落叶松人工林枝条直径和长度的非线性混合模型

陈东升; 孙晓梅; 李凤日

doi:10.3969/j.issn.1000-2006.2015.06.014

陈东升,孙晓梅,李凤日

南京林业大学学报（自然科学版） ›› 2015, Vol. 39 ›› Issue (06) : 74-80.

PDF(2344933 KB)

国家林草科技领军期刊
中国精品科技期刊
中国高校百佳科技期刊
江苏省新闻出版政府奖期刊奖
RCCSE林学权威期刊（A+）
CSCD核心期刊
Scopus数据库收录期刊
中文核心期刊
SCD核心期刊

作者加群：102861116

微信公众号：南京林业大学学报

高级检索

PDF(2344933 KB)

南京林业大学学报（自然科学版） ›› 2015, Vol. 39 ›› Issue (06) : 74-80. DOI: 10.3969/j.issn.1000-2006.2015.06.014

研究论文

落叶松人工林枝条直径和长度的非线性混合模型

陈东升¹,孙晓梅^1*,李凤日²

作者信息 +

Nonlinear mixed models of branch diameter and length in larch plantation

CHEN Dongsheng¹,SUN Xiaomei^1*,LI Fengri²

Author information +

文章历史 +

摘要

基于95株落叶松解析木、843个枝条实测数据,构建了枝条直径和长度的传统非线性模型、含树木变量的非线性模型、非线性混合模型和含有误差结构的非线性混合模型,比较了各模型的拟合精度,分析了枝条直径和长度的变化规律。结果表明:含有误差结构的落叶松人工林枝条直径和长度非线性混合模型拟合精度最优,决定系数R²分别为0.783 7和0.865 7,均方根误差(RMSE)分别为0.377 7和0.286 6,且消除了异方差现象,独立样本检验结果也证实该模型是最优预测模型; 落叶松人工林枝条直径和长度与枝条所在位置和树木胸径、冠幅、高径比紧密相关,在树冠顶部分布的一级枝条直径和长度都较小,而在树冠底部分布的则较大,树冠下部枝条的直径和长度受树木形态因子的影响更明显。

Abstract

The objective of this work was to establish the models for predicting branch diameters and lengths in the larch plantations. The traditional nonlinear model, including the trees variable nonlinear model, the nonlinear mixed models and the nonlinear mixed model containing the error structure of branch diameter and length were constructed based on the data of 843 standard branches collected from 95 sample trees, and the prediction accuracies were also evaluated, by the analyses of the changing rule of the branch diameters and lengths. The results indicated that the nonlinear mixed model with the error structure for the branch diameter and length prediction was the best, with R² values of 0.783 7 and 0.865 7, and RMSE values of 0.377 7 and 0.286 6, respectively, and the phenomenon of heteroscedasticity was also elminated. The validation by using independent samples also verified that this model was optimal. The model showed that the branch diameter and length were closely related to branch location within the living crown and diameter at breast height, crown width, ratio of height to diameter. The diameter and length of branches were smaller in the top but was bigger in the bottom of crown. The diameter and length of branches in the bottom of crown were more obvious in different trees.

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用

陈东升,孙晓梅,李凤日. 落叶松人工林枝条直径和长度的非线性混合模型[J]. 南京林业大学学报（自然科学版）. 2015, 39(06): 74-80 https://doi.org/10.3969/j.issn.1000-2006.2015.06.014

CHEN Dongsheng,SUN Xiaomei,LI Fengri. Nonlinear mixed models of branch diameter and length in larch plantation[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY. 2015, 39(06): 74-80 https://doi.org/10.3969/j.issn.1000-2006.2015.06.014

