Simpson’s Diversity Index Calculator

Understanding Simpson's Diversity, Reciprocal & Dominance Index

Simpson's Diversity Index is a measure of diversity that represents the probability that two individuals randomly selected from a sample will belong to the same species.

Formula for Simpson's Diversity Index

Simpson's Diversity Index \( D \) is calculated as:

$$ D = \sum_{i=1}^S p_i^2 $$

Where:

• \( S \): Total number of species
• \( p_i \): Proportion of individuals belonging to species \( i \)

The Reciprocal Simpson's Index \( 1/D \) provides an alternative measure where higher values indicate greater diversity.

Dominance Index

The Dominance Index \( 1 - D \) is a measure of dominance, where a higher value indicates that a few species dominate the sample.

Example Calculation

Assume a sample with the following species counts:

• Species #1: 80
• Species #2: 125
• Species #3: 95

1. First, calculate the total count of individuals: \( 80 + 125 + 95 = 300 \).
2. Calculate \( p_i \) for each species:
   • For Species #1: \( p_1 = \frac{80}{300} \approx 0.2667 \)
   • For Species #2: \( p_2 = \frac{125}{300} \approx 0.4167 \)
   • For Species #3: \( p_3 = \frac{95}{300} \approx 0.3167 \)
3. Calculate \( p_i^2 \) for each species and sum them:
   • \( p_1^2 = (0.2667)^2 \approx 0.0711 \)
   • \( p_2^2 = (0.4167)^2 \approx 0.1736 \)
   • \( p_3^2 = (0.3167)^2 \approx 0.1003 \)
4. Sum these values to get \( D \):

   $$ D = 0.0711 + 0.1736 + 0.1003 = 0.345 $$

5. Calculate the Reciprocal Simpson's Index \( 1/D \):

   $$ 1/D = \frac{1}{0.345} \approx 2.899 $$

6. Calculate the Dominance Index \( 1 - D \):

   $$ 1 - D = 1 - 0.345 = 0.655 $$

Thus, Simpson's Diversity Index is approximately 0.345, the Reciprocal Index is approximately 2.899, and the Dominance Index is approximately 0.655.