Uniform Angle Index (W) Confidence Interval of the Random Distribution and Its Application

HU Yan-bo; HUI Gang-ying; WANG Hong-xiang; LI Yuan-fa; ZHAO Zhong-hua; LIU Wen-zhen

Volume 27 Issue 3

Article Contents

Turn off MathJax

Article Navigation > Forest Research > 2014 > 27(3): 302-308

Citation:

Uniform Angle Index (W) Confidence Interval of the Random Distribution and Its Application

1.
Research Institute of Forestry, Chinese Academy of Forestry
2.
Key Laboratory of Tree Breeding and Cultivation, State Forestry Administration, Beijing 100091, China

Received Date: 2012-09-12

Abstract

The Uniform angle index(W) method is a parameter analyzing forest spatial structure through describing the evenness of neighboring trees around reference tree to judge the distribution pattern of trees. 80 000 simulated randomly distributed stands were analyzed, and it was found that the standard deviation of the mean value of the W (W) of those stands was mainly influenced by the tree number of simulation (N), while the simulation window size was not so important for the result. The tree number of simulation related closely to the standard deviation of W, the fewer the former are, the larger the latter will be. Moreover, the standard deviation decreased with the tree number of simulation. Such relationship can be well expressed by the power function σW=0.210 34N-0.488 72, and the correlation index R2 was up to 0.998. Based on the normal distribution principle in statistics, a confidence interval was established for the W of the Random Distribution stands, and the 95% confidence limit is 0.5±1.96σW=0.5±1.96×0.210 34N-0.488 72, while the 99% confidence limit is 0.5±2.58σW=0.5±2.58×0.210 34N-0.488 72. When the σW of a stand or a specific population is within the established confidence interval [WLd, WLu], then it should be described as a random distribution on relevant confidence level, and clustered distribution should be judged if W > WLu, while uniform distribution if W WLd.
- stand structure,
- spatial structure parameter,
- uniform angle index,
- confidence interval,
- pattern testing method

References

[1]	Pukkala T, Gadow K V. Continuous Cover Forestry. Book Series Managing Forest Ecosystems Vol 24 [M]. Netherlands:Springer Science Business Media B.V, 2011
[2]	Zenner, E K, Hibbs D E. A new method for modeling the heterogeneity of forest structure[J]. For Ecol Manage, 2000, 129: 75-87
[3]	Franklin J F, Spies T A, Robert V P, et al. Disturbances and structural development of natural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example [J]. For Ecol Manage, 2002, 155: 399-423
[4]	Spies T A. Forest Structure: A Key to the Ecosystem [J]. Northwest sci, 1998, 72: 34-36
[5]	Clark P J, Evans F C. Distance to nearest neighbor as measure of spatial relationships in populations [J]. Ecology, 1954, 35: 445-453
[6]	Stoyan D, Stoyan, H, Fraktale Formen Punktfelder. Methodender Geometrie-Statistik [M]. Berlin: Akademie-Verlag, 1992: 394S
[7]	Pommerening A. Approaches to quantifying forest structures [J]. Forestry, 2002, 75: 305-324
[8]	Ripley B D. Modeling spatial patterns [M]. J R Stat Soc Series B, 1977, 39: 172-179
[9]	Gadow K V, Hui G Y, Albert M. Das Winkelmaβ-ein Strukturparameter zur Beschreibung der Individualverteilung in Waldbeständen [J]. Cbl f d ges Forstw, 1998, 115.Jg., Heft1 : S. 1-10
[10]	Hui G Y, Gadow K V. Das Winkelmass-Theoretische überlegungen zum optimalen Standardwinkel [J]. Allg Forst-u J-Ztg, 2002, 173: 173-177
[11]	Aguirre O, Hui G Y, Gadow K V, Jiménez J. An analysis of spatial forest structure using neighborhood-based variables [J]. Forest Ecology and Management, 2003, 183: 137-145
[12]	Pommerening A. Evaluating structural indices by reversing forest structural analysis [J]. Forest Ecology and Management, 2006, 224: 266-277
[13]	Hui G Y, Albert M. Stichprobensimulationen zur Schätzung nachbarschaftsbezogener Strukturparameter in Waldbeständen [J]. Allg Forst-u J-Ztg, 2004, 175: 199-209
[14]	Hui G Y, Zhao X H, Zhao Z H, et al. Evaluating tree species diversity based on neighborhood relationships [J]. Forest Science, 2011, 57: 292-300
[15]	Gadow K V, Hui G Y. Characterizing forest spatial structure and diversity [C]. "Sustainable Forestry in Temperate Regions" Proceedings of the SUFOR International Workshop, University of Lund, Sweden, 2002: 7-9
[16]	Hui G Y, Albert M, Chen B W, Reproduktion der Baumverteilung im Bestand unter Verwendung des Strukturparameters Winkelmaβ [J]. Allg Forst-u J-Ztg, 2003, 174: 109-116
[17]	惠刚盈, Gadow K V, 胡艳波,等. 林木分布格局类型的角尺度均值分析方法[J].生态学报, 2004, 4(6): 1225-1229
[18]	Sachs L. Angewandte Statistik [M]. Springer-Verlag Berlin,Heidelberg,New York. 1992: 51-197
[19]	童一中. 作物育种常用的统计分析法[M]. 上海: 上海科学技术出版社, 1979: 60-61
[20]	Li Y F, Hui G Y, Zhao Z H, et al. The bivariate distribution characteristics of spatial structure in natural Korean pine broad-leaved forest [J]. Journal of Vegetation Science,2012,23:1180-1190
[21]	Kint V, Lust N, Ferris R, Olsthoorn A F M. Quantification of forest stand structure applied to Scots pine (Pinus sylvestris L.) forests [J]. Investigación Agraria: Sistemas y Recursos Forestales, Fuera de serie, 2000, 1: 147-163
[22]	Cox F. Dichtebestimmung und Strukturanalyse von Pflanzenpopulationen mit Hilfe von Abstandsmessungen. Dissertation Forstl [M]. Germany: Fak Goettingen,1971
[23]	Füldner K. Strukturbeschreibung von Buchen-Edellaubholz-Mischwäldern[M]. Dissertation Universität Göttingen. Germany: Cuvillier Verlag, 1995, 146

