Biodiversity Science ›› 2019, Vol. 27 ›› Issue (4): 449-456.doi: 10.17520/biods.2018341

• Methodology • Previous Article     Next Article

Comparison of distinguish ability on seven tree size diversity indices

Lou Minghua1, Bai Chao2, *(), Hui Gangying3, Tang Mengping4   

  1. 1 Ningbo Academy of Agricultural Sciences, Ningbo, Zhejiang 315040
    2 Ningbo Scientific Research and Design Institute of Environmental Protection, Ningbo, Zhejiang 315010
    3 Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing 100091
    4 Zhejiang Provincial Key Laboratory of Carbon Cycling in Forest Ecosystems and Carbon Sequestration, Zhejiang A & F University, Hangzhou 311300;
  • Received:2018-12-26 Accepted:2019-03-19 Online:2019-06-05
  • Bai Chao E-mail:506064788@qq.com

Tree size diversity directly reflects forest ecosystem health and stability. Objective and appropriate evaluation of tree size is essential for understanding the economic, ecological and social value of natural forests or plantations as well as for effective forest stand management. Four distance-free diversity indices (simpson size diversity index, DN; shannon size diversity index, HN; gini coefficient index of basal area, GC; diameter coefficient of variation index, CVd) and three distance-related indices (simpson size differentiation index, DT; shannon size differentiation index, HT; mean size differentiation index, $\bar{T}$) were selected to analyze the tree size diversity of six types of simulated stands and four measured stand plots with different diameter distribution and spatial patterns. The results show that regardless of extreme that such as compared stands have the same diameter composition but have different size mingling, GC, CVd, $\bar{T}$, DT and HT can distinguish tree size diversity between stand types which have different diameter distributions objectively and properly. CVd had the best result followed by GC. Accounting for extreme, the distance-related indices, namely $\bar{T}$, DT and HT can distinguish the difference between different size mingling stands. CVd and GC can be used as the preferred indices in the practical application for calculating simple facilitate. $\bar{T}$can be used to analyze the dynamic changes of forest structural characteristics for its high distinction ability of spatial difference that due to its sensitivity to regeneration.

Key words: tree size diversity, diameter distribution, size differentiation, size mingling, size segregation

Table 1

Distance-free indices of tree size diversity"

指数
Index
公式
Formula
指数值的理论范围
Theoretical index value range
参考文献
Reference
Simpson大小多样性指数 Simpson size diversity index ${{D}_{N}}=1-\underset{j=1}{\overset{S}{\mathop \sum }}\,p_{j}^{2}$ [0, 1] Valbuena, 2012
Shannon大小多样性指数 Shannon size diversity index ${{H}_{N}}=-\underset{j=1}{\overset{S}{\mathop \sum }}\,{{p}_{j}}\ln ({{p}_{j}})$ [0, ln(S)] Buongiorno, 2001
断面积Gini系数 Gini coefficient index of basal area $GC=\frac{\sum\limits_{i=1}^{n}{(2i-n-1)B{{A}_{i}}}}{\sum\limits_{i=1}^{n}{B{{A}_{i}}(n-1)}}$ [0, 1] Duduman, 2011
直径变异系数 Diameter coefficient of variation index $C{{V}_{d}}={\sqrt{\frac{\sum\limits_{i=1}^{n}{{{({{d}_{i}}-\bar{d})}^{2}}}}{n-1}}}/{{\bar{d}}}\;$ [0, 1] Huang, 2000

Table 2

Distance-related indices of tree size diversity"

指数
Index
公式
Formula
指数值理论范围
Theoretical index value range
参考文献
Reference
Simpson大小分化度指数 Simpson size differentiation index ${{D}_{T}}=1-\underset{i=1}{\overset{5}{\mathop \sum }}\,P_{i}^{2}$ [0, 1] Bai & Hui, 2016
Shannon大小分化度指数 Shannon size differentiation index ${{H}_{T}}=-\underset{i=1}{\overset{5}{\mathop \sum }}\,{{P}_{i}}\ln ({{P}_{i}})$ [0, ln(5)] Bai & Hui, 2016
大小分化度均值指数 Mean size differentiation index $\overline{T}=\frac{1}{N}\sum\limits_{i=1}^{N}{{{T}_{i}}}$ [0, 1] Gadow & Füldner, 1992
${{T}_{i}}=1-\frac{\min ({{d}_{i}},{{d}_{1}})}{\max ({{d}_{i}},{{d}_{1}})}$ [0,1) Gadow & Füldner, 1992

Table 3

Range and coefficient of variation (CV) of seven tree size diversity indices for the simulated stands"

