Ecology calculator: Simpson's diversity index and mark-recapture

A Simpson's diversity index calculator measures how diverse a community is from the number of individuals of each species: D = 1 − Σ(n/N)², from 0 for one species to near 1 for many evenly shared species. Our Ecology Calculator does this, and estimates a population size by mark-release-recapture with the Lincoln index, Chapman's estimate and a 95% interval, with every step of the working.

It opens on capture-recapture: 60 animals marked, 45 caught the second time and 9 of them marked, which estimates a population of 300. Switch to Simpson's index for diversity.

Try it

Ecology Calculator

Estimate populations by capture recapture and Simpson's diversity index

Open the calculatorGo to its page

How to use the ecology calculator

1. Choose Capture-recapture or Simpson's index.
2. For capture-recapture, type the number Marked and released (M), the Second sample (C) and the number Recaptured with a mark (R).
3. For Simpson's index, type each species' name and count in the table, adding or removing rows as you need.
4. Read the results and follow the working.

The calculator checks the counts make sense: it says so if more animals were recaptured than were caught, or if nothing was recaptured. Practice and help sets capture-recapture and diversity questions with worked solutions.

Simpson's diversity index

Two common forms give the same ranking of communities:

Here n is the count of each species and N the total count. D is the chance that two individuals picked at random (with replacement) are different species, from 0 to 1. The reciprocal form d runs from 1 upwards. Some courses use a third form, 1 − Σn(n − 1)/N(N − 1), which is 1 − 1/d; the calculator shows D and d.

Example 1: Simpson's index from counts

A quadrat survey finds 12, 8, 5, 3 and 2 individuals of five species, 30 in all:

Type the five counts and the calculator gives D = 0.7267 and d = 4.028. The third form is 1 − 216/870 = 0.752.

Example 2: evenness matters

Spread the same 30 individuals evenly, 6 of each species, and D rises to 0.8 and d to 5.8. Richness, the number of species, is the same; the community is more diverse because no species dominates.

Check yourself:

Mark and recapture: the Lincoln index

Catch M animals, mark them and release them. Later, catch a second sample of C, of which R are marked. If the marked share of the sample matches the marked share of the population:

Example 3: estimating a population

40 woodlice are marked and released. A week later, 50 are caught and 8 of them are marked:

The calculator gives the Lincoln index, 250, and Chapman's estimate, ((M + 1)(C + 1) ÷ (R + 1)) − 1 = 231.3, which is less biased for small samples. Its 95% interval, 115.9 to 346.8, shows how uncertain a single survey is.

The method assumes the population is closed (no births, deaths or migration between samples), marks do not fall off or harm the animals, and marked animals mix back in at random.

What the calculator does not do

• No other diversity indices. It has Simpson's index only, not Shannon's.
• No quadrat or transect calculations. For mean count per quadrat or percentage cover, work them out first, then use the counts here.
• One recapture only. It handles a single mark and recapture, not repeated sampling.

Common mistakes

• Mixing up the Simpson forms. Check which one your course uses: 1 − Σ(n/N)², N(N − 1)/Σn(n − 1), or 1 − Σn(n − 1)/N(N − 1).
• Using n² instead of n(n − 1) in the reciprocal form.
• Swapping C and R. C is the whole second sample; R is the marked ones in it.
• Ignoring the assumptions. If marked animals are easier to catch again, the estimate comes out too small.

Practise ecology in a short timed paper

Capture-recapture comes up in A-level Biology: Year 2 and GCSE Biology Higher practice. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics.

Read next

Biology · Ecology and evolutionIndex of diversity: Simpson's diversity index with examplesHow to calculate an index of diversity: the AQA formula and Simpson's diversity index, what the values mean, and worked examples with a free calculator.