M2) Fig.2 Maximum-size density curve and 95% interval of Chinese fir for model M2

5 结论与讨论