Index of diversity and Simpson's diversity index

An index of diversity is a number that measures the biodiversity of a community. It combines two things: how many species there are, and how evenly the individuals are shared between them. AQA A-level Biology uses the formula d = N(N − 1) ÷ Σn(n − 1), where a higher value means a more diverse community. OCR uses Simpson's diversity index, D = 1 − Σ(n/N)², which runs from 0 to 1.

Species richness and why it is not enough

Species richness is the number of different species in a community. It is easy to count, but it ignores how many of each species there are. Picture two fields, each with four species of wildflower:

• Field A: 10 plants of each species.
• Field B: 34 plants of one species and 2 of each of the other three.

Both have a species richness of 4, but field A is clearly more diverse: field B is almost all one species. An index of diversity captures this, because it describes the relationship between the number of species and the number of individuals in each species. OCR calls this second idea species evenness.

The index of diversity formula (AQA)

• N is the total number of organisms of all species.
• n is the total number of organisms of each species.
• Σ means add up the value of n(n − 1) for every species.

If every organism belongs to one species, the top and bottom are equal and d = 1, the lowest possible value. The more species there are, and the more evenly the individuals are spread, the larger d becomes.

How to calculate the index of diversity

1. Make a table with one row per species and its count, n.
2. Add up the counts to get N.
3. Work out n(n − 1) for each species, then add them up.
4. Work out N(N − 1).
5. Divide N(N − 1) by Σn(n − 1).

Simpson's diversity index (OCR)

For each species, find its share of the total, n/N, square it, and add the squares up. Then take the total away from 1. D is 0 when there is only one species and gets closer to 1 as diversity rises. OCR says the formula is given in the exam where needed, so you do not have to learn it, but you do have to use it and explain what high and low values mean.

Both are versions of Simpson's index, so they rank communities the same way in most real data. Use the one your exam board names. The Ecology Calculator works out both from a species table and shows the working.

Try it

Ecology Calculator

Estimate populations by capture recapture and Simpson's diversity index

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Worked examples

Example 1: the AQA index of diversity

A sample from a pond contains five species of invertebrate. Calculate the index of diversity.

1. N(N − 1) = 30 × 29 = 870.
2. d = 870 ÷ 216 = 4.03 (to 3 significant figures).

Example 2: Simpson's index for the same pond

1. Square each count: 144, 64, 25, 9 and 4. Their total is 246.
2. N² = 30² = 900, so Σ(n/N)² = 246 ÷ 900 = 0.273.
3. D = 1 − 0.273 = 0.727.

A value of 0.727 is fairly high: if you picked two organisms at random, they would usually belong to different species.

Example 3: comparing two fields

Use the AQA formula for fields A and B from earlier. Each field has N = 40, so N(N − 1) = 40 × 39 = 1,560.

The species richness is the same, but field A has an index of diversity more than three times higher, because its individuals are spread evenly. In Simpson's form, field A gives D = 0.750 and field B gives D = 0.270.

What the index of diversity tells you

• A high value means many species with similar numbers of each, so no single species dominates.
• A low value means few species, or one or two species making up most of the individuals, as in a field planted with a single crop.
• Changes over time show the effect of events such as pollution, habitat management or a new farming method.

AQA links the index of diversity to farming: farming techniques reduce biodiversity, and you may be asked to weigh conservation against farming. OCR lists human population growth, agriculture (monoculture) and climate change as factors that affect biodiversity. A monoculture, a large area of one crop, has very low species richness and evenness, so its index of diversity is close to the minimum.

Collecting the data

Counts usually come from random sampling with quadrats for plants and slow-moving animals, or sweep nets, pitfall traps and pooters for insects, which are the techniques OCR names. Sample enough of the habitat that the counts are representative, and compare sites using the same method and sampling effort. For estimating the size of one animal population, see mark release recapture.

Common mistakes

• Using n² instead of n(n − 1) in the AQA formula. For 12 organisms it is 12 × 11 = 132, not 144.
• Forgetting the Σ. Add n(n − 1) for every species before you divide.
• Dividing the wrong way up. N(N − 1) goes on top, so d is never less than 1.
• Forgetting to take Simpson's sum from 1. Σ(n/N)² on its own goes the other way: higher means less diverse.
• Comparing d with D. They are on different scales; only compare values found with the same formula.
• Saying a higher index means more species. It might mean more even numbers instead. Look at richness and evenness separately.

Practise with a short timed paper

Biodiversity is in the first year of A-level Biology for AQA (3.4.6) and OCR (4.2.1). The daily A-level Biology: Year 1 paper is a short timed paper of 8 questions, with a new one every day.

Read next

Biology · Ecology and evolutionSimpson's diversity index calculator and mark-recaptureFree ecology calculator: find Simpson's diversity index from species counts, or estimate a population by mark-release-recapture with a 95% interval.