How diverse is a community — a meadow, a microbiome, a stretch of reef? Simpson’s index answers with a probability: pick two individuals at random, and ask whether they belong to the same species. This Simpson’s Diversity Index Calculator takes the count of individuals in each species and returns all three standard forms — D, the Gini–Simpson index 1 − D, and the reciprocal 1/D — because the literature uses each of them and confusing them reverses conclusions.
Worked Example: Three Species, Twenty Individuals
Counts of 10, 5 and 5 give N = 20 individuals across S = 3 species. The numerator Σn(n−1) = 10×9 + 5×4 + 5×4 = 90 + 20 + 20 = 130; the denominator N(N−1) = 20×19 = 380; so D = 130/380 ≈ 0.3421 — a 34% chance that two randomly drawn individuals are the same species. The diversity readings flip it: 1 − D ≈ 0.6579 (a 66% chance the pair differs) and 1/D ≈ 2.92, the “effective number of species”: this community, dominated by its first species, has the diversity of just under three equally common species — intuitively right, since it is three species with one holding half the individuals. Push the counts toward dominance, say 18, 1, 1, and D leaps to (306 + 0 + 0)/380 ≈ 0.805 while 1/D falls to 1.24: effectively barely more than one species, exactly the ecological story the raw species count of 3 would conceal.
The Three Forms and Why All of Them Exist
Simpson’s original D is a dominance index: it rises as diversity falls, which confuses every first-time reader, so ecology standardized on two repairs. The Gini–Simpson index 1 − D converts it into a probability of difference, bounded in [0, 1), rising with diversity. The reciprocal 1/D converts it into species units — the effective number of species — which behaves linearly in a way probabilities do not: a community with 1/D = 6 is, in a defensible sense, twice as diverse as one with 1/D = 3, a sentence you cannot say about 1 − D values of 0.83 and 0.67. The finite-sample formula used here, Σn(n−1)/N(N−1), is the unbiased version (sampling without replacement); the large-sample shortcut D = Σp², squaring each species’ proportion, agrees closely once N is large. Whichever form a paper reports, the conversion runs through D — compute it once, as this page does, and the other two are arithmetic.
Where Simpson’s Index Is Used
Ecology and conservation compare habitats, track restoration, and detect disturbance: a stressed community typically sheds rare species first and concentrates into a few tolerant ones, which Simpson’s index registers loudly because it weights common species most. Microbiome research reports it for gut and soil samples (often as 1/D, the inverse Simpson). Beyond biology, the identical formula measures market concentration (as the Herfindahl–Hirschman Index, Σp² over market shares), income and demographic diversity, and portfolio concentration — anywhere “how dominated is this distribution?” is the question. Its blind spot is the mirror of its strength: rare species barely move it, so studies that care about rarity pair Simpson with a richness-sensitive measure like the Shannon index rather than asking one number to tell both stories.
Common Mistakes
Reporting D while calling it diversity — D is dominance, and a “higher diversity” claim built on raw D is backwards. Comparing indices computed from different sample sizes without noting that small samples bias D upward slightly (the n(n−1) form here corrects the worst of it). Feeding percentages into the count formula: the finite-sample version needs raw counts, though the Σp² form accepts proportions — know which you are holding. And ranking two communities by Simpson alone when their species counts differ wildly: a 3-species even community can outscore a 30-species dominated one, which is a true statement about dominance and a misleading one about richness.
A Two-Community Comparison at Realistic Scale
Scale the example up to a proper field sample of 200. Community A, counts 100, 50, 50, gives D = 0.3719 and 1 − D = 0.6281. Community B, nearly even at 67, 67, 66, gives D = 0.3300 and 1 − D = 0.6700. Same three species, same total — yet B is measurably more diverse on every Simpson reading, purely because its individuals are shared more equally. Note also how the small-sample example (10, 5, 5: D = 0.3421) and its scaled twin (100, 50, 50: D = 0.3719) differ slightly: the n(n−1) correction matters most at small N, which is why the calculator uses counts rather than the Σp² shortcut.
Related Tools
Continue with the Benford’s Law Calculator, the MSE Calculator, the Weibull Distribution Calculator, or browse the full Statistics Calculators hub.
Frequently Asked Questions
What is Simpson’s diversity index?
From counts n per species and total N: D = Σn(n−1) / N(N−1), the probability that two randomly drawn individuals are the same species. Diversity is usually reported as 1 − D or 1/D.
What do the values 0.3421, 0.6579 and 2.92 mean?
For counts 10, 5, 5: D = 0.3421 (34% chance a random pair matches), 1 − D = 0.6579 (66% chance it differs), and 1/D = 2.92 — the community has the diversity of about 2.92 equally common species.
Which form should I report?
Match your field’s convention and label it explicitly: ecologists often use 1 − D or 1/D (inverse Simpson); the effective-number form 1/D is the most interpretable across audiences. Never report an unlabeled “Simpson index.”
How is Simpson different from Shannon diversity?
Simpson weights common species heavily and barely notices rare ones; Shannon (entropy-based) is more sensitive to rare species and total richness. They answer different questions and are often reported together.
Can I enter proportions instead of counts?
The calculator expects counts, because the unbiased formula needs them. With only proportions p, use the large-sample form D ≈ Σp² — close for big samples, and this page’s counts can be recovered by scaling proportions to a total.
What is the maximum possible diversity for 3 species?
Perfect evenness: counts as equal as possible, where 1/D approaches 3 — the actual species count. Any dominance pulls the effective number below the true count, as the 10, 5, 5 example shows at 2.92.