What is Simpson's Diversity Index?
Simpson's Diversity Index measures the biodiversity in an ecosystem by considering both the number of species present and their relative abundance. It answers the question: if you randomly select two individuals from a sample, what is the probability they belong to different species?
Why does this matter? Understanding biodiversity is crucial for ecological research, conservation efforts, and environmental management. By determining how evenly species are distributed in an area, you can make informed decisions to maintain or improve ecosystem health. Simpson's Reciprocal Index provides another perspective by focusing on the effective number of species.
How to Calculate Simpson's Diversity Index
Simpson's Diversity Index Formula:
[\text{Diversity Index} = 1 - \left( \frac{\sum (n \cdot (n - 1))}{N \cdot (N - 1)} \right)]
Where:
- n = Number of individuals of each species
- N = Total number of individuals across all species
Simpson's Reciprocal Index Formula:
[\text{Reciprocal Index} = \frac{1}{1 - D}]
Where:
- D = The Diversity Index value
Calculation Example
Imagine you're surveying a small pond and record the following species counts:
- Species 1: 5 individuals
- Species 2: 12 individuals
- Species 3: 7 individuals
- Species 4: 10 individuals
- Species 5: 3 individuals
Step 1: Calculate the total number of individuals:
[\text{Total} = 5 + 12 + 7 + 10 + 3 = 37]
Step 2: Calculate the sum of n(n-1) for each species:
[\sum (n \cdot (n - 1)) = 5 \times 4 + 12 \times 11 + 7 \times 6 + 10 \times 9 + 3 \times 2 = 20 + 132 + 42 + 90 + 6 = 290]
Step 3: Calculate the denominator:
[N \cdot (N - 1) = 37 \times 36 = 1332]
Step 4: Calculate the Diversity Index:
[\text{Diversity Index} = 1 - \left( \frac{290}{1332} \right) \approx 1 - 0.2177 = 0.7823]
Step 5: Calculate the Reciprocal Index:
[\text{Reciprocal Index} = \frac{1}{1 - 0.7823} \approx \frac{1}{0.2177} \approx 4.59]
The Diversity Index of 0.7823 indicates fairly high diversity, while the Reciprocal Index of 4.59 suggests the effective number of equally abundant species is about 4.6.