How Do You Calculate Simpson's Reciprocal Diversity Index?

Calculate Simpson's reciprocal diversity index by dividing the total number of possible organism pairs by the sum of possible same-species pairs. A higher index indicates greater species diversity when comparing ecosystems or samples.

The Formula and Method

In IB ESS Subtopic 3.1, Biodiversity and evolution (SL and HL), the formula is:

$$D = \frac{N(N-1)}{\sum n(n-1)}$$

Here, $N$ is the total number of organisms of all species, while $n$ is the number of organisms belonging to each individual species. The index combines species richness, the number of species present, with species evenness, how equally organisms are distributed among those species.

Consider simplified, illustrative counts from a sample in the Sundarbans mangrove ecosystem:

Substitute the values:

$$D = \frac{20(20-1)}{118} = \frac{380}{118} = 3.22$$

Therefore, Simpson's reciprocal diversity index is $3.22$. The value has no units and is most useful when compared with an index calculated for another site or for the same site at a different time.

To compare two sites fairly, use samples collected with the same method, sampling effort, area, and season. For example, a second mangrove site with $D = 5.10$ would be more diverse than this sample because its organisms are distributed across species more evenly and/or it contains greater richness. However, the index does not identify which species are present, their conservation importance, or the causes of any difference; these require ecological context and further evidence.

A common misconception is that a high number of organisms automatically means high diversity. Diversity depends on both richness and evenness, not simply total abundance.

Exam Technique

For a calculate question, show the total $N$, calculate every $n(n-1)$ value, substitute correctly, and give the final answer. The formula will normally be provided in the question, but you must interpret the result: a higher value means greater relative diversity, which may indicate greater ecosystem resilience. Avoid claiming that one value is “high” without comparative data.