中图分类号： S758.1

参考文献

[1] Chmura D J, Rahman M S, Tioelker M G. Crown structure and biomass allocation patterns modulate aboveground productivity in young loblolly pine and slash pine[J].Forest Ecology and Management, 2007,243(2):219-230.
[2] 刘兆刚,李凤日. 樟子松人工林树冠内一级枝条空间的分布规律[J]. 林业科学,2007,43(10):19-27. Liu Z G, Li F R. Modeling of spatial distribution of primary branches within the crowns of Pinus sylvestris stands[J]. Scientia Silvae Sinicae, 2007, 43(10): 19-27.
[3] Cluzeau C, Le Goff N, Ottorini J M.Development of primary branches and crown profile of Fraxinus excelsior[J]. Canadian Journal of Forest Research, 1994, 24(12): 2315-2323.
[4] Roeh R L, Maguire D A. Crown profile models based on branch attributes in coastal Douglas fir[J]. Forest Ecology and Management,1997, 96(1): 77-100.
[5] Mäkinen H, Ojansuu R, Sairane P, et al. Predicting branch characteristics of Norway spruce(Picea abies(L.)Karst.)from simple stand and tree measurements[J]. Forestry, 2004, 76(5):525-546.
[6] Hein S, Weiskittel A R, Kohnle U. Branch characteristics of widely spaced Douglas fir in south-western Germany: comparisons of modelling approaches and geographic regions[J]. Forest Ecology and Management, 2008, 256(5): 1064-1079.
[7] Maguire D A, Moeur M, Bennett W S. Models for describing basal diameter and vertical distribution of primary branches in young Douglas fir[J]. Forest Ecology and Management, 1994,63(1): 23-55.
[8] Mäkinen H, Colin F. Predicting the number, death, and self-pruning of branches in Scots pine[J]. Canadian Journal of Forest Research, 1999, 29(8):1225-1235.
[9] Mäkinen H, Niemisto O R. Predicting external branch characteristics of planted silver birch(Betula pendula Roth)on the basis of routine stand and tree measurements[J]. Forest Science, 2003,49(2): 301-317
[10] Achim A, Gardiner B, Daquitaine R. Predicting the branching properties of sitka spruce grown in Great Britain[J]. New Zealand Journal of Forestry Science, 2006, 36(2/3):246-264.
[11] Hein S, Spiecker H.Comparative analysis of occluded branch characteristics for Fraxinus excelsior and Acer pseudoplatanus with natural and articial pruning[J]. Canadian Journal of Forest Research, 2007, 37(8):1414-1426.
[12] Beaulieu E, Schneider R, Berninger F, et al. Modeling jack pine branch characteristics in Eastern Canada[J]. Forest Ecology and Management, 2011, 262(9):1748-1757.
[13] Weiskittel A R, Maguire D A, Monserud R A. Response of branch growth and mortality to silvicultural treatments in coastal Douglas fir plantations: Implications for predicting tree growth[J]. Forest Ecology and Management, 2007, 251(3):1-13.
[14] 刘兆刚.樟子松人工林树冠动态三维图形模拟技术的研究[D].哈尔滨:东北林业大学,2007. Liu Z G. The three dimensional computer graphics simulation technique of tree grown dynamic for Mongolian Scots pine in plantation[D]. Harbin:Northeast Forestry University, 2007.
[15] 李永慈,唐守正. 用Mixed和Nlmixed过程建立混合生长模型[J].林业科学研究,2004,17(3):279-283. Li Y C, Tang S Z. Establishment of tree height growth model based on Mixed and Nlmixed of SAS[J]. Forest Research, 2004, 17(3):279-283.
[16] 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. Li C M. Application of mixed effects models in forest growth model[J]. Scientia Silvae Sinicae, 2009, 45(4):131-138.
[17] Fabian C U, William W O.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(3): 438-445.
[18] Weiskittel A R, Garber S M, Johnson G P, et al. Annualized diameter and height growth equations for Pacific Northwest plantation-grown Douglas-fir western hemlock and red alder[J]. Forest Ecology and Management, 2007, 250(3): 266-278.
[19] 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. Lei X D, Li Y C, Xiang W. Individual basal area growth model using multi-level linear mixed model with repeated measures[J].Scientia Silvae Sinicae, 2009, 45(1): 74-80.
[20] 姜立春,杜书立. 基于非线性混合模型的东北兴安落叶松树高和直径生长模拟[J]. 林业科学研究,2012,25(1):11-16. Jiang L C, Du S L. Height and diameter growth modeling of dahurian larch based on nonlinear mixed model in northeastern China[J].Forest Research, 2012, 25(1): 11-16.