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Get Citation

PDF

XML

Article views(3301) PDF downloads(1093) Cited by()

Proportional views

Uniform Angle Index (W) Confidence Interval of the Random Distribution and Its Application

1. Research Institute of Forestry, Chinese Academy of Forestry

2. Key Laboratory of Tree Breeding and Cultivation, State Forestry Administration, Beijing 100091, China

Received Date: 2012-09-12

Abstract: The Uniform angle index(W) method is a parameter analyzing forest spatial structure through describing the evenness of neighboring trees around reference tree to judge the distribution pattern of trees. 80 000 simulated randomly distributed stands were analyzed, and it was found that the standard deviation of the mean value of the W (W) of those stands was mainly influenced by the tree number of simulation (N), while the simulation window size was not so important for the result. The tree number of simulation related closely to the standard deviation of W, the fewer the former are, the larger the latter will be. Moreover, the standard deviation decreased with the tree number of simulation. Such relationship can be well expressed by the power function σW=0.210 34N-0.488 72, and the correlation index R2 was up to 0.998. Based on the normal distribution principle in statistics, a confidence interval was established for the W of the Random Distribution stands, and the 95% confidence limit is 0.5±1.96σW=0.5±1.96×0.210 34N-0.488 72, while the 99% confidence limit is 0.5±2.58σW=0.5±2.58×0.210 34N-0.488 72. When the σW of a stand or a specific population is within the established confidence interval [WLd, WLu], then it should be described as a random distribution on relevant confidence level, and clustered distribution should be judged if W > WLu, while uniform distribution if W WLd.

