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VCE Environmental Science (Year 12) · Unit 3 — Ecosystems and Processes and Human Impacts · 16m read

Measuring Biodiversity — Sampling and Diversity Indices

You cannot count every organism in a forest, so scientists sample and calculate. Diversity indices turn field counts into a single comparable number — and calculating one is a reliable exam question.

Learning objective: Use sampling techniques and calculate Simpson’s index of diversity to compare communities.

By the end of this lesson you can:

  • I can choose a suitable sampling method.
  • I can calculate Simpson’s index of diversity.
  • I can compare richness and evenness between sites.

Diversity indices are a biodiversity scorecard. They combine how many species (richness) and how evenly individuals are spread (evenness) into one score.

Sampling and indices

SAMPLING METHODS:
• QUADRATS — square frames for plants and slow-moving animals; randomly placed.
• TRANSECTS — lines across an environmental gradient (e.g. shore to dune).
• CAPTURE–MARK–RECAPTURE — estimates population size of mobile animals.
• Camera traps, eDNA and acoustic monitoring for hard-to-see species.

RICHNESS AND EVENNESS:
• SPECIES RICHNESS — number of species.
• EVENNESS — how evenly individuals are spread among species.
• Two sites can have equal richness but very different evenness.

SIMPSON INDEX OF DIVERSITY:
• D = 1 − Σ n(n − 1) ÷ (N(N − 1)).
• n = number of individuals of each species; N = total individuals.
• D ranges from 0 (no diversity) to close to 1 (high diversity).

RELIABILITY:
• Larger, random and repeated samples give more reliable estimates.

Diversity

  • Simpson's index of diversity: D = 1 - \dfrac{\sum n(n-1)}{N(N-1)}
  • Capture–recapture: N \approx \dfrac{M \times C}{R}

Quick reference

| Concept | Meaning |
|---|---|
| Species richness | Number of species |
| Evenness | Spread of individuals |
| Simpson's index | Probability two individuals differ |
| Quadrat | Plants/slow animals |
| Transect | Change along a gradient |
| Capture–mark–recapture | Mobile animals |

Key ideas at a glance

  • Random sampling: Reduce bias.
  • Replicate: Reliability.
  • Higher index = more diverse: Interpret.
  • Record abiotic factors: Context.

Worked example (Medium)

Site A has 10, 5 and 5 individuals of three species; Site B has 18, 1 and 1. Calculate D for each and compare.

  1. Site A. Σ n(n−1) = 90 + 20 + 20 = 130; N(N−1) = 20 × 19 = 380; D = 1 − 130/380 ≈ 0.66.
  2. Site B. Σ n(n−1) = 306 + 0 + 0 = 306; D = 1 − 306/380 ≈ 0.19.
  3. Compare. Same richness (3 species), but A is far more even, so more diverse.

Answer: D(A) ≈ 0.66, D(B) ≈ 0.19 — Site A is more diverse because it is more even.

Common mistakes

  • Using n² instead of n(n − 1) The formula samples without replacement. Fix: Use n(n − 1) and N(N − 1).
  • Reporting richness as diversity Diversity also depends on evenness. Fix: Calculate an index that includes abundance.

Lincoln–Petersen estimate

Capture and mark animals, release them, then recapture a sample. Population ≈ (marked first × caught second) ÷ marked recaptured.

The method assumes marks don't affect survival and the population is closed.

Practice questions

  1. In capture–recapture, 40 birds are marked; later 50 are caught and 10 are marked. Estimate the population.

    1. 100
    2. 200
    3. 400
    4. 2000

    (1 marks)

Summary

  • Quadrats, transects and capture–recapture estimate biodiversity.
  • Diversity combines richness and evenness.
  • D = 1 − Σ n(n − 1) ÷ N(N − 1).

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