Simpson Diversity Index Calculator

Simpson's D is a probability, which is what distinguishes it from entropy-based measures: it is the chance that two individuals drawn from the community belong to the same species. Squaring each proportion is the mathematical core, and it is precisely why the index tracks dominance: a species holding 50 percent of individuals contributes 0.25 to the sum while one holding 1 percent contributes only 0.0001, so rare species barely move the result. This calculator reports two variants of the concentration term: the finite form, the sum of ni times ni minus 1 divided by N times N minus 1, which samples without replacement and suits a census or small sample, and the proportional form, the sum of pi squared, which assumes an infinite population. The two converge once N exceeds roughly a thousand. Three presentations of the same information are in common use and must not be confused. D itself runs from near 0 at maximum diversity to 1 when one species remains, an inverted scale that causes frequent misreporting. The Gini-Simpson index, 1 minus D, restores the intuitive direction between 0 and 1, with values above 0.9 read as high diversity and below 0.5 as dominated. The reciprocal 1 over D, the inverse Simpson index or Hill number of order two, gives the effective number of abundant species and runs from 1 up to S; dividing it by observed richness yields the evenness shown here. The chief limitation mirrors the strength: because the measure is insensitive to rare taxa, it can rate two communities as nearly identical when one has lost many uncommon species, so it should not stand alone where rare species conservation is the question.

The mathematical quantity predates its ecological use. Corrado Gini introduced closely related concentration measures in Italian statistics from 1912 onward, and the same sum-of-squares appears in economics as the Herfindahl-Hirschman index of market concentration, developed by Albert Hirschman in 1945 and Orris Herfindahl in 1950, and in cryptanalysis as William Friedman's index of coincidence from 1922. Each field arrived at it independently because it answers the same underlying question about the probability of a repeated draw. The ecological version comes from Edward Hugh Simpson, a British statistician who worked at Bletchley Park during the Second World War and later at the Ministry of Education. His paper Measurement of Diversity was a short note published in Nature in 1949, occupying barely a page, in which he set out the probability interpretation and the finite population correction. Simpson is better known today for Simpson's paradox, described in a 1951 paper. Ecologists took up the index during the 1950s and 1960s alongside the Shannon measure, and Stuart Hurlbert's influential 1971 critique The Nonconcept of Species Diversity actually favoured the Simpson family, recasting 1 minus D as the probability of interspecific encounter, a quantity with a clearer biological meaning than entropy. Mark Hill placed it as the order-two member of his diversity number family in 1973, and Lou Jost's 2006 work on effective numbers cemented the reciprocal form as the preferred way to report it.