Practical skills · Fieldwork · SL & HL

Lincoln index explorer

Learn how the capture, mark, release and recapture method works, then estimate the size of a mobile population with the Lincoln index.

When could this come up?

This skill has two separate parts. You may be asked to describe the method, carry out a calculation from a given set of data, or do both.

In exams, you may also be asked to explain why the result is only an estimate, or to comment on the assumptions and sources of error behind it.

It is especially useful for the IA if you want to study a mobile organism, such as insects, small mammals or fish, where quadrats alone are not enough.

1. Describe the method

Explain how capture, mark, release and recapture estimates the abundance of a mobile population, including assumptions, limitations and possible sources of error.

2. Use the data

Use M, N and R from the two samples to calculate estimated population abundance with the Lincoln index.

How it works

  1. Select a clearly defined study area.
  2. Capture and safely mark a first sample. The number marked is M.
  3. Release them and allow enough time for complete mixing back into the population.
  4. Capture a second sample. Its total size is N.
  5. Count how many in the second sample are already marked. This is R.
  6. Calculate the estimated population using the Lincoln index.
  7. Check whether the assumptions are reasonable before trusting the estimate.
Estimated population size = (M × N) ÷ R
First marked sampleM
Second sampleN
Marked organisms recapturedR

Follow the bees through the method

Click each stage, or use Back and Next. The jar shows a representative visual sample; the large number is the actual number of bees captured.

Large blue paint mark = marked bee
Field is schematic · icons are not individual counts
First sampleRepresentative view
40captured
The jar shows the sample composition clearly. The large number is the actual sample size; the bee icons are representative only.

Capture the first sample

M40
N-
R-
Key idea: the moving bees are representative. In the second sample, 6 of 30 bees are marked, so 20% of the sample is marked. The same proportion is assumed for the whole population.

What has to be true?

Click each assumption to see why breaking it could bias the estimate.

Bee example

If 40 bees are marked in the first sample, and a second sample of 30 bees contains 6 marked bees:

Estimated population = (40 × 30) ÷ 6 = 200 bees

This is an estimate, not an exact count. Its reliability depends on the sampling method and assumptions.

Exercise: grasshopper population

A student captures, marks and releases 28 grasshoppers. Later, a second sample contains 35 grasshoppers, of which 7 are marked.

Large blue paint mark = previously captured

* You do not need this visual to get the answer. Use the values given in the question.

1. Calculate population size

2. Identify the broken assumption

Some of the marks rubbed off before the second capture.

3. Predict the effect

If marks are lost, would the Lincoln index tend to overestimate or underestimate population size?

IB ESS revision on FirstHandIB