Biodiversity Index Calculator

Diversity indices compress a species abundance list into a single number capturing both richness, meaning how many species are present, and evenness, meaning how equally individuals are spread among them. The Shannon index H is the negative sum of pi times ln(pi), where pi is the proportion of the sample belonging to species i; it is Shannon entropy applied to a species list and is most sensitive to changes in the rare tail. Simpson's D is the probability that two individuals drawn at random belong to the same species, so 1 minus D and the reciprocal 1/D weight the dominant species instead. Margalef's index (S-1)/ln(N) is a richness measure partially corrected for sample size, and the Berger-Parker index is simply the share of the sample held by the commonest species. Interpretation is comparative rather than absolute. Shannon values computed with natural logarithms usually fall between 1.5 and 3.5 for real communities; tropical forest and coral reef assemblages can exceed 4, while tundra or heavily disturbed sites sit below 1.5. Evenness E = H/ln(S) is bounded between 0 and 1 and separates the two signals, since a site can gain species while losing evenness. The chief limitation is sampling effort. Rare species are missed at low effort, biasing richness and Shannon downward, so comparisons require equal effort or rarefaction to a common sample size, and Simpson's index is the more robust of the two at small N. None of these measures record which species are present, so a community of invasives can score as highly as an intact native one.

The Shannon index is borrowed mathematics. Claude Shannon published A Mathematical Theory of Communication in the Bell System Technical Journal in 1948, defining entropy as a measure of uncertainty in a message source. Norbert Wiener developed related ideas in parallel, which is why the ecological literature often writes Shannon-Wiener. Edward Simpson, who had worked at Bletchley Park during the war alongside Alan Turing, published his measure of concentration as a one-page note in Nature in 1949, deriving it as a sampling probability rather than an information quantity. Ecologists adopted both quickly. Ramon Margalef argued in the late 1950s for treating a community as an information system and introduced his richness index, and Robert MacArthur applied information measures to bird community structure through the 1950s and 1960s. E. C. Pielou formalised evenness as the ratio of observed to maximum entropy in 1966. Wolfgang Berger and Frances Parker proposed their dominance measure in 1970 from planktonic foraminifera in deep-sea sediments. The unifying step came from Mark Hill in 1973, who showed that richness, Shannon and Simpson are members of a single family of diversity numbers differing only in the order of the exponent. Lou Jost revived that argument in 2006, and effective species counts, now called Hill numbers, are the current standard.