指数
Indices
正态径级分布 Normal-shaped diameter distribution 倒J径级分布 Inverse J-shaped diameter distribution 变异系数
CV (%)
均匀 Uniform 随机 Random 聚集 Aggregation 均匀 Uniform 随机 Random 聚集 Aggregation
DN 0.930-0.941 0.926-0.942 0.930-0.942 0.814-0.924 0.816-0.913 0.815-0.921 3.5
HN 2.820-2.964 2.796-2.968 2.801-2.969 1.963-2.790 1.985-2.724 2.011-2.783 10.1
GC 0.269-0.317 0.270-0.323 0.271-0.313 0.520-0.627 0.530-0.631 0.529-0.639 37.0
CVd 0.259-0.305 0.255-0.308 0.253-0.298 0.532-0.684 0.547-0.691 0.543-0.704 42.2
DT 0.617-0.696 0.624-0.696 0.616-0.694 0.727-0.773 0.731-0.775 0.733-0.779 7.8
HT 1.070-1.267 1.092-1.279 1.049-1.274 1.361-1.524 1.366-1.533 1.373-1.548 12.1
$\bar{T}$ 0.238-0.303 0.234-0.297 0.227-0.298 0.334-0.464 0.345-0.452 0.351-0.464 23.5

Table 4

Mean (standard deviation) of seven tree size diversity indices for the simulated stands"

指数
Indices
正态径级分布 Normal-shaped diameter distribution 倒J径级分布 Inverse J-shaped diameter distribution
均匀 Uniform 随机 Random 聚集 Aggregation 均匀 Uniform 随机 Random 聚集 Aggregation
DN 0.936 (0.002)a 0.936 (0.003)a 0.935 (0.002)a 0.877 (0.022)b 0.877 (0.022)b 0.881 (0.023)b
HN 2.890 (0.033)a 2.892 (0.039)a 2.884 (0.032)a 2.394 (0.169)bc 2.388 (0.166)c 2.426 (0.176)b
GC 0.292 (0.010)a 0.291 (0.011)a 0.290 (0.010)a 0.588 (0.023)b 0.585 (0.022)b 0.589 (0.023)b
CVd 0.278 (0.010)a 0.278 (0.011)a 0.276 (0.010)a 0.625 (0.034)b 0.621 (0.032)b 0.627 (0.033)b
DT 0.657 (0.016)a 0.659 (0.017)a 0.656 (0.016)a 0.757 (0.010)b 0.757 (0.009)b 0.759 (0.010)b
HT 1.173 (0.041)a 1.180 (0.043)a 1.171 (0.042)a 1.463 (0.037)b 1.462 (0.035)b 1.470 (0.038)b
$\bar{T}$ 0.262 (0.013)a 0.262 (0.014)a 0.261 (0.013)a 0.404 (0.025)b 0.403 (0.025)b 0.406 (0.026)b

Table 5

Tree size diversity indices of different size mingling and size segregation for twelve different simulated stands"

林分类型 Stand type DN HN GC CVd DT HT $\bar{T}$
倒J均匀混交 Inverse J-shaped uniform mingling type 0.897 2.610 0.633 0.692 0.770 1.512 0.437
倒J均匀隔离 Inverse J-shaped uniform segregation type 0.897 2.610 0.633 0.692 0.054 0.154 0.067
倒J随机混交 Inverse J-shaped random mingling type 0.897 2.610 0.633 0.692 0.769 1.510 0.421
倒J随机隔离 Inverse J-shaped random segregation type 0.897 2.610 0.633 0.692 0.049 0.140 0.050
倒J聚集混交 Inverse J-shaped aggregated mingling type 0.897 2.610 0.633 0.692 0.772 1.521 0.421
倒J聚集隔离 Inverse J-shaped aggregated segregation type 0.897 2.610 0.633 0.692 0.035 0.107 0.041
正态均匀混交 Normal-shaped uniform mingling type 0.937 2.906 0.299 0.282 0.673 1.208 0.275
正态均匀隔离 Normal-shaped uniform segregation type 0.937 2.906 0.299 0.282 0.078 0.196 0.040
正态随机混交 Normal-shaped random mingling type 0.937 2.906 0.299 0.282 0.665 1.184 0.269
正态随机隔离 Normal-shaped random segregation type 0.937 2.906 0.299 0.282 0.044 0.123 0.032
正态聚集混交 Normal-shaped aggregated mingling type 0.937 2.906 0.299 0.282 0.660 1.177 0.268
正态聚集隔离 Normal-shaped aggregated segregation type 0.937 2.906 0.299 0.282 0.030 0.085 0.024

Table 6

Tree size diversity indices for four measured plots"

指数 Index HZ NB BJ GS CV (%)
GC 0.16 0.543 0.204 0.553 0.581
CVd 0.146 0.554 0.186 0.566 0.628
DT 0.330 0.726 0.489 0.750 0.350
HT 0.557 1.368 0.792 1.421 0.413
$\bar{T}$ 0.126 0.324 0.169 0.396 0.502
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