HTML

Reference (23)

[1]	Pukkala T, Gadow K V. Continuous Cover Forestry. Book Series Managing Forest Ecosystems Vol 24 [M]. Netherlands:Springer Science Business Media B.V, 2011
[2]	Zenner, E K, Hibbs D E. A new method for modeling the heterogeneity of forest structure[J]. For Ecol Manage, 2000, 129: 75-87
[3]	Franklin J F, Spies T A, Robert V P, et al. Disturbances and structural development of natural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example [J]. For Ecol Manage, 2002, 155: 399-423
[4]	Spies T A. Forest Structure: A Key to the Ecosystem [J]. Northwest sci, 1998, 72: 34-36
[5]	Clark P J, Evans F C. Distance to nearest neighbor as measure of spatial relationships in populations [J]. Ecology, 1954, 35: 445-453
[6]	Stoyan D, Stoyan, H, Fraktale Formen Punktfelder. Methodender Geometrie-Statistik [M]. Berlin: Akademie-Verlag, 1992: 394S
[7]	Pommerening A. Approaches to quantifying forest structures [J]. Forestry, 2002, 75: 305-324
[8]	Ripley B D. Modeling spatial patterns [M]. J R Stat Soc Series B, 1977, 39: 172-179
[9]	Gadow K V, Hui G Y, Albert M. Das Winkelmaβ-ein Strukturparameter zur Beschreibung der Individualverteilung in Waldbeständen [J]. Cbl f d ges Forstw, 1998, 115.Jg., Heft1 : S. 1-10
[10]	Hui G Y, Gadow K V. Das Winkelmass-Theoretische überlegungen zum optimalen Standardwinkel [J]. Allg Forst-u J-Ztg, 2002, 173: 173-177
[11]	Aguirre O, Hui G Y, Gadow K V, Jiménez J. An analysis of spatial forest structure using neighborhood-based variables [J]. Forest Ecology and Management, 2003, 183: 137-145
[12]	Pommerening A. Evaluating structural indices by reversing forest structural analysis [J]. Forest Ecology and Management, 2006, 224: 266-277
[13]	Hui G Y, Albert M. Stichprobensimulationen zur Schätzung nachbarschaftsbezogener Strukturparameter in Waldbeständen [J]. Allg Forst-u J-Ztg, 2004, 175: 199-209
[14]	Hui G Y, Zhao X H, Zhao Z H, et al. Evaluating tree species diversity based on neighborhood relationships [J]. Forest Science, 2011, 57: 292-300
[15]	Gadow K V, Hui G Y. Characterizing forest spatial structure and diversity [C]. "Sustainable Forestry in Temperate Regions" Proceedings of the SUFOR International Workshop, University of Lund, Sweden, 2002: 7-9
[16]	Hui G Y, Albert M, Chen B W, Reproduktion der Baumverteilung im Bestand unter Verwendung des Strukturparameters Winkelmaβ [J]. Allg Forst-u J-Ztg, 2003, 174: 109-116
[17]	惠刚盈, Gadow K V, 胡艳波,等. 林木分布格局类型的角尺度均值分析方法[J].生态学报, 2004, 4(6): 1225-1229
[18]	Sachs L. Angewandte Statistik [M]. Springer-Verlag Berlin,Heidelberg,New York. 1992: 51-197
[19]	童一中. 作物育种常用的统计分析法[M]. 上海: 上海科学技术出版社, 1979: 60-61
[20]	Li Y F, Hui G Y, Zhao Z H, et al. The bivariate distribution characteristics of spatial structure in natural Korean pine broad-leaved forest [J]. Journal of Vegetation Science,2012,23:1180-1190
[21]	Kint V, Lust N, Ferris R, Olsthoorn A F M. Quantification of forest stand structure applied to Scots pine (Pinus sylvestris L.) forests [J]. Investigación Agraria: Sistemas y Recursos Forestales, Fuera de serie, 2000, 1: 147-163
[22]	Cox F. Dichtebestimmung und Strukturanalyse von Pflanzenpopulationen mit Hilfe von Abstandsmessungen. Dissertation Forstl [M]. Germany: Fak Goettingen,1971
[23]	Füldner K. Strukturbeschreibung von Buchen-Edellaubholz-Mischwäldern[M]. Dissertation Universität Göttingen. Germany: Cuvillier Verlag, 1995, 146

Uniform Angle Index (W) Confidence Interval of the Random Distribution and Its Application

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Proportional views

Uniform Angle Index (W) Confidence Interval of the Random Distribution and Its Application

HTML

Catalog

Export File

Citation

Format

Content