Calculate Simpson's Diversity Index, Reciprocal Index, and Dominance Index for a population using individual species counts.

## 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

- First, calculate the total count of individuals: \( 80 + 125 + 95 = 300 \).
- 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: \( p_3 = \frac{95}{300} \approx 0.3167 \)

- Calculate \( p_i^2 \) for each species and sum them:
- \( p_1^2 = (0.2667)^2 \approx 0.0711 \)
- \( p_2^2 = (0.4167)^2 \approx 0.1736 \)
- \( p_3^2 = (0.3167)^2 \approx 0.1003 \)

- Sum these values to get \( D \):
$$ D = 0.0711 + 0.1736 + 0.1003 = 0.345 $$

- Calculate the Reciprocal Simpson's Index \( 1/D \):
$$ 1/D = \frac{1}{0.345} \approx 2.899 $$

- 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.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.