Simpson's Index Calculators
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Simpson's Index Formulas
D = Σ(nᵢ/N)² = Σpᵢ² (dominance; high D = low diversity). 1−D (Simpson's diversity index; range 0–1; 0 = minimum diversity; 1 = maximum). 1/D (Simpson's reciprocal index; minimum 1 when all individuals are one species; maximum = S when all species equally abundant).
Example: 3 species: n₁=70, n₂=20, n₃=10; N=100. pᵢ: 0.70, 0.20, 0.10. D = 0.70² + 0.20² + 0.10² = 0.49 + 0.04 + 0.01 = 0.54. 1−D = 0.46. 1/D = 1.85.
Interpretation
- D close to 1: one species dominates (low diversity)
- D close to 0: many species, equal abundance (high diversity)
- 1−D close to 1: high diversity
- 1/D = 1: monoculture; 1/D = S: perfectly even community
Comparison with Shannon H'
Both measure diversity but differ in emphasis: Shannon H' is more sensitive to rare species (uses ln(pᵢ) — small pᵢ contributes disproportionately to H'). Simpson D is dominated by abundant species (uses pᵢ² — large pᵢ contributes disproportionately). For communities with many rare species: Shannon H' will be higher than indicated by 1/D.
Glossary
Frequently Asked Questions
Simpson's index (D) = Σpᵢ² = the probability that two randomly chosen individuals from the community belong to the same species. Interpretation: D = 1.0: all individuals belong to one species (maximum dominance, minimum diversity). D = 0.0: infinitely many species, each with infinitesimally small proportion (maximum diversity — unreachable in practice). Usually reported as 1−D (Simpson's diversity index, 0 to 1) or 1/D (reciprocal index, 1 to S). Sample: 50 oak, 30 birch, 20 maple (N=100): D = (0.5)² + (0.3)² + (0.2)² = 0.25 + 0.09 + 0.04 = 0.38. 1−D = 0.62. 1/D = 2.63 (community has the effective diversity of 2.63 equally abundant species).
Step 1: Count individuals of each species (nᵢ). Step 2: Calculate total individuals: N = Σnᵢ. Step 3: Calculate proportion of each species: pᵢ = nᵢ/N. Step 4: Square each proportion: pᵢ². Step 5: Sum all squared proportions: D = Σpᵢ². Step 6: Calculate diversity: 1−D or 1/D. Example: 4 bird species with counts 25, 15, 8, 2 (N = 50): pᵢ = 0.50, 0.30, 0.16, 0.04. pᵢ² = 0.2500, 0.0900, 0.0256, 0.0016. D = 0.2500 + 0.0900 + 0.0256 + 0.0016 = 0.3672. 1−D = 0.633. 1/D = 2.72.
Both measure diversity from species abundance data, but differ in sensitivity: Shannon H' = −Σpᵢ ln(pᵢ): equally sensitive to all species — rare species with small pᵢ contribute meaningfully to H' via ln(pᵢ) term. More sensitive to rare species. Simpson D = Σpᵢ²: dominated by abundant species — pᵢ² amplifies the contribution of common species; rare species with tiny pᵢ contribute negligibly to D. When to use which: Shannon H': when rare species are ecologically important; when interested in total information content of the community; general diversity comparison. Simpson 1−D or 1/D: when you want to emphasize the most abundant species; when communicating to non-specialists (1−D easily interpreted as 'probability two random individuals are different species').
1/D = the 'effective number of species' — the number of equally abundant species that would produce the same Simpson D as the observed community. This is the Hill number of order 2 (²D in Hill's notation). Properties: 1/D = 1: monoculture (one species). 1/D = S (species richness): all S species equally abundant. 1/D is always between 1 and S. Communities with the same S but different evenness will have different 1/D. Example interpretation: if 1/D = 5 for a community with 20 species, it has the 'effective diversity' of 5 equally abundant species — dominated by 5 common species while 15 are rare. Advantage over 1−D: 1/D is a true effective species count (linear scale); 1−D is bounded by 0–1 and has a compressed scale at high diversity.