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This is a parametric index of diversity that assumes that the abundance of species follows the log series distribution:
where each term gives the number of species predicted to have 1,2,3,....n individuals in the sample. The index is the alpha parameter.
This is a useful index, which has been widely used. To test if a log series distribution is appropriate see Fitting abundance distributions - Log series. It is estimated by an iterative procedure that may take an appreciable amount of time with large data sets.
A number of authors argue strongly in favour of this index (eg Kempton, and Taylor, 1976)..
Hayek & Buzas (1997) believe it to be a useful index provided the ratio of the total number of individuals to the species number (N/S) exceeds 1.44. In many situations, alpha is approximately equal to the number of species represented by a single individual. The value of alpha is independent of sample size when the number of individuals in the sample exceeds 1000.
A simple plot of the way the index changes between samples is displayed by clicking on the Graph tab on the output window.
To compare two indices see Testing for significant differences between indices.