Evenness Index Calculator

Diversity has two independent components: how many species are present, and how equally individuals are shared among them. Evenness isolates the second. Pielou J takes the observed Shannon index and divides it by the maximum that index could reach for the same number of species, which occurs when every species is equally abundant and equals ln(S). A community of ten equally abundant species has H = ln(10) = 2.303 and J = 1.0; if one species holds 91 of 100 individuals, H falls near 0.5 and J to about 0.22. Simpson evenness rescales the Simpson index by its own ceiling of 1 - 1/S, and Berger-Parker dominance is simply the proportion held by the commonest species, with its complement serving as a crude evenness measure. The three disagree by design. Shannon-based J responds strongly to rare species, Simpson-based evenness is weighted toward the abundant ones, and Berger-Parker ignores everything except the single dominant. Most intact natural communities return J between 0.6 and 0.9; values below 0.4 usually indicate eutrophication, chronic disturbance or invasion by a dominant. Two errors are common. The Shannon value entered must use natural logarithms, since an H computed in log base 2 or base 10 will produce a J that is wrong by a constant factor. And although J was intended to be independent of richness, it is not fully so in practice: undetected rare species inflate the estimate in small samples, so evenness should be compared only across samples of similar or rarefied effort.

The mathematics came from outside biology. Claude Shannon published his measure of information entropy in 1948 in the Bell System Technical Journal, addressing signal transmission rather than ecology. Ecologists adopted it within a decade, with Robert MacArthur applying it to bird communities in 1955 and Ramon Margalef promoting information theory as a framework for community ecology in 1958. The index is still cited inconsistently as Shannon-Wiener or Shannon-Weaver, the latter a persistent misattribution to Warren Weaver, who wrote an expository chapter rather than the theory. Edward Hugh Simpson had meanwhile proposed his own dominance measure in a one-page 1949 note in Nature. Evenness became a separate quantity when Evelyn Chrystalla Pielou, a Canadian mathematical ecologist, defined J as the ratio of observed to maximum Shannon diversity in the Journal of Theoretical Biology in 1966, arguing that richness and equitability answered different ecological questions and should not be collapsed into one number. Wolfgang Berger and Frances Parker introduced their dominance index in Science in 1970 while analysing planktonic foraminifera in deep-sea cores. Criticism followed the proliferation: Stuart Hurlbert argued in 1971 that species diversity had become a non-concept through vague usage, and Ben Smith and J. Bastow Wilson evaluated fourteen evenness indices against formal criteria in Oikos in 1996, finding that several widely used measures, including Pielou J, fail the requirement of independence from species richness.