Simpson's Evenness Index and Shannon-Weiner Index of Biodiversity
Measuring Biodiversity
with Precision
A deep-dive into two foundational indices used to quantify the richness and equity of life in ecological communities.
Overview — Why Measure Biodiversity?
Biodiversity is not simply a count of species. Two communities may share the same number of species yet differ profoundly in how individuals are distributed among those species. A forest with 1,000 oak trees and one of every other species is far less diverse in character than one where individuals are evenly spread across all species.
Ecologists therefore measure biodiversity along two axes:
- Species Richness (S) — the raw count of species present.
- Species Evenness (E) — how equitably individuals are distributed among those species.
Diversity indices combine these dimensions into single, comparable numbers that allow scientists to rank communities, track change over time, monitor the impacts of pollution or habitat destruction, and guide conservation priorities.
Two Complementary Lenses
Consider three communities, each with 4 species and 100 individuals:
| Community | n₁ | n₂ | n₃ | n₄ | Character |
|---|---|---|---|---|---|
| A | 97 | 1 | 1 | 1 | Dominated |
| B | 60 | 25 | 10 | 5 | Moderate |
| C | 25 | 25 | 25 | 25 | Perfectly even |
All three have S = 4, but their diversity character is entirely different. Indices capture this.
A History of Diversity Measurement
The formalisation of biodiversity measurement emerged from information theory, statistics, and field ecology converging in the mid-twentieth century — a story of mathematicians and ecologists working in parallel.
Simpson's Evenness Index
A probability-based measure of dominance and equitability, rooted in combinatorial statistics
Conceptual Foundation
Simpson's original D asks a simple probabilistic question: "If you randomly pick two individuals from a community, what is the probability they belong to the same species?"
A high D means most pairs would be from the same species — indicating low diversity / high dominance by one or few species. A low D means pairs are more likely from different species — indicating high diversity.
To make D intuitive (higher value = more diverse), ecologists compute:
- Simpson's Diversity Index: 1 − D
- Simpson's Reciprocal Index: 1/D
- Simpson's Evenness Index: E = (1/D) ÷ S
The Formulae
Simpson's Evenness — Step-by-Step Calculation
| Species | Individuals (nᵢ) | nᵢ(nᵢ − 1) | Notes |
|---|---|---|---|
| Chironomus sp. (Midge larvae) | 45 | 45 × 44 = 1,980 | Dominant species |
| Gammarus pulex (Freshwater shrimp) | 30 | 30 × 29 = 870 | Sub-dominant |
| Baetis sp. (Mayfly nymph) | 15 | 15 × 14 = 210 | Moderate |
| Lymnaea stagnalis (Pond snail) | 7 | 7 × 6 = 42 | Uncommon |
| Planaria sp. (Flatworm) | 3 | 3 × 2 = 6 | Rare |
| TOTAL (N = 100, S = 5) | 100 | Σ = 3,108 | N(N−1) = 9,900 |
For each species, multiply its count by (count − 1). This is the number of ways to choose 2 individuals of that species.
N = 100 total individuals. This is the total number of ways to pick any 2 individuals from the community.
D = 0.314 means there is a 31.4% probability that two randomly picked individuals belong to the same species. This is moderate dominance.
Interpretation: the community behaves as if it contained approximately 3.19 equally abundant species — the "effective number of species."
Interpreting Simpson's Evenness (E)
Shannon-Wiener Diversity Index (H′)
An information-theoretic measure of uncertainty and diversity, borrowed from communication engineering
Conceptual Foundation
Shannon's H′ asks: "How much uncertainty is there in predicting the species identity of a randomly chosen individual?"
In information theory, entropy measures uncertainty. If a community has only one species, there is zero uncertainty (H′ = 0) — you know exactly what every individual is. If the community has many equally abundant species, uncertainty is maximised (H′ is high) because any species could be picked.
