Simpson's Diversity Index Calculator

How to Use the Simpson's Diversity Index Calculator

1. 1. Enter the counts. Put one species per line, the name and then the number of individuals (Oak 25), or paste just the numbers. Species with a count of zero are ignored.
2. 2. Choose the formula for D. Use Finite sample for counts from a quadrat, transect or trap sample, which is what most coursework expects. Use Proportions for percent cover or biomass, or when you have the whole community.
3. 3. Read the three indices. D, 1 − D and 1 ÷ D appear together, with evenness and the number of species.
4. 4. Check the table. The side-by-side table gives both formulas for all three, so you can find the one your textbook, lab manual or examiner uses.

Three Different Numbers, One Name

Simpson (1949) defined D as the probability that two individuals drawn at random from a community belong to the same species. High D means one or two species dominate, so the number falls as diversity rises, which many students find backwards. Because of that, textbooks report it in one of three ways:

Courses differ. Edexcel International A-level and IB Environmental Systems and Societies materials use the reciprocal, written D = N(N − 1) ÷ Σ n(n − 1), where a bigger number means more diversity. OCR A-level and AP Biology revision materials give the 0-to-1 form, 1 − Σ(n ÷ N)². Ecology texts such as Magurran favor 1 ÷ D. Check which your own specification or lab manual means before comparing numbers.

There are two ways to compute D. The finite-sample form, Σ n(n − 1) ÷ N(N − 1), asks about drawing two individuals without putting the first back, and it is an unbiased estimate of the community's true Σ p². The proportion form, Σ p² with p = n ÷ N, asks about drawing with replacement. It is slightly biased low as an estimate for small samples, but it is the only one that accepts non-integer abundances such as percent cover. For large N the two agree closely.

Worked Example

A woodland sample has six tree species with 25, 18, 12, 8, 5 and 2 individuals, so N = 70. These are the calculator's default inputs.

• Σ n(n − 1) = 600 + 306 + 132 + 56 + 20 + 2 = 1,116, and N(N − 1) = 70 × 69 = 4,830.
• D = 0.2311, 1 − D = 0.7689, 1 ÷ D = 4.328.
• With the proportion form, Σ p² = 0.2420, so D = 0.2420, 1 − D = 0.7580 and 1 ÷ D = 4.1315.
• The most 1 − D can be with six species is 1 − 1 ÷ 6 = 0.8333, so this sample is fairly even. Its evenness, (1 ÷ D) ÷ S, is 0.7213 on the finite-sample form.

To compare two sites, keep the formula the same. A second sample of 100 individuals in five species (40, 30, 15, 10 and 5) gives 1 − D = 0.7222 on the finite-sample form, lower than the 0.7689 above, so site one is the more diverse by this index. Five equally common species would give 1 − D = 0.8081 on the finite-sample form and exactly 0.8 on the proportion form.

Using It Well

• Simpson weights common species. It is dominated by the most abundant species, so it barely moves when rare species are added. For a measure more sensitive to rare species, use the Shannon Diversity Index Calculator.
• Sample size matters. Counts need to be individuals, not percentages, for the n(n − 1) form, and small samples give unreliable indices.
• Define what you count. Individuals of a clonal plant, tillers of grass and percent cover are not the same kind of abundance, so do not mix them in one list.
• Compare like with like. Use the same method, area and sampling effort for each site.

Frequently Asked Questions

What is the formula for Simpson's diversity index?

The most common coursework form is D = Σ n(n − 1) ÷ N(N − 1), where n is the number of individuals of each species and N the total. The diversity index is then 1 − D. Another common form is D = Σ p², with p the proportion of each species.

What is a good Simpson's diversity index value?

For 1 − D, values near 0 mean one species dominates and values near 1 mean many evenly spread species. There is no universal good value, because the maximum depends on the number of species. Compare sites sampled in the same way.

What is the difference between D, 1 − D and 1/D?

D is the chance that two individuals drawn at random are the same species, so a higher D means lower diversity. 1 − D is the chance that they differ, and 1 ÷ D converts it to an effective number of equally common species. All three carry the same information on different scales.

Why does my teacher's answer differ from this calculator's?

Most often the formula is different: n(n − 1) versus Σ p², or D versus 1 − D versus 1 ÷ D. Pick the matching option and compare the side-by-side table. Rounding is the other likely cause.

Can Simpson's index be greater than 1?

D and 1 − D cannot, because both are probabilities. The reciprocal 1 ÷ D can, since it counts effective species and ranges from 1 up to the number of species.

Is Simpson's index better than Shannon's?

Neither is better. Simpson's gives more weight to the commonest species and is more robust to small samples; Shannon's gives more weight to rare species. Reporting both, or the Hill numbers they relate to, is common practice.