Simpson's Diversity Index

What biodiversity means

Biodiversity is the variety of living things in a habitat, ecosystem or on Earth as a whole. Ecologists measure it in two ways at once.

A habitat with 4 species of 10 individuals each is both rich and even. A habitat with 4 species where one has 97 individuals and the others 1 each is just as rich, but very uneven. Most of it is one species, so it is less diverse in practice.

Richness alone cannot tell these two samples apart. We need an index that uses both richness and evenness.

Calculating Simpson's Diversity Index

Simpson's Diversity Index ($D$) takes the number of individuals of each species into account. Let $n$ be the number of individuals of one species and $N$ the total number of individuals of all species.

Why does it work? The fraction $\frac{n}{N}$ is the share of the sample that belongs to one species. Squaring and adding the shares gives a large number when one species dominates, and a small one when the shares are even. Taking $1-$ that sum flips it, so a high $D$ means high diversity. $D$ lies between $0$ (one species only) and $1$ (never reached).

Two limiting cases help you check your answer.

• One species only (say 40 individuals): the share is $\frac{40}{40} = 1$, so $D = 1 - 1^2 = 0$. There is no diversity at all.

• $S$ species, all equally abundant: each share is $\frac{1}{S}$, so $\sum \left(\frac{n}{N}\right)^2 = S \times \frac{1}{S^2} = \frac{1}{S}$ and $D = 1 - \frac{1}{S}$. With 4 equal species, $D = 1 - \frac{1}{4} = 0.75$.

Using the index to interpret a habitat

Ecologists use $D$ to compare habitats, or the same habitat at different times. Always say what the number tells you in the context given. A falling $D$ over time can signal biodiversity loss, which is why $D$ is used to monitor habitats and plan conservation.

When you compare two sites:

1. Calculate $D$ for each.

2. Compare richness (count the species) and evenness (look at how the numbers are spread).

3. Link the result to wildlife: more species and a more even spread usually mean more food sources, more niches and more shelter, so more wildlife is supported.

The other form of the index

The specification gives the index in a second form, where individuals are counted in a different way:

Here $n$ is the number of individuals of one species and $N$ the total of all species. This form is the probability that two individuals picked at random, without replacement, belong to the same species. So a low value means high diversity, the reverse of the first form.

Evaluating and reasoning with the index

Higher Level questions ask you to go beyond the arithmetic.

Use these ideas in "discuss" and "evaluate" answers.

• A monoculture such as intensive ryegrass has very low $D$: one species fills almost all the space. It supports fewer pollinators, because there are few flowers and a short flowering season. It also gives the soil one type of root and one type of plant litter, so there is less food for a varied soil community.

• A mixed farm with hedgerows and wildflower margins has a high $D$, with more habitats, flowers and shelter.

• Evaluate a claim like "high $D$ is always better for conservation": $D$ ignores which species are present (invasive, rare, native), so a site with a low $D$ but rare specialists can matter more. Good practice is to combine $D$ with species lists and repeated sampling.

Back to the start: both Kildare hedgerows have five species, but the one with an even spread has a high $D$ and the one dominated by hawthorn a very low $D$. Simpson's index captures richness and evenness together.

Summary

• Biodiversity is the variety of life in a habitat. Species richness is the number of species. Species evenness is how equally individuals are shared among them.

• Simpson's Diversity Index: $D = 1-\sum\left(\frac{n}{N}\right)^2$, with $n$ the individuals of one species and $N$ the total of all species. A high $D$ means high diversity.

• The form on the specification, $D = \frac{\sum n(n-1)}{N(N-1)}$, is the opposite way round: a low value means high diversity, and $1-D$ turns it round so it reads like the first form (close to it, but not exactly equal, especially for small samples).

• One species gives $D = 0$. $S$ equally abundant species give $D = 1 - \frac{1}{S}$.

• $D$ ignores which species are present, so evaluate it alongside species lists and the limits of the sampling.