Simpson Diversity Index Calculator
Compute Simpson's dominance index, Simpson's index of diversity (1 − D) and the reciprocal Simpson index (1/D) from a list of species abundances.
How it works
D = Σ nᵢ(nᵢ−1) / [N(N−1)] · Index of diversity = 1 − D · Reciprocal Simpson = 1 / Σ pᵢ² where pᵢ = nᵢ / N
Simpson's index measures the probability that two individuals drawn at random belong to the same species — a dominance measure D. Because high dominance means low diversity, ecologists usually report 1 − D (the index of diversity), which rises toward 1 as a community becomes more even and species-rich. The reciprocal form 1/Σpᵢ² expresses diversity as an 'effective number of species', which is easier to compare between communities. Unlike a raw species count, all three weight abundant and rare species by how common they are.
Worked example
For counts 40, 30, 20, 10 (N = 100): Σn(n−1) = 1560 + 870 + 380 + 90 = 2900, and N(N−1) = 9900, so D = 0.293. The index of diversity is 1 − 0.293 = 0.707. With Σpᵢ² = 0.30, the reciprocal Simpson index is 1/0.30 ≈ 3.33 effective species.
Sources: Diversity index — Wikipedia
Frequently asked questions
Does a higher Simpson value mean more diversity?
It depends which form you read. The dominance index D falls as diversity rises, while 1 − D and the reciprocal 1/D both increase with diversity. Always state which version you are quoting.
What is the reciprocal Simpson index good for?
It converts the index into an effective number of equally-common species. A value of 3.3 means the community is about as diverse as 3.3 species present in equal numbers, which is intuitive to compare across sites.
How is Simpson different from the Shannon index?
Simpson weights common species more heavily and is less sensitive to rare species, whereas the Shannon index gives rare species relatively more influence. Reporting both is common practice.
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This calculator is for educational purposes. Double-check important results before acting on them.