What is Simpson's Index?
Simpson's indices are a way of quantifying the biodiversity of communities. The value of Simpson's index reflects how many different types of species are in a community and how evenly distributed the population of each species is.
The Simpson's Index D (introduced by Simpson in 1949) is the probability that any two individuals randomly selected from an infinitely large community will belong to the same species:
D = Σ pᵢ²
where pᵢ is the proportion of individuals belonging to the i-th species.
For a finite-size community, the formula becomes:
D = Σ nᵢ(nᵢ − 1) / N(N − 1)
where nᵢ is the number of individuals in the i-th species and N is the total number of individuals.
As D increases, diversity decreases. Although originally proposed to measure diversity in ecological communities, Simpson's Index is now widely used to quantify diversity in many other contexts — for example, gender or ethnicity diversity in organizations.
Simpson's Diversity Index Formula
Three related indices are derived from Simpson's D:
- Simpson's Index (D) — probability that two randomly chosen individuals belong to the same species. Range: 0–1. Higher D = lower diversity.
- Simpson's Diversity Index (1 − D) — the complement of D. Range: 0–1. Higher value = higher diversity. This is the most commonly cited measure.
- Simpson's Reciprocal Index (1 / D) — the reciprocal of D. Minimum value = 1 (one species dominates completely); maximum = S (number of species, when all are equally abundant).
How to Use the Simpson's Diversity Index Calculator
- Enter the name of each species or group (optional, for labeling).
- Enter the count (number of individuals) for each species.
- Add up to 10 species using the + Add Species button.
- Click Calculate to get D, 1−D, and 1/D instantly.
The calculator uses the finite-population formula D = Σnᵢ(nᵢ−1) / N(N−1) and requires at least 2 species with at least 1 individual each.
Example of Simpson's Diversity Index Calculation
Suppose a forest plot contains three tree species:
- Oak: 40 individuals
- Pine: 35 individuals
- Birch: 25 individuals
Step 1: N = 40 + 35 + 25 = 100
Step 2: Compute nᵢ(nᵢ−1) for each species:
Oak: 40 × 39 = 1560 | Pine: 35 × 34 = 1190 | Birch: 25 × 24 = 600
Step 3: D = (1560 + 1190 + 600) / (100 × 99) = 3350 / 9900 ≈ 0.3384
Step 4: Diversity Index = 1 − 0.3384 = 0.6616 (medium-high diversity)
Step 5: Reciprocal Index = 1 / 0.3384 ≈ 2.956
Simpson's Diversity Index Interpretation
| Diversity Index (1−D) | Interpretation | Example |
|---|---|---|
| 0.00 – 0.49 | Low diversity — one or a few species dominate | A monoculture plantation |
| 0.50 – 0.74 | Medium diversity — reasonably balanced community | A managed forest |
| 0.75 – 1.00 | High diversity — many species, evenly distributed | A tropical rainforest or coral reef |
A value of 0 means the community consists of only one species. A value of 1 (or a very high reciprocal index) indicates maximum evenness across all species.
FAQs
What is the difference between Simpson's Index and the Shannon Diversity Index?
Both measure species diversity, but Simpson's Index (D) focuses on dominance — the probability that two random individuals are the same species. The Shannon Index (H) uses information theory and is more sensitive to rare species. For most practical applications, Simpson's 1−D is preferred for its intuitive 0–1 scale.
Can I use this calculator for non-ecological data?
Yes! Simpson's Index applies to any nominal categorical data: ethnic diversity in a workforce, language diversity in a country, product variety in a market, etc. Just replace "species" with your category and "individuals" with your count.
Does the calculator handle large populations?
Yes. The formula D = Σnᵢ(nᵢ−1) / N(N−1) is the exact finite-population version and works correctly for any size of community. For very large communities (N → ∞), it converges to the infinite-population formula D = Σpᵢ².
What unit systems does this calculator support?
Simpson's Diversity Index is a dimensionless ratio — it uses raw individual counts, so no unit conversion (metric or US customary) is needed. Enter counts in any consistent unit (individuals, observations, records, etc.).