Simpson’s index, introduced by Edward Simpson in 1949, captures two things at once: how many species a community holds (richness) and how evenly the individuals are spread among them (evenness). D is the probability that two individuals picked at random, without putting the first back, belong to the same species. A community dominated by one species has D close to 1; a rich, even community has D close to 0.
Because “bigger means less diverse” is confusing, ecologists usually report the Simpson’s diversity index 1 − D, the probability that the two individuals are different species, or the reciprocal index 1/D, which can be read as the “effective number” of equally common species. A meadow with 1/D = 3.7 is as diverse as one with about 3.7 equally abundant species.
Simpson’s measures are weighted towards the common species, so adding a few rare species barely changes them – unlike the Shannon index, which is more sensitive to rare species. The same formula is used outside ecology: in economics Σp² is the Herfindahl–Hirschman index of market concentration, and in genetics 1 − Σp² is the expected heterozygosity.
How to use the Simpson’s Diversity Index Calculator
- Number of individuals of each species
Results update as you type, and everything is calculated in your browser.
How it works
Enter the count of individuals for each species. The calculator adds them to get N, sums nᵢ(nᵢ − 1) over the species and divides by N(N − 1) to get D. Then it derives 1 − D, 1/D, evenness and the with-replacement form Σ(nᵢ ÷ N)².
Worked example
A pond survey counts 40, 25, 20, 10 and 5 individuals of five species (N = 100). Σn(n − 1) = 1,560 + 600 + 380 + 90 + 20 = 2,650 and N(N − 1) = 9,900, so D = 0.2677, 1 − D = 0.7323 and 1/D = 3.736. Evenness is 3.736 ÷ 5 = 0.747. The with-replacement form gives Σp² = 0.275 and 1 − Σp² = 0.725.
Same richness, different evenness
| Community (4 species) | 1 − D | 1/D |
|---|---|---|
| 25, 25, 25, 25 | 0.758 | 4.13 |
| 40, 30, 20, 10 | 0.707 | 3.41 |
| 85, 5, 5, 5 | 0.273 | 1.38 |
What each result means
- Simpson’s index D = simpson([Number of individuals of each species])
- Simpson’s diversity index 1 − D = 1 – [Simpson’s index D]
- Simpson’s reciprocal index 1/D = 1÷[Simpson’s index D]
- Species richness S = count([Number of individuals of each species])
- Total individuals N = sum([Number of individuals of each species])
- Simpson’s evenness (1/D) ÷ S = [Simpson’s reciprocal index 1÷D]÷[Species richness S]
- Infinite-population form Σp² = ss([Number of individuals of each species])÷sum([Number of individuals of each species])^2
- 1 − Σp² (with replacement) = 1 – [Infinite-population form Σp²]
Formula
D = Σnᵢ(nᵢ − 1) ÷ (N(N − 1)) · Gini–Simpson = 1 − D · Inverse Simpson = 1/D · evenness E = (1/D) ÷ S
Worked example
Inputs — Number of individuals of each species: 40, 25, 20, 10, 5.
Results — Simpson's index D = 0.2677; Simpson's diversity index 1 − D = 0.7323; Simpson's reciprocal index 1/D = 3.7358; Species richness S = 5; Total individuals N = 100; Simpson's evenness (1/D) ÷ S = 0.7472; Infinite-population form Σp² = 0.275; 1 − Σp² (with replacement) = 0.725; Diversity level = High.
Key terms
- Species richness
- The number of different species in the sample.
- Species evenness
- How similar the abundances of the species are.
- Simpson's index (D)
- The probability that two individuals drawn without replacement are the same species.
- Effective number of species
- 1/D – the number of equally common species that would give the same diversity.
Frequently asked questions
What does Simpson's diversity index tell you?
1 − D is the chance that two randomly chosen individuals are of different species. 0.73 means a 73% chance of picking two different species.
What is the range of Simpson's index?
D and 1 − D lie between 0 and 1. 1/D ranges from 1 (a single species) up to the number of species S when all are equally common.
What is the difference between D, 1 − D and 1/D?
They carry the same information on different scales: D measures dominance, 1 − D diversity as a probability and 1/D diversity as an effective number of species.
Which formula should I use, n(n − 1) or p²?
Use Σn(n − 1) ÷ N(N − 1) for counted samples (sampling without replacement). Σp² is the version for an infinite population or for percentages; the two agree closely for large samples.
What is Simpson's index of 300, 335 and 365 individuals?
N = 1,000, Σn(n − 1) = 334,450, so D = 334,450 ÷ 999,000 = 0.335, 1 − D = 0.665 and 1/D = 2.99.
Simpson or Shannon – which is better?
Neither. Simpson is dominated by common species and is robust to sample size; Shannon gives more weight to rare species. Many studies report both.
Can Simpson's index be used outside ecology?
Yes – for market shares (Herfindahl–Hirschman index), genetic diversity, language diversity, or the variety of answers to a survey question.