Biodiversity is a fundamental indicator of ecosystem health, and ecologists use various indices to quantify it. Among the most widely used is Simpson’s Index of Diversity, which provides a robust measure of both species richness and evenness in a community. This article explains the formula for Simpson’s Index of Diversity, its ecological meaning, and how it is calculated using the probability of capturing an individual of a certain species.

What Is Simpson’s Index of Diversity?

Simpson’s Index of Diversity measures the probability that two individuals randomly selected from a sample will belong to different species. It accounts for both the number of species present (richness) and the relative abundance of each species (evenness), making it a comprehensive metric for assessing biodiversity.

The Formula

If the probability of capturing an individual of a certain species is denoted as PiPi, then Simpson’s Index of Diversity is calculated as:

^{Simpson’s Index of Diversity=1−∑(Pi)2Simpson’s Index of Diversity=1−∑(Pi)2}

• PiPi = Proportion (probability) of individuals belonging to species $i$

• ∑(Pi)2∑(Pi)2 = Sum of the squared probabilities for all species in the community

This formula gives a value ranging from 0 to 1, where values closer to 1 indicate higher diversity1348.

Why Use 1−∑(Pi)21−∑(Pi)2?

• The term ∑(Pi)2∑(Pi)2 by itself (sometimes called Simpson’s Index, D) measures the probability that two randomly selected individuals belong to the same species.

• Subtracting this value from 1 gives the probability that two individuals belong to different species, which is a more intuitive measure of diversity.

• Thus, a higher value of Simpson’s Index of Diversity means greater biodiversity in the community.

Ecological Significance

• High diversity value (close to 1): Indicates a community with many species and/or a balanced abundance among species.

• Low diversity value (close to 0): Indicates dominance by one or a few species, with most individuals belonging to the same species.

Conclusion

Simpson’s Index of Diversity is a powerful tool for quantifying biodiversity, especially when comparing different habitats or monitoring changes over time. Its formula, 1−∑(Pi)21−∑(Pi)2, makes it easy to interpret and apply in ecological research and conservation planning.

Correct answer:
(2) 1- ∑(Pi)²