use Simpson’s index of diversity (D) to calculate the biodiversity of an area, and state the significance of different values of D (the formula for Simpson’s index of diversity will be provided, as shown in the Mathematical requirements)

Simpson’s Index of Diversity (D) – Cambridge AS & A‑Level Biology (Topic 18)

Learning outcomes (Syllabus AO1‑AO3)

  • AO1 – Knowledge & understanding: Define the terms biodiversity, species richness, species evenness and Simpson’s index of diversity. State the formula and explain what the index measures.

  • AO2 – Application & analysis: Calculate D for a given data set, interpret the ecological significance of the result and evaluate the usefulness and limitations of the index.

  • AO3 – Evaluation: Discuss how Simpson’s index can be used in conservation and management, comparing it with other diversity indices.

Where Simpson’s Index fits in the “biodiversity toolbox”

IndexWhat it measuresTypical use
Species richness (S)Number of different species presentQuick, qualitative assessment
Species evenness (E)How equally individuals are distributed among speciesShows dominance patterns
Shannon–Wiener index (H′)Combines richness & evenness, gives more weight to rare speciesWhen rare species are ecologically important
Simpson’s index of diversity (D)Probability that two individuals drawn at random belong to different species (focus on common species)Assessing dominance & overall community stability

Key concepts

  • Biodiversity: Variety of living organisms within a habitat or ecosystem.

  • Species richness (S): Simple count of species.

  • Species evenness (E): Equality of individual numbers among species.

  • Simpson’s index of diversity (D): Probability that two randomly chosen individuals belong to different species; ranges 0 → 1.

Mathematical reminder (syllabus requirements)

  • Manipulating fractions and large numbers.

  • Algebraic substitution.

  • Using a scientific calculator (especially for division of large products).

Symbols used

  • S – total number of species in the sample.

  • ni – number of individuals of species i (i = 1 … S).

  • N – total number of individuals, N = Σ ni.

  • Σ ni(ni − 1) – sum of the products ni(ni − 1) for all species.

Formula

\$ D \;=\; 1 \;-\; \frac{\displaystyle\sum{i=1}^{S} ni (n_i - 1)}{N (N - 1)} \$

Interpretation: the larger the value of D, the higher the diversity (greater evenness and/or richness).

Step‑by‑step calculation

  1. List each species and its abundance (ni).

  2. Calculate the total number of individuals, N = Σ ni.

  3. For each species compute ni(ni − 1).

  4. Sum the values from step 3 to obtain Σ ni(ni − 1).

  5. Insert the numbers into the formula and solve for D.

  6. Interpret the result using the “Interpretation of D” table (see below).

  7. Answer a critical‑thinking question to satisfy AO2/AO3 (see box).

Worked example – moderate‑to‑high diversity woodland

Four tree species are recorded in a 100‑tree plot:

Speciesnini(ni − 1)
Oak (A)4040 × 39 = 1 560
Birch (B)3030 × 29 = 870
Hazel (C)2020 × 19 = 380
Willow (D)1010 × 9 = 90

  • Total individuals: N = 40 + 30 + 20 + 10 = 100

  • Σ ni(ni − 1): 1 560 + 870 + 380 + 90 = 2 900

Substituting:

\$\$

D = 1 - \frac{2\,900}{100 \times 99}

= 1 - \frac{2\,900}{9\,900}

= 1 - 0.2939

\approx 0.706

\$\$

Interpretation: D ≈ 0.71 falls in the “moderate‑to‑high diversity” range (0.5 ≤ D < 0.8).

Illustrative example – dominance of a single species

A grassland contains 90 individuals of Species X and 5 individuals each of Species Y and Z (total N = 100).

