If you’ve just run your first plankton or vegetation count and opened a stats guide to calculate “diversity,” you’ve probably hit the same wall every student does: there isn’t one diversity index, there are several, and they don’t always agree with each other. Shannon-Wiener, Simpson’s, and Pielou’s Evenness show up together in almost every ecology thesis, but they’re measuring different things, and mixing them up (or reporting the wrong version of Simpson’s) is one of the most common mistakes examiners flag. Here’s what each one actually tells you, and how to decide what to report.
What These Indices Are Actually Measuring
Before the formulas, it helps to separate two ideas that get lumped together under “diversity”: richness and evenness. Richness is simply how many different species you found, species count and nothing else. Evenness is how evenly the individuals are spread across those species: a community with 100 individuals split 25/25/25/25 across four species is more even than one split 94/2/2/2 across the same four species, even though both have identical richness. “Diversity” in the ecological sense usually means some combination of the two, more species and a more even spread both push diversity up. Shannon-Wiener and Simpson’s are both combined diversity measures; Pielou’s Evenness isolates just the evenness part.
Shannon-Wiener Diversity Index (H′)
The Shannon-Wiener index (sometimes called the Shannon index or Shannon-Weaver index) is the one you’ll see cited most often. It’s calculated as H′ = −Σ(pᵢ × ln pᵢ), where pᵢ is the proportion of individuals belonging to species i out of the total sample, and the sum runs across every species you recorded. In plain terms: for each species, you take its share of the total, multiply by the natural log of that share, sum all those values, and flip the sign. Most real ecological communities produce an H′ between about 1.5 and 3.5; values above 4.5 are rare. There’s no universal “good” or “bad” cutoff, what matters is how your sites compare to each other, not the number in isolation.
Simpson’s Diversity Index, and the Version Mix-Up That Trips Up Half of Students
Simpson’s index is where most confusion happens, because there are three versions floating around under the same name, and they point in opposite directions. The original Simpson’s D = Σ(pᵢ²) is a dominance index: it’s the probability that two individuals picked at random from your sample belong to the same species. Because of that, a higher D means lower diversity, more of the community is “dominated” by a few common species. To turn it into a diversity index that behaves like Shannon-Wiener (higher number = more diverse), most papers report either 1 − D (the Gini-Simpson index) or 1/D (the inverse Simpson index, also called Hill’s N2). The single most important habit here: state clearly which version you’re reporting. A reviewer or examiner seeing “Simpson’s Index = 0.85” has no way to know whether that means high dominance or high diversity unless you tell them.
Pielou’s Evenness Index (J′)
Pielou’s Evenness strips out richness entirely and tells you only how evenly individuals are distributed. It’s calculated as J′ = H′ / ln(S), where H′ is your Shannon-Wiener value and S is the number of species you recorded (richness). J′ always falls between 0 and 1: a value of 1 means every species is represented by exactly the same number of individuals (perfectly even), while values closer to 0 mean the community is increasingly dominated by one or two species. It’s a useful companion to Shannon-Wiener because two sites can have an identical H′ for completely different reasons, one because it’s genuinely balanced, another because a middling species count offsets uneven distribution, and evenness is what separates the two stories.
| Index | What It Measures | Range | Higher Value Means |
|---|---|---|---|
| Shannon-Wiener (H′) | Richness + evenness combined | Typically 0–4.5 | More diverse community |
| Simpson’s D (original) | Dominance (chance two random individuals match) | 0–1 | Less diverse (more dominance) |
| Simpson’s 1−D or 1/D | Diversity (inverted dominance) | 0–1 (for 1−D) | More diverse community |
| Pielou’s Evenness (J′) | Evenness only, richness removed | 0–1 | More even distribution |
A Small Worked Example
Say a quadrat count turns up four species with 40, 30, 20, and 10 individuals (100 individuals total). The proportions are 0.4, 0.3, 0.2, and 0.1. Working through the formulas: H′ works out to about 1.28. Species richness S is 4, so Pielou’s Evenness J′ = 1.28 / ln(4) = 1.28 / 1.386 ≈ 0.92, close to perfectly even. Simpson’s original D = (0.4² + 0.3² + 0.2² + 0.1²) = 0.30, so the Gini-Simpson value (1 − D) is 0.70 and the inverse Simpson (1/D) is about 3.33. Notice that all three diversity-direction numbers, H′ = 1.28, 1−D = 0.70, 1/D = 3.33, tell a consistent story (this is a fairly diverse, fairly even community), just on different scales. That’s normal: the indices agree on direction far more often than they agree on scale.
So Which Diversity Index Should You Report?
Most thesis committees and journals in ecology expect at least Shannon-Wiener and Pielou’s Evenness reported together, since H′ alone can’t tell a reader whether a low value came from low richness or low evenness. Add Simpson’s (clearly labelled as to which version) if your comparison is specifically about dominance, for example, comparing a polluted site where a few pollution-tolerant species take over against a cleaner site with a more balanced community. If you’re short on space or your supervisor hasn’t specified, reporting all three side by side, in a table like the one above, is the safest default and is exactly the layout most published aquatic ecology papers use.
Common Mistakes Worth Avoiding
A few errors come up again and again in thesis drafts: using log base 10 or log base 2 instead of the natural log (ln) for Shannon-Wiener without saying so, since the choice changes the numeric value even though the underlying formula is the same; reporting a Simpson’s value without specifying whether it’s D, 1−D, or 1/D; pooling samples from different sites before calculating indices when the comparison is actually between sites, which erases the differences you’re trying to show; and treating an index value as inherently “good” or “bad” without a comparison baseline, since diversity indices are only meaningful relative to another site, another season, or another study, not as standalone numbers.
If you’d rather not do these calculations by hand every time you get a new plankton or vegetation count, ZoologyFix’s free Biodiversity & Plankton Suite calculates Shannon-Wiener, Simpson’s, and Pielou’s Evenness directly in your browser, no software install, and your data never leaves the page. For more on presenting these results, see our Data & Statistics guide.
Frequently Asked Questions
Shannon-Wiener weighs both richness and evenness and is more sensitive to rare species, while Simpson’s index is weighted toward the most dominant species and is less sensitive to rare ones — they can tell different stories about the same community.
Pielou’s Evenness measures how evenly individuals are distributed across the species present, independent of how many species there are, with a value of 1 meaning perfectly even distribution.
Most theses report all three together rather than picking one, since each captures a different aspect of community structure — richness, dominance, and evenness — and examiners generally expect to see that fuller picture.
Generally yes, higher values indicate a more diverse, balanced community, but it should be interpreted alongside the site’s other water-quality and pollution data rather than in isolation.
References
- Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3), 379–423.
- Simpson, E.H. (1949). Measurement of Diversity. Nature, 163, 688. View paper.
- Pielou, E.C. (1966). The Measurement of Diversity in Different Types of Biological Collections. Journal of Theoretical Biology, 13, 131–144.
- Magurran, A.E. (2004). Measuring Biological Diversity. Blackwell Publishing, Oxford.