Table 1 Proposed evenness indices varying over the interval from 0 to 1 and based on the species abundance probabilities (proportions) p 1, …, p S and species richness S
From: Evenness indices once again: critical analysis of properties
Designation | Formula | Reference | Notes |
|---|---|---|---|
E 1 | \( H/ logS=-{\displaystyle \sum_{i=1}^S{p}_i log{p}_i/ logS} \) | Pielou (1966) | |
E 2 | (e H − 1)/(S − 1) | Heip (1974) | a |
E 3 | \( \Big(1-{\displaystyle \sum_{i=1}^S{p}_i^2\Big)/\left(1-1/S\right)} \) | Smith and Wilson (1996) | |
E 4 | \( - log{\displaystyle \sum_{i=1}^S{p}_i^2/ logS} \) | Smith and Wilson (1996) | |
E 5 | \( \Big(1/{\displaystyle \sum_{i=1}^S{p}_i^2-1\Big)/\left({e}^H-1\right)} \) | Alatalo (1981) | a |
E 6 | \( \left(1-\sqrt{{\displaystyle \sum_{i=1}^S{p}_i^2}}\right)/\left(1-\sqrt{1/S}\right) \) | Pielou (1969) | |
E 7 | \( \Big(1/{\displaystyle \sum_{i=1}^S{p}_i^2-1\Big)/\left(S-1\right)} \) | Kvålseth (1991) | |
E 8 | \( \left({\displaystyle \sum_{i=1}^S \min \left\{{p}_i,1/S\right\}-1/S}\right)/\left(1-1/S\right) \) | Bulla (1994) | |
E 9 | \( 1-{\left[\left(S{\displaystyle \sum_{i=1}^S{p}_i^2-1}\right)/\left(S-1\right)\right]}^{1/2} \) | Williams (1977) | b |
E 10 | \( 2{\displaystyle \sum_{i=1}^S\left(i-1\right){p}_i/\left(S-1\right)} \) | Solomon (1979) | c |
E 11 | \( \left(1-{\displaystyle \sum_{i=1}^S{p}_i/i}\right)/\left[1-\left(1/S\right){\displaystyle \sum_{i=1}^S1/i}\right] \) | New | c |