ShannonIndex

ShannonIndex, commonly called the Shannon diversity index, is a metric used to quantify biodiversity in ecological communities and, by extension, in information theory. It measures the uncertainty in predicting the species identity of a randomly chosen individual from a community, reflecting both species richness and evenness.

The index is computed as H' = - sum_{i=1}^S p_i log p_i, where S is the number of species and p_i is the relative abundance of species i (the number of individuals of species i divided by the total number of individuals). Terms with p_i = 0 contribute zero. With natural logarithms, H' is measured in nats; using base 2 yields bits. The theoretical maximum for a given S is H'max = ln(S), achieved when all species are equally abundant. The evenness, E = H' / H'max, ranges from 0 to 1 and summarizes how evenly individuals are distributed among species.

ShannonIndex is widely used to compare biodiversity across sites, treatments, or time, in ecology and microbiology. It can be computed from abundance data or, less informatively, presence-absence data. Higher values indicate greater diversity.

Interpretation caveats: H' is sensitive to sample size and the presence of rare species; under-sampling can bias estimates downward. Comparability between studies requires standardization of sampling effort and, when possible, rarefaction or other sample-size corrections and an explicit statement of the logarithm base used.