Pielou's Evenness (J′)

Two things make a community diverse: how many species there are, and how equally the individuals are spread among them. The Shannon index folds both into one number, which is convenient until you want to know which of the two is driving a difference. Evelyn Pielou's 1966 answer was to divide H′ by the largest value it could possibly take for that species count. That maximum is ln S, achieved when every species holds exactly 1/S of the individuals, so J′ = H′/ln S is diversity expressed as a fraction of its own ceiling. A community at 0.4, 0.3, 0.2 and 0.1 has H′ = 1.2799 against a ceiling of ln 4 = 1.3863, so J′ = 0.923 — that community is 92% as even as four species can be.

J′ is a proportion, always between 0 and 1, and it never carries a unit. That is worth saying because the two quantities either side of the division do not behave the same way: H′ is a pure number of nats, and S is a count of things. The ratio is a fraction of a maximum, which is precisely the kind of quantity people report as a percentage without thinking, and 92% evenness is a perfectly good way to say it.

Solving backwards for S is the interesting direction and the page will do it: S = e^(H′/J′). It is not a species count you should go looking for in the field. It is the richness a reported pair implies, and it is a good way to catch a paper that has quoted an H′ from one sample and a J′ from another. It will almost never be a whole number, which is the honest signal that it is an inference rather than a tally.

The trap in evenness is the denominator, and it is a bad one. ln S depends on S, and S is the number of species you FOUND, not the number that live there. Sample the same wood harder and you add rare species; each one adds only a sliver to H′ but pushes ln S up straight away, so measured evenness falls even though nothing about the wood changed. Between two surveys of unequal effort, a lower J′ can mean nothing more than a longer afternoon with the sweep net. This is the same comparability problem the Shannon page carries, sharpened: evenness inherits the effort-dependence of H′ and adds its own through S. Fix the effort, or do not compare the numbers.

A second, quieter trap is reading a low J′ as damage. Some perfectly healthy communities are dominated by design: a salt marsh, a reedbed, a mature beech wood in deep shade. Evenness is a description of structure, not a score out of ten, and the reason to compute it is to separate the two things Shannon glues together. A site whose H′ has fallen might have lost species, or might have kept them all and become more lopsided — those need different responses, and J′ is how you tell which happened.