Shannon Diversity Index Calculator

The Shannon index is Shannon entropy applied to a species abundance vector. Each species contributes minus pi times the natural log of pi, where pi is its share of all individuals counted, and the sum measures the average uncertainty in guessing the identity of one randomly drawn individual. The logarithm gives the index its characteristic behaviour: because log of pi grows large in magnitude as pi shrinks, rare species pull more weight than in dominance-based measures, so H prime responds to the tail of the abundance distribution. The index has no fixed upper bound. Its ceiling is Hmax equal to the natural log of species richness S, reached only when every species is equally abundant, and Pielou evenness J is defined as H prime divided by that ceiling, ranging from 0 to 1. Reported values in the ecological literature usually fall between 1.5 and 3.5, with heavily disturbed or monoculture systems below 1 and species-rich tropical forest plots occasionally exceeding 4. Because H prime is measured in nats when natural log is used, bits under log base 2, and decits under log base 10, the log base must always be stated for values to be comparable. Two limitations matter. H prime is biased downward at small sample sizes since undetected rare species cannot contribute, which is why rarefaction and estimators such as Chao1 are applied before comparing sites. And because entropy is logarithmic, a community with H prime of 4 is not twice as diverse as one with 2, which is why many ecologists report the exponential of H prime, the effective number of species.

Claude Shannon derived the entropy function at Bell Telephone Laboratories and published it in A Mathematical Theory of Communication in the Bell System Technical Journal in 1948, as a measure of the information content of a message source. Norbert Wiener developed closely related ideas in his 1948 book Cybernetics, which is why the index is often labelled Shannon-Wiener; the alternative spelling Shannon-Weaver is a persistent misattribution stemming from Warren Weaver, who wrote an interpretive essay accompanying the 1949 book edition of Shannon's paper but did not derive the formula. Ecologists adopted the measure almost immediately. Frank Preston and Robert MacArthur explored species abundance distributions in the 1950s, and Ramon Margalef argued explicitly in his 1958 paper Information Theory in Ecology that a community could be treated as an information source, which established the index in ecological practice. Evelyn Chrystalla Pielou formalized the evenness ratio J in 1966 and wrote extensively on the sampling statistics of diversity measures. Criticism followed as the analogy was stretched: Stuart Hurlbert's 1971 paper The Nonconcept of Species Diversity attacked the proliferation of indices, and Mark Hill's 1973 paper introduced the unified family of Hill numbers in which the exponential of Shannon entropy appears as the order-one diversity. Lou Jost revived and extended that framework in 2006, arguing that entropies should be converted to effective species numbers before being compared, and this is now standard advice.