Worked example 1
An ecologist sampled two different woodland areas, Woodland P and Woodland Q, to compare their biodiversity. The number of individuals for five tree species was recorded in the table below. Calculate Simpson's Index of Diversity (D) for both woodlands and determine which is more diverse.
| Species | Woodland P | Woodland Q |
|---|---|---|
| Oak | 50 | 15 |
| --- | --- | --- |
| Ash | 10 | 15 |
| Birch | 12 | 15 |
| Sycamore | 8 | 15 |
| Holly | 20 | 40 |
Show solution outline
Step 1: Calculate N (total individuals) for each woodland.
- Woodland P: N = 50 + 10 + 12 + 8 + 20 = 100
- Woodland Q: N = 15 + 15 + 15 + 15 + 40 = 100
Step 2: Calculate Σ(n/N)² for Woodland P.
- Oak: (50/100)² = 0.25
- Ash: (10/100)² = 0.01
- Birch: (12/100)² = 0.0144
- Sycamore: (8/100)² = 0.0064
- Holly: (20/100)² = 0.04
- Σ(n/N)² = 0.25 + 0.01 + 0.0144 + 0.0064 + 0.04 = 0.3208
Step 3: Calculate D for Woodland P.
- D = 1 - 0.3208 = 0.6792
Step 4: Calculate Σ(n/N)² for Woodland Q.
- Oak: (15/100)² = 0.0225
- Ash: (15/100)² = 0.0225
- Birch: (15/100)² = 0.0225
- Sycamore: (15/100)² = 0.0225
- Holly: (40/100)² = 0.16
- Σ(n/N)² = (4 × 0.0225) + 0.16 = 0.09 + 0.16 = 0.25
Step 5: Calculate D for Woodland Q.
- D = 1 - 0.25 = 0.75
Step 6: Conclusion.
- Woodland P has D ≈ 0.68. Woodland Q has D = 0.75.
- Since 0.75 > 0.68, Woodland Q has a higher species diversity than Woodland P. Although both have the same species richness (5 species), the individuals in Woodland Q are more evenly distributed (higher species evenness), making it more diverse.