Speciesnini(ni − 1)
Species X9090 × 89 = 8 010
Species Y55 × 4 = 20
Species Z55 × 4 = 20

  • N = 100

  • Σ ni(ni − 1) = 8 010 + 20 + 20 = 8 050

\$\$

D = 1 - \frac{8\,050}{100 \times 99}

= 1 - \frac{8\,050}{9\,900}

= 1 - 0.8131

\approx 0.187

\$\$

Interpretation: D ≈ 0.19 indicates very low diversity; the community is dominated by Species X.

Interpretation of Simpson’s Index (D)

Range of DEcological significance (AO2)
0 ≤ D < 0.2Very low diversity – one or two species dominate.
0.2 ≤ D < 0.5Low to moderate diversity – a few common species, many rare.
0.5 ≤ D < 0.8Moderate to high diversity – relatively even distribution.
0.8 ≤ D ≤ 1.0Very high diversity – no single species dominates; high evenness.

Critical‑thinking box (AO2/AO3)

Question: Would Simpson’s index be an appropriate measure for a highly seasonal insect community where many species are present only briefly each year? Explain your reasoning, referring to the index’s sensitivity to common versus rare species.

Suggested points for answer:

  • D emphasises the abundance of common species; short‑lived rare species contribute little.

  • Seasonal turnover may lead to under‑estimation of true diversity if sampling is restricted to a single period.

  • In such cases, the Shannon–Wiener index (which gives more weight to rare species) might be more informative.

  • Sampling design (multiple seasons, random transects) would be essential to obtain a reliable D.

Comparison with the Shannon–Wiener index (H′)

Both indices combine richness and evenness, but they differ in emphasis:

  • Simpson’s D is dominated by the most abundant species; it is less affected by sampling error in large datasets and is easier to calculate by hand.

  • Shannon–Wiener (H′) gives greater weight to rare species, making it more sensitive to changes in low‑abundance taxa.

  • In practice, ecologists often calculate both: D to detect dominance or disturbance, H′ to assess overall community complexity.

Limitations & assumptions (AO2)

  • Closed community: No immigration, emigration or births/deaths during sampling.

  • Random sampling: Biased collection (e.g., targeting large individuals) can inflate or deflate D.

  • Sensitivity to common species: A single dominant species can drive D towards 0, masking the presence of many rare species.

  • Sample size: Very small N may give artificially high D values; larger samples reduce random error.

  • Taxonomic resolution: Mis‑identification or lumping of species alters ni values and therefore D.

Use of Simpson’s Index in conservation and management (AO3)

  • Monitoring change: Re‑calculate D after habitat restoration, fire, or invasive‑species removal to detect shifts in community structure.

  • Prioritisation: Areas with low D may be targeted for management actions such as removal of a dominant invasive plant.

  • Impact assessment: Compare D before and after a development proposal to quantify potential biodiversity loss.

  • Reporting: D provides a single, comparable figure for biodiversity that can be incorporated into conservation status reports and policy briefs.

Suggested visual aid

Pie chart (or stacked bar) illustrating the proportional abundance of each species in the woodland example – a visual reminder of how evenness contributes to a higher D value.

Topic‑by‑topic checklist (AS & A‑Level syllabus)

TopicCovered in this note
1. Cell structure✗
2. Cell metabolism✗
3. Enzymes✗
4. Nutrition✗
5. Transport in plants✗
6. Gas exchange✗
7. Respiration✗
8. Coordination & response✗
9. Homeostasis✗
10. Reproduction in plants✗
11. Inheritance✗
12. DNA & gene expression✗
13. Evolution & natural selection✗
14. Classification & biodiversity (incl. Simpson’s D)✓
15. Ecology (energy flow, cycles)✗
16. Human impacts✗
17. Conservation✓ (use of D in management)
18. Genetic technology (Topic 19 in syllabus)✗ – see separate hand‑out

Further reading & practice

  • Past paper questions on Simpson’s index (e.g., 9700/12/II Q12).

  • Cambridge International AS & A Level Biology – “Biodiversity” chapter, sections on diversity indices.

  • Online calculator tutorials for large‑number fractions (useful for exam speed).