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Capture–mark–release–recapture and the Lincoln index

Ecosystems (Interaction and interdependence) · Populations and communities · note 2 of 9

Spec C4.1.4Download all Populations and communities notes (PDF)Download all notes (PDF)12 pages

Capture–mark–release–recapture and the Lincoln indexSpec C4.1.4

In short

Capture–mark–release–recapture estimates the size of a population of motile animals. A sample is caught, marked and released; later a second sample is caught and the marked individuals in it are counted. The Lincoln index gives the estimate: population size = (M × N) ÷ R. It assumes marked animals mix randomly and are as likely to be recaught.

Animals that move about (motile organisms) cannot be counted in quadrats. Instead, the proportion of marked animals in a second sample is used to estimate the whole population.

  1. Capture as many individuals as possible in a set time with a suitable method (pitfall traps for beetles, sweep nets for insects, small mammal traps).
  2. Mark each one in a way that does not harm it or make it more visible to predators (a dot of non-toxic paint, a fur clip, a ring). Count them: this is M.
  3. Release them where they were caught and allow time for them to mix back into the population.
  4. Capture a second sample with the same method and effort. Count the total caught (N) and the number already marked (R).
Population size estimate = (M × N) ÷ R

M = number caught and marked initially; N = total number recaptured in the second sample; R = number of marked individuals recaptured.

Using the Lincoln index

In a woodland, 45 ground beetles are caught in pitfall traps, marked and released. Two days later 60 beetles are caught, of which 15 are marked. Estimate the population.

  1. M = 45, N = 60, R = 15.
  2. Estimate = (45 × 60) ÷ 15 = 2700 ÷ 15.
  3. = 180.

Answer: About 180 ground beetles.

Assumptions

  • Marking does not harm the animals or change their behaviour or chance of being eaten.
  • Marks are not lost (worn off or moulted) between the two samples.
  • Marked individuals mix randomly back into the whole population before the second sample.
  • Marked and unmarked animals have an equal chance of being caught (no trap-shyness or trap-happiness).
  • No significant births, deaths, immigration or emigration between the two samples.
Maths skill:

Check your answer is at least as big as M + N − R, the number of different animals actually seen. If R is very small, the estimate is very unreliable.

Three panels showing capture–mark–release–recapture of beetles: in the first capture 12 beetles are caught and marked with a paint dot (M = 12) and released; the marked beetles mix randomly among about 60 beetles in the population; in the second capture 10 beetles are caught (N = 10), of which 2 are marked (R = 2), giving an estimate of (12 × 10) ÷ 2 = 60. (opens full size in a new tab)
The Lincoln index: population estimate = (M × N) ÷ R. Here (12 × 10) ÷ 2 = 60 beetles.

Written and checked against the IB Biology SL specification · Updated October 2026

Frequently asked questions

What is carrying capacity in biology?

Carrying capacity is the maximum population size of a species that an environment can support. It is set by limited resources such as food, water, light, space or nesting sites. Near carrying capacity, competition, predation and disease increase, so density-dependent factors push the population back towards it by negative feedback.

How do you estimate population size using the Lincoln index?

Catch and mark a sample (M), release it and let it mix, then catch a second sample (N) and count the marked individuals in it (R). Population size = (M × N) ÷ R. The method assumes marks are not lost, marking does no harm, and there is no migration, birth or death between samples.

Why does a population grow exponentially at first?

A population grows exponentially at first because resources are plentiful, so there is little competition, and predators and pathogens are scarce. The birth rate is far higher than the death rate, so numbers multiply at a constant rate. Later, density-dependent factors slow growth and the population levels off at carrying capacity.

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