Simpson's Diversity Index Calculator
Calculate Simpson's diversity index D, 1-D, and 1/D from species abundance data. Compare biodiversity between communities using this probability-based measure of dominance.
🌳 Ecology📐 D = Σ(pi²) or Σni(ni-1)/N(N-1)🧬 Biology
Species 1 count n1
Species 2 count n2
Species 3 count n3
Species 4 count n4 (optional)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Simpson's Diversity Index Calculator | — | D = Σ(pi²) or Σni(ni-1)/N(N-1) | 0 to 1 |
Step-by-Step Examples
Example 1
Mixed forest
60, 30, 8, 2 individuals of 4 species. N=100.
- D = Σni(ni-1)/N(N-1)
- = (60×59+30×29+8×7+2×1)/(100×99)
- = (3540+870+56+2)/9900 = 4468/9900 = 0.451
- 1-D = 0.549
✓ D=0.451, 1-D=0.549, 1/D=2.22
Example 2
Equal abundance
25 each of 4 species, N=100.
- D = 4×(25×24)/(100×99) = 4×600/9900 = 2400/9900 = 0.242
- 1-D = 0.758 (higher diversity than unequal case)
✓ D=0.242, 1-D=0.758
Example 3
Near monoculture
95, 2, 2, 1 individuals, N=100.
- D = (95×94+2×1+2×1+1×0)/9900 = 8930/9900 = 0.902
- 1-D = 0.098: very low diversity
✓ D=0.902: nearly complete dominance
Real-World Applications
Biodiversity Surveys
Compare diversity across sites, habitats, or time periods. Simpson is more robust to rare species than Shannon.
Environmental Impact Assessment
Before/after biodiversity assessment for development projects.
Microbial Communities
Gut microbiome, soil microbiome diversity analysis. Often more informative than OTU richness alone.
Water Quality
Macroinvertebrate Simpson D used as biotic index for stream health assessment.
Common Mistakes to Avoid
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D is dominance, 1-D is diversity
D (Simpson concentration) = probability two random individuals are same species. High D = low diversity. Use 1-D or 1/D for diversity.
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Use ni(ni-1) for sample data
When working with counts (not proportions), use Σni(ni-1)/N(N-1) instead of Σpi². The latter is for true population proportions.
⚠️
More weight to common species than Shannon
Simpson emphasizes dominant species. Shannon gives more weight to rare species. Choose based on your ecological question.
Frequently Asked Questions
How does Simpson differ from Shannon? ▾
Simpson: probability-based, weights dominant species more. Shannon: information-based, more sensitive to rare species. Both valid; choose based on community structure and research question.
What does 1/D mean? ▾
Reciprocal Simpson (1/D): effective number of equally abundant species that would give the same D. 1/D = 2 means diversity equivalent to 2 equally common species.
What is the Berger-Parker index? ▾
Simplest dominance measure: d = n_max/N (most abundant species / total). Easy to calculate, focuses entirely on the most dominant species.
When is Simpson preferred over Shannon? ▾
When the dominant species is most important ecologically (fisheries, pest ecology). When dealing with large datasets where rare species counting is unreliable.
What is the effective number of species? ▾
Converting diversity indices to effective species: exp(H) for Shannon, 1/D for Simpson. Intuitive unit: how many equally common species would give this diversity value.