Capture Recapture
Capture-recapture is a method for estimating the size of a population, such as an animal population, that would be impractical to count directly. A first sample is caught, marked and released; a second sample is caught later, and the proportion of marked individuals found within it is used to estimate the population size using N = (n1 x n2) / m, where m is the number marked in the second sample.
Before you start
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Method
- Capture a first sample of size n1 from the population, mark every individual, then release them so they can mix back in with the rest of the population.
- After giving the marked individuals time to mix randomly, capture a second sample of size n2.
- Count m, the number of marked individuals found within the second sample.
- Use the formula estimated population N = (n1 x n2) / m.
- Round the estimate to a sensible degree of accuracy, usually the nearest whole number, unless told otherwise.
- State the assumptions the method relies on: the population is closed (no significant births, deaths, immigration or emigration between the two samples), marking does not affect survival or behaviour, and marked individuals mix randomly with the rest of the population.
Worked example
In a lake, 50 fish are caught, marked and released. A week later, 80 fish are caught and 16 of them are found to be marked. Estimate the total number of fish in the lake.
- n1 = 50 (first sample, all marked), n2 = 80 (second sample), m = 16 (marked fish found in the second sample).
- N = (n1 x n2) / m = (50 x 80) / 16.
- N = 4000 / 16 = 250.
- Final answer: an estimated 250 fish in the lake.
Practice questions
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Q140 birds are caught, ringed and released. Later, 60 birds are caught and 12 are found to be ringed. Estimate the population.Show answer
Answer: 200 ((40 x 60)/12)
Q225 deer are tagged and released. In a second sample of 50 deer, 5 are found to be tagged. Estimate the deer population.Show answer
Answer: 250 ((25 x 50)/5)
Q3100 fish are marked and released. A second catch of 40 fish contains 8 marked fish. Estimate the fish population.Show answer
Answer: 500 ((100 x 40)/8)
Q4A population estimate using capture-recapture gives N = 300, with n1 = 60 and n2 = 50. How many marked individuals, m, were found in the second sample?Show answer
Answer: 10 (m = (60 x 50)/300)
Q5Explain why the capture-recapture method requires the marked animals to have time to mix randomly with the rest of the population before the second sample is caught.Show answer
Answer: So that the proportion of marked animals in the second sample fairly represents the proportion of marked animals in the whole population, giving an unbiased estimate
Q6A conservationist worries that marking makes animals easier for predators to catch, reducing their survival before the second sample. Explain how this would affect the population estimate.Show answer
Answer: Fewer marked animals would survive to appear in the second sample, so m would be too small, making N = (n1 x n2)/m an overestimate of the true population
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A biologist catches, tags and releases 45 rabbits in a field. Two weeks later, she catches 60 rabbits and finds that 9 of them are tagged. (a) Use the capture-recapture method to estimate the total population of rabbits in the field. (b) State one assumption needed for this estimate to be reliable.
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A capture-recapture estimate of a population of otters is carried out. 30 otters are caught, tagged and released. Some weeks later, 45 otters are caught, of which 10 are tagged. (a) Calculate the estimated population of otters. (b) A full survey later finds the true population to be 100 otters. Calculate the percentage error in the capture-recapture estimate.
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Give two conditions that must hold for a capture-recapture estimate of population size to be valid.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the capture recapture worksheet pack - 18 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 2 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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