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en:div-ind [2017/05/24 22:29]
David Zelený
en:div-ind [2019/03/22 22:03] (current)
David Zelený
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-====== Diversity analysis ======+Section: [[en:​diversity_analysis]]
 ===== Diversity indices ===== ===== Diversity indices =====
 +
  
 [[{|width: 7em; background-color:​ light; color: firebrick}div-ind|**Theory**]] [[{|width: 7em; background-color:​ light; color: firebrick}div-ind|**Theory**]]
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 [[{|width: 7em; background-color:​ white; color: navy}div-ind_examples|Examples]] [[{|width: 7em; background-color:​ white; color: navy}div-ind_examples|Examples]]
 [[{|width: 7em; background-color:​ white; color: navy}div-ind_exercise|Exercise {{::​lock-icon.png?​nolink|}}]] [[{|width: 7em; background-color:​ white; color: navy}div-ind_exercise|Exercise {{::​lock-icon.png?​nolink|}}]]
-==== Theory ==== 
  
 This section will overview commonly used indices measuring diversity of ecological community (species richness, Shannon index, Simpson index). We will also introduce the measures of evenness, concept of effective number of species and general framework of Hill numbers. This section will overview commonly used indices measuring diversity of ecological community (species richness, Shannon index, Simpson index). We will also introduce the measures of evenness, concept of effective number of species and general framework of Hill numbers.
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 === Comparison of species richness, Shannon index and Simpson index === === Comparison of species richness, Shannon index and Simpson index ===
-In case of perfectly even communities,​ the Shannon and Gini-Simpson index increases non-linearly with number of species in the community; Gini-Simpson index increases faster. This relationship also illustrates that Gini-Simpson index changes very fast in low diversities ​(0.5 for //S// = 2, 0.67 for //S// = 3, 0.75 for //S// = 4, ... 0.9 for //S// = 10), and with diversity ​over 10 it changes much slower (0.95 for //S// = 20 and 0.99 for //S// = 100).+In case of perfectly even communities,​ the Shannon and Gini-Simpson index increases non-linearly with number of species in the community; Gini-Simpson index increases faster. This relationship also illustrates that Gini-Simpson index changes very fast in low species richness values ​(0.5 for //S// = 2, 0.67 for //S// = 3, 0.75 for //S// = 4, ... 0.9 for //S// = 10), and with richness ​over 10 it changes much slower (0.95 for //S// = 20 and 0.99 for //S// = 100).
  
 {{:​obrazky:​shannon-and-simpson-on-sp-richness.png?​direct&​400|}} {{:​obrazky:​shannon-and-simpson-on-sp-richness.png?​direct&​400|}}
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 <​m>​{}^2{D}~=~1/​D</​m>​ <fs x-small>​(reciprocal of Simpson index)</​fs>​\\ <​m>​{}^2{D}~=~1/​D</​m>​ <fs x-small>​(reciprocal of Simpson index)</​fs>​\\
 </​WRAP>​ </​WRAP>​
-Mark Hill (British scientist ​whoamong others, introduced ​DCA, Twinspan, and recallibrated ​Ellenberg species indicator values for Britain) realized that species richness, Shannon entropy and Simpson'​s concentration index are all members of the same family of diversity indices, later called as Hill numbers. Individual Hill numbers differ by the parameter //q//, which quantifies how much the measure discounts rare species when calculating diversity. Hill number for //q// = 0 is simply species richness, for //q// = 1((In fact the Hill's formula is not defined for //q// = 1, but it can be shown that when q approaches 1 from below or above, the index gets equal to exponential Shannon.)) it is effective number of species derived from Shannon entropy, and for //q// = 2 it is ENS for Simpson index. For //q// > 0, indices discount rare species, while for //q// < 0 the indices discount common species and focus on number of rare species (usually not meaningful).+Mark Hill (British scientist, ​known also for introducing Detrended correspondence analysis (DCA), Twinspan, and recallibrating ​Ellenberg species indicator values for Britain) realized that species richness, Shannon entropy and Simpson'​s concentration index are all members of the same family of diversity indices, later called as Hill numbers. Individual Hill numbers differ by the parameter //q//, which quantifies how much the measure discounts rare species when calculating diversity. Hill number for //q// = 0 is simply species richness, for //q// = 1((In fact the Hill's formula is not defined for //q// = 1, but it can be shown that when q approaches 1 from below or above, the index gets equal to exponential Shannon.)) it is **Shannon diversity**,​ i.e. effective number of species derived from Shannon entropy, and for //q// = 2 it is **Simpson diversity**,​ i.e. ENS for Simpson ​concentration ​index. For //q// > 0, indices discount rare species, while for //q// < 0 the indices discount common species and focus on number of rare species (usually not meaningful).
  