[21] Yang Y, Huang S, Meng S X. Development of a tree-specific stem profile model for white spruce: a nonlinear mixed model approach with a generalized covariance structure[J]. Forestry, 2009, 82(5):541-555.
[22] Yang Y, Huang S, Trincado G, et al. Nonlinear mixed-effects modelling of variable-exponent taper equations for lodgepole pine in Alberta Canada[J]. Europe Journal of Forest Research,2009.128(4):415-429.
[23] 姜立春,杜书立,李凤日.基于随机效应的兴安落叶松材积生长模拟[J].应用生态学报,2011,22(11):2963-2969. Jiang L C, Du S L, Li F R. Simulation of Larix gmelinii tree volume growth based on random effect[J].Chinese Journal of Applied Ecology, 2011, 22(11): 2963-2969.
[24] 曾伟生,唐守正,夏忠胜,等. 利用线性混合模型和哑变量模型方法建立贵州省通用性生物量方程[J].林业科学研究,2011,24(3):285-291. Zeng W S, Tang S Z, Xia Z S, et al. Using linear mixed model and dummy variable model approaches to construct generalized single-tree biomass equations in Guizhou[J]. Forest Research, 2011, 24(3): 285-291.
[25] Fehrmann L, Lehtonen A, Kleinn C, et al. Comparison of linear and mixed-effect regression models and a k-nearest neighbour approach for estimation of single-tree biomass[J]. Canadian Journal of Forest Research, 2008, 38(1):1-9.
[26] 符利勇,雷渊才,曾伟生. 几种相容性生物量模型及估计方法的比较[J]. 林业科学,2014,50(6):42-54. Fu L Y, Lei Y C, Zeng W S. Comparison of several compatible biomass models and estimation approaches[J]. Scientia Silvae Sinicae, 2014, 50(6): 42-54.
[27] 姜立春,张锐,李凤日. 基于线性混合模型的落叶松枝条长度和角度模型[J]. 林业科学,2012,48(5):53-60. Jiang L C, Zhang R, Li F R. Modeling branch length and branch angle with linear mixed effects for dahurian larch[J].Scientia Silvae Sinicae, 2012, 48(5): 53-60.
[28] 董灵波,刘兆刚,李凤日,等. 基于线性混合模型的红松人工林一级枝条大小预测模拟[J].应用生态学报,2013,24(9): 2447-2456. Dong L B, Liu Z G, Li F R, et al. Primary branch size of Pinus koraiensis plantation: a prediction based on linear mixed effect model[J].Chinese Journal of Applied Ecology, 2013, 24(9): 2447-2456.
[29] 李凤日. 长白落叶松人工林树冠形状的模拟[J]. 林业科学,2004,40(5):16-24. Li F R. Modeling crown profile of Larix olgensis trees[J]. Scientia Silvae Sinicae, 2004, 40(5):16-24.
[30] Zeide B. Analysis of growth equations[J]. Forest Science, 1993, 39(2): 594-616.
[31] Roeh R L, Maguire D A. Crown profile models based on branch attributes in coastal Douglas fir[J]. Forest Ecology and Management, 1997, 96(1/2): 77-100.
[32] Lindstrom J M, Bates D M. Nonlinear mixed effects models for repeated measures data[J]. Biometrics 1990, 46(3): 673-687.
[33] Pinheiro J C, Bates D M. Mixed-effects models in S and S-PLUS[M]. New York:Springer, 2000:528.
[34] Trincado G, Burkhart H E. A generalized approach for modeling and localizing stem profile curves[J]. Forest Science, 2006, 52(6): 670-682.
[35] 陈东升,李凤日,孙晓梅,等.基于线性混合模型的落叶松人工林节子大小预测模型[J].林业科学,2011,47(11):121-128. Chen D S, Li F R, Sun X M, et al. Models to predict knot size for larch plantation using linear mixed model[J]. Scientia Silvae Sinicae, 2011, 47(11):121-128.
[36] Mäkinen H, Colin F. Predicting branch angle and branch diameter of Scots pine from usual tree measurements and stand structural information[J]. Canadian Journal of Forest Research, 1998, 28(11):1686-1696.
[37] Umeki K, Kikuzawa K.Patterns in individual growth, branch population dynamics and growth and mortality of first-order branches of Betula platyphylla in northern Japan[J]. Annals of Forest Science, 2000, 57(5/6): 587-598.
[38] Haapanen M, Velling P, Annala M. Progeny trial estimates of genetic parameters for growth and quality traits in scots pine[J]. Silva Fennica, 1997, 31(1):3-12.
[39] Kantola A, Mäkinen H, Makela A. Stem form and branchiness of Norway spruce as a sawn timber predicted by a process based model[J]. Forest Ecology and Management, 2007, 241(1/3): 209-222.
[40] 刘兆刚,李凤日. 落叶松人工林动态三维可视化模拟系统软件(3D Tree For Larix 1.0v):中国,2010SR000440[P]. 2010-01-05. Liu Z G, Li F R. The three dimensional visualization simulation system of larch plantation(3D Tree For Larix 1.0v): China, 2010SR000440[P]. 2010-01-05.

基金

收稿日期:2015-01-16 修回日期:2015-06-26
基金项目:国家自然科学基金青年基金项目(31300536); 国家自然科学基金重点项目(31430017)
第一作者:陈东升,助理研究员,博士。*通信作者:孙晓梅,研究员。E-mail: xmsun@caf.ac.cn。
引文格式:陈东升,孙晓梅,李凤日. 落叶松人工林枝条直径和长度的非线性混合模型[J]. 南京林业大学学报:自然科学版,2015,39(6):74-80.