https://doi.org/10.1351/goldbook.15034
Dominance index weighted toward the abundance of the most common species, giving the probability of any two individuals drawn at random from an infinitely large community belonging to different species. The bias corrected mathematical form of Simpson’s index is \[D = \sum \limits_{i=1}^{S} p_{i}^{2}\] where \(p_{i}\) is the fraction of all organisms which belong to the \(i\)-th species and \(S\) is the number of species.
Note: Since \(D\) and diversity are negatively related, Simpson’s index is usually expressed as either a reciprocal or a complementary form (\(1/D\) or \(1 - D\)) so that as the index goes up, so does measure of diversity.
See also: diversity index