Diversity Index Calculators

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A diversity index is a mathematical measure that quantifies the biodiversity of a community, combining information about both the number of species (richness) and their relative abundances (evenness) into a single value. The two most widely used diversity indices are Shannon's H' (H' = −Σpᵢ ln(pᵢ); higher = more diverse) and Simpson's D (D = Σpᵢ²; higher = more dominance; usually reported as 1−D). Shannon index is more sensitive to rare species; Simpson is dominated by abundant species. Additional indices include Margalef's D, Chao1 (species richness estimator), and Hill numbers (unified framework using effective species counts).

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Shannon Index H'

H' = −Σ pᵢ × ln(pᵢ)

pᵢ = relative abundance of species i. Range: 0 (monoculture) to ln(S) (perfect evenness). Pielou's evenness: J = H'/ln(S).

Simpson Index D

D = Σ pᵢ²

High D = dominance by few species. Reported as 1−D (Simpson diversity index, 0–1) or 1/D (effective species). For finite sample: D = Σ nᵢ(nᵢ−1)/N(N−1).

Comparison

  • Shannon H': sensitive to rare species; most widely used
  • Simpson 1−D: dominated by abundant species; robust to sampling incompleteness
  • Margalef D = (S−1)/ln(N): corrects richness for sample size
  • Hill numbers: unified framework; ¹D = e^H'; ²D = 1/Simpson D

Example Calculation

3 species: n = 60, 30, 10 (N=100). pᵢ = 0.6, 0.3, 0.1. H' = −(0.6×ln0.6 + 0.3×ln0.3 + 0.1×ln0.1) = −(−0.306 − 0.361 − 0.230) = 0.897. 1−D = 1 − (0.36+0.09+0.01) = 0.54.

Glossary

Shannon Diversity Index (H')
H' = −Σpᵢ ln(pᵢ); ranges 0 to ln(S); sensitive to rare species; paired with Pielou's evenness J = H'/ln(S); widely used standard ecological diversity measure.
Simpson Index (D and 1−D)
D = Σpᵢ²; probability two random individuals belong to the same species; reported as 1−D (0–1 diversity) or 1/D (effective species); dominated by abundant species.
Hill Numbers
A unified diversity framework: ⁰D = S (richness); ¹D = e^H' (Shannon effective species); ²D = 1/Simpson D; all in 'species' units; allow multiplicative beta partitioning.

Frequently Asked Questions

A diversity index is a single number that summarizes the biodiversity of a community by combining species richness (how many species) and species evenness (how equally abundant they are). No diversity index captures all aspects of diversity — each emphasizes different features. Shannon H': weighted by log of relative abundance; sensitive to rare species; information-theoretic interpretation. Simpson D (or 1−D): weighted by squared relative abundance; dominated by common species; intuitive as 'probability two random individuals differ in species.' The choice of index affects which community appears 'more diverse' — a community with many rare species will score higher on Shannon, while one dominated by a few common species may score similarly on Simpson.

Data: species counts n₁, n₂, ..., nₛ; total N = Σnᵢ. Step 1: relative abundance pᵢ = nᵢ/N. Shannon H': H' = −Σ pᵢ × ln(pᵢ). For each species: multiply pᵢ × ln(pᵢ); sum all; multiply by −1. Simpson D: D = Σpᵢ². For each species: square pᵢ; sum. Report as 1−D (diversity) or 1/D (effective species). Example: species A=50, B=30, C=20 (N=100): p = 0.5, 0.3, 0.2. H' = −(0.5×(−0.693) + 0.3×(−1.204) + 0.2×(−1.609)) = −(−0.347 − 0.361 − 0.322) = 1.030. D = 0.25 + 0.09 + 0.04 = 0.38. 1−D = 0.62. 1/D = 2.63.

Pielou's J = H'/H'_max = H'/ln(S). J ranges from 0 (complete dominance by one species) to 1 (all species equally abundant). It is the evenness component of Shannon diversity, standardized to the number of species present. Why useful: a community with 10 species and H' = 2.0 may seem more diverse than a 5-species community with H' = 1.5; but ln(10) = 2.303 → J = 2.0/2.303 = 0.87; while ln(5) = 1.609 → J = 1.5/1.609 = 0.93. The 5-species community actually has higher evenness. Reporting both H' and J gives a complete picture.

Shannon H': use when rare species are important; for general community comparisons; when information-theoretic interpretation is desired; most commonly expected in ecological publications. Simpson 1−D: use when sampling is incomplete (rare species often missed; Simpson is robust); when dominant species drive function; when communicating to non-specialists (1−D = 'probability two random individuals belong to different species' is intuitive). Margalef D: quick estimate when only S and N are available. Chao1 (non-parametric estimator): estimates true richness from incomplete samples; use when richness comparison is the goal. Hill numbers (all three orders): modern recommendation; report ⁰D (richness), ¹D (Shannon effective species = e^H'), and ²D (Simpson effective species = 1/D) as a diversity profile.