Species diversity

Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant). Species diversity consists of two components: species richness and species evenness. Species richness is a simple count of species, whereas species evenness quantifies how equal the abundances of the species are.

Species diversity in a dataset can be calculated by first taking the weighted average of species proportional abundances in the dataset, and then taking the inverse of this. The equation is:

The denominator equals mean proportional species abundance in the dataset as calculated with the weighted generalized mean with exponent q - 1. In the equation, S is the total number of species (species richness) in the dataset, and the proportional abundance of the ith species is ${\displaystyle p_{i}}$. The proportional abundances themselves are used as weights. The equation is often written in the equivalent form:

The value of q defines which kind of mean is used. q = 0 corresponds to the weighted harmonic mean, which is 1/S because the ${\displaystyle p_{i}}$ values cancel out. q = 1 is undefined, except that the limit as q approaches 1 is well defined:

...
Wikipedia