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Simpson's D, Shannon H' — Biodiversity

Simpson's D, Shannon-Wiener H', species richness, evenness. Ecology, microbiome, conservation.

Concept Fundamentals
0.1583
D
1.8769
H'
Compute DiversitySimpson, Shannon

Why This Statistical Analysis Matters

Why: Diversity indices quantify species evenness and richness. Used in ecology, microbiology, conservation.

How: Enter species abundances. Get D, 1−D, Shannon H', evenness, effective species.

  • ●D = Σnᵢ(nᵢ−1)/(N(N−1))
  • ●H' = −Σ(pᵢ ln pᵢ)
  • ●1/D = effective species
Sources:Simpson (1949) - Measurement of DiversityMagurran - Measuring Biological Diversity
D
STATISTICSDescriptive Statistics

Simpson's D, Shannon-Wiener H', Species Richness — Biodiversity

Compute Simpson's Diversity Index, Shannon entropy, effective species. Ecology, microbiome, conservation.

IQV (Categorical) →Shannon Entropy →

Real-World Scenarios — Click to Load

Species Abundance Data

Species / CategoryAbundance
simpson_diversity.sh
CALCULATED
$ simpson_diversity --site="Site A"
Simpson's D
0.1583
Simpson's Diversity
0.8417
Shannon H'
1.8769
Species Richness
7
Simpson Reciprocal
6.32
Shannon Evenness
0.9645
Effective Species
6.53
Total N
202
Share:
Simpson's Diversity Index
Site A
D = 0.158
1−D = 0.842H' = 1.877S = 7
numbervibe.com/calculators/statistics/simpsons-diversity-index-calculator

Species Abundance

Proportions (Pie)

Calculation Breakdown

INPUT
Total individuals N
202
Σnᵢ = 45 + 32 + 28 + 22 + 18 + 15 + 42
INPUT
Species richness S
7
ext{Number} ext{of} ext{species}
COMPUTATION
Σnᵢ(nᵢ−1)
6428
ext{Sum} ext{of} nᵢ(nᵢ-1) ext{for} ext{each} ext{species}
COMPUTATION
N(N−1)
40602
Denominator
Simpson's D
0.1583
D = Σnᵢ(nᵢ−1)/(N(N−1)) = 6428/40602
Simpson's Diversity (1−D)
0.8417
ext{Probability} ext{two} ext{random} ext{individuals} ext{differ}
DIVERSITY METRICS
Simpson's Reciprocal
6.32
1/D = ext{effective} ext{number} ext{of} ext{species}
Shannon H'
1.8769
H' = -\text{Sigma} (pᵢ \text{ln} pᵢ)
Shannon Evenness
0.9645
E = H'/ln(S) = 1.8769/ln(7)
Effective species
6.53
\text{exp}(H')

For educational and informational purposes only. Verify with a qualified professional.

📈 Statistical Insights

D

Simpson's D

— Same species

1−D

Diversity

— Different

H'

Shannon

— Entropy

Key Takeaways

  • Simpson's D = probability that two randomly chosen individuals are the same species (0 = infinite diversity, 1 = no diversity)
  • Simpson's Index of Diversity = 1 − D — higher means more diverse
  • Simpson's Reciprocal = 1/D — interpreted as "effective number of species"
  • Shannon-Wiener H' measures information/uncertainty; Shannon Evenness = H'/ln(S)
  • Species Richness S = number of species; diversity combines richness and evenness

Did You Know?

🌿Simpson's index was developed by Edward H. Simpson in 1949 for measuring concentration in ecology.Source: Simpson (1949)
📊Two communities can have the same species richness but different diversity if one is dominated by a single species.Source: Ecology
🧬Shannon entropy is used in microbiome research to quantify bacterial diversity in gut samples.Source: Microbiology
🦋Diversity indices help conservation biologists prioritize habitats for protection.Source: Conservation
📐Simpson's Reciprocal equals species richness when all species have equal abundance.Source: Evenness
🌍Tropical rainforests typically have Simpson's Diversity > 0.9 due to high species richness and evenness.Source: Biogeography

How Simpson's Diversity Index Works

Simpson's Index D measures the probability that two individuals drawn at random from the community are the same species. High D = low diversity. Low D = high diversity.

Formula

D = Σ(nᵢ(nᵢ−1)) / (N(N−1)), where nᵢ = abundance of species i, N = total individuals.

Shannon-Wiener

H' = −Σ(pᵢ ln pᵢ). From information theory. Sensitive to rare species.

Expert Tips

Sample Size

Use the finite-sample formula D = Σnᵢ(nᵢ−1)/(N(N−1)) for small samples.

Comparing Sites

Use Simpson's Reciprocal or Shannon Evenness to account for different species richness.

Simpson vs Shannon

Simpson weights common species more. Shannon is more sensitive to rare species.

Reporting

Report D, 1−D, Shannon H', species richness S, and sample size N for full context.

Diversity Indices Compared

IndexRangeInterpretation
Simpson's D0 to 1Prob. two random individuals same species
Simpson's Diversity0 to 1Prob. two random individuals different
Simpson's Reciprocal1 to SEffective number of species
Gini-Simpson0 to 11 − Σpᵢ², large-sample approx
Shannon H'0 to ln(S)Information/uncertainty
Shannon Evenness0 to 1H'/ln(S), how even the distribution

When to Use Simpson's Diversity Index

Ecology & Conservation

Species diversity in forests, reefs, grasslands. Habitat comparison and prioritization.

Microbiology

Gut microbiome, soil bacteria, water quality. Alpha diversity metrics.

Agriculture

Crop diversity, pest surveys, pollinator communities.

Environmental Monitoring

Bioassessment, restoration success, impact studies.

Worked Example

Species: A(50), B(30), C(20). N = 100, S = 3.

Σnᵢ(nᵢ−1) = 50×49 + 30×29 + 20×19 = 2450 + 870 + 380 = 3700. N(N−1) = 9900.

D = 3700/9900 ≈ 0.374. Simpson's Diversity = 1 − 0.374 = 0.626.

Simpson's Reciprocal = 1/0.374 ≈ 2.67 effective species.

Shannon H' = −(0.5 ln 0.5 + 0.3 ln 0.3 + 0.2 ln 0.2) ≈ 1.03. Evenness = 1.03/ln(3) ≈ 0.94.

Frequently Asked Questions

What is the difference between Simpson's D and Simpson's Index of Diversity?

D = probability two random individuals are the same species. 1−D (Simpson's Index of Diversity) = probability they are different. High 1−D means high diversity.

When is Simpson's Reciprocal equal to species richness?

When all species have equal abundance. Otherwise it is less than S, reflecting dominance by some species.

Which index should I use for ecology?

Simpson's is standard in ecology. Shannon is also common. Use Simpson's Reciprocal for intuitive 'effective number of species'.

How do I compare two habitats?

Use Simpson's Reciprocal or Shannon Evenness to account for different species counts. Plot both sites side by side.

What does high evenness mean?

Species are similarly abundant. Low evenness = one or few species dominate.

Can I use this for microbiome data?

Yes. Shannon and Simpson indices are standard for bacterial diversity in gut, soil, or water samples.

Disclaimer: Simpson's and Shannon indices measure diversity from abundance data. Ensure consistent sampling effort when comparing sites. Results are for educational and research purposes.

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