H′ thus captures both richness and evenness simultaneously:
- Adding more species increases H′
- Making abundance more even increases H′
- A dominated community has lower H′ than an even one with the same richness
The Formula
Shannon-Wiener Index — Step-by-Step Calculation
| Species | nᵢ | pᵢ = nᵢ/N | ln(pᵢ) | pᵢ × ln(pᵢ) |
|---|---|---|---|---|
| Chironomus sp. | 45 | 0.45 | −0.7985 | −0.3593 |
| Gammarus pulex | 30 | 0.30 | −1.2040 | −0.3612 |
| Baetis sp. | 15 | 0.15 | −1.8971 | −0.2846 |
| Lymnaea stagnalis | 7 | 0.07 | −2.6593 | −0.1862 |
| Planaria sp. | 3 | 0.03 | −3.5066 | −0.1052 |
| TOTAL | 100 | 1.00 | — | Σ = −1.2965 |
Natural log of a proportion (0–1) is always negative. Larger proportions (dominant species) have ln values closer to 0.
H′ = 1.30 nats indicates moderate diversity. The community is not maximally diverse because Chironomus (45%) dominates strongly.
Interpreting Shannon-Wiener H′ Values
Interpreting Pielou's Evenness J′
Comparison of Both Indices
Using the same pond dataset (5 species, 100 individuals) allows a direct, meaningful comparison of what each index reveals and emphasises.
D = 0.314 | E = 0.637
- Probability of picking same species twice = 31.4%
- Effective species count = 3.19 of 5 actual
- Evenness = 63.7% of maximum
- Registers moderate-low evenness due to Chironomus dominance
H′ = 1.297 | J′ = 0.806
- Information content = 1.297 nats
- H′_max for 5 species = 1.609 nats
- Evenness (J′) = 80.6% of maximum
- Registers moderately high evenness — rarer species contribute more
Why Do the Two Evenness Values Differ?
Simpson's E = 0.637 vs. Shannon's J′ = 0.806 — same dataset, different answers. This reflects their mathematical sensitivity:
The n(n−1) term squares the abundance effect, so Chironomus (45 individuals) contributes 1,980 to the numerator — disproportionately high. This makes D and E sensitive to the dominant species and registers lower evenness.
The p·ln(p) term amplifies the contribution of rare species (Planaria at p = 0.03 contributes −0.105 nats). Rare species inflate H′ slightly and raise J′. Shannon is a better detector of rare-species presence.
| Attribute | 🟤 Simpson's Index | 🔵 Shannon-Wiener Index |
|---|---|---|
| Theoretical origin | Probability / combinatorics (statistics) | Information theory (communication engineering) |
| Core question | "Probability two random individuals = same species?" | "How much uncertainty is there in species identity?" |
| Published by | E.H. Simpson, Nature, 1949 | C. Shannon, 1948; N. Wiener, 1949 |
| Primary formula | D = Σ nᵢ(nᵢ−1) / N(N−1) | H′ = −Σ pᵢ ln(pᵢ) |
| Evenness derivative | E = (1/D) / S | J′ = H′ / ln(S) [Pielou 1966] |
| Range (diversity) | D: 0–1 (higher D = lower diversity) | H′: 0 to ln(S); higher = more diverse |
| Range (evenness) | E: 0–1; 1 = perfectly even | J′: 0–1; 1 = perfectly even |
| Sensitivity | Heavily weighted to abundant species | More sensitive to rare species |
| Dominance detection | Excellent — specifically designed for it | Moderate — H′ decreases with dominance |
| Rare species detection | Poor — rare species negligible effect on D | Good — rare species can elevate H′ notably |
| Interpretability | Intuitive probability interpretation | Abstract (information / entropy concept) |
| Units | Dimensionless (proportion) | Nats (ln), bits (log₂), or decibans (log₁₀) |
| Common application | Dominance assessment, pollution monitoring | General diversity comparison, microbial ecology |
| Statistical properties | Less sensitive to sampling effort | More sensitive to sample size / rare species |
| Our example result | E = 0.637 (moderate evenness) | J′ = 0.806 (high evenness) |
Interactive Diversity Calculator
Enter your own species counts below to calculate Simpson's Evenness Index (E) and Shannon-Wiener Diversity Index (H′) in real time.
Species Abundance Data
Enter the number of individuals for each species. Add up to 15 species. Minimum 2 species required.
| # | Species Name (optional) | Individuals (nᵢ) |
|---|