GiniSimpson

GiniSimpson, or the Gini-Simpson index, is a measure of biodiversity that quantifies the probability that two individuals drawn at random from a community belong to different species (or categories). It is defined as 1 minus the sum of the squared species proportions: 1 − ∑ p_i^2, where p_i is the relative abundance of species i.

The index is related to the Simpson index of diversity. If D = ∑ p_i^2, then the Gini-Simpson index equals 1 − D. In some literature, the term Simpson’s diversity index is used for 1 − D, which can lead to terminology variation. The maximum achievable value depends on species richness: for S species with equal abundances, the maximum is 1 − 1/S, approaching 1 as S grows. The minimum is 0, occurring when only a single species is present.

Calculation can be illustrated by a simple example: a community with four species with relative abundances 0.4, 0.3, 0.2, and 0.1 has ∑ p_i^2 = 0.16 + 0.09 + 0.04 + 0.01 = 0.30, so the Gini-Simpson index is 0.70.

Applications of the Gini-Simpson index span ecology, conservation biology, microbiology, and population genetics. It is often interpreted as the probability that two randomly chosen individuals belong to different species and can be used to compare biodiversity across communities. The index is more sensitive to common species and can be complemented by the effective number of species, 1/∑ p_i^2, for intuitive comparisons.