 Dependence of species richness, Shannon diversity (effective number of species based on Shannon entropy index) and Simpson'​s diversity (effective number of species based on Simpson'​s index) on (un)evenness and diversity is illustrated below. Dependence of species richness, Shannon diversity (effective number of species based on Shannon entropy index) and Simpson'​s diversity (effective number of species based on Simpson'​s index) on (un)evenness and diversity is illustrated below.
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 === Diversity profiles === === Diversity profiles ===
-{{ :​obrazky:​diversity-profile-even-mod-high.png?​direct&​400|}} 
 It is possible to draw the effective number of species as a function of coefficient //q// - increasing //q// decreases the impact of rare species on the measure of diversity. The value for //q// = 0 equals to species richness (in the diagram displayed by squares), for //q// = 1 equals to Shannon diversity (circles) and for //q// = 2 Simpson diversity (triangles). The shape of the diversity profile considers the differences in evenness between the three communities;​ the more is the community species abundance uneven, the faster the curve declines with increasing coefficient //q//. The future will see what exactly can this form of diversity visualization bring new. It is possible to draw the effective number of species as a function of coefficient //q// - increasing //q// decreases the impact of rare species on the measure of diversity. The value for //q// = 0 equals to species richness (in the diagram displayed by squares), for //q// = 1 equals to Shannon diversity (circles) and for //q// = 2 Simpson diversity (triangles). The shape of the diversity profile considers the differences in evenness between the three communities;​ the more is the community species abundance uneven, the faster the curve declines with increasing coefficient //q//. The future will see what exactly can this form of diversity visualization bring new.
 +
 +{{:​obrazky:​diversity-profile-even-mod-high.png?​direct|}}
  
 === Summary of values for diversity measures discussed in this chapter === === Summary of values for diversity measures discussed in this chapter ===
-                  ​^ Community A\\ (perfectly even)  ^ Community B\\ (moderately uneven) ​ ^ Community C\\ (highly uneven) ​ ^ +                                               ^ Community A\\ (perfectly even)  ^ Community B\\ (moderately uneven) ​ ^ Community C\\ (highly uneven) ​ ^ 
-Species richness ​ |  12                             ​| ​ 12                                |  12                            | +Species richness ​                              ​|  12                             ​| ​ 12                                |  12                            | 
-Shannon entropy ​  ​|  2.48                            |  1.81                                   ​|  0.87                              +Shannon entropy ​                               |  2.48                           ​|  1.81                              |  0.87                          
-Simpson index     ​|  0.92                               ​|  0.79                                  |  0.46                              +Simpson index                                  |  0.92                           ​|  0.79                              |  0.46                          
-Shannon evenness ​ |  1                               ​|  0.73                                  |  0.35                              +Shannon evenness ​                              ​|  1                              |  0.73                              |  0.35                          
-Simpson evenness ​ |  1                               ​|  0.38                                  |  0.15                              |+Simpson evenness ​                              ​|  1                              |  0.38                              |  0.15                          | 
 +| Shannon diversity (<​sup>//​1//</​sup>//​D//,​ N1)  |  12                              |  6.14                               ​| ​ 2.39                           | 
 +| Simpson diversity (<​sup>//​2//</​sup>//​D//,​ N2)  |  12                              |  4.66                               ​| ​ 1.86                           |
  
en/div-ind.1495636152.txt.gz · Last modified: 2017/10/11 20:36 (external edit)