9.9.2 Capture - Recapture

Capture - Recapture

What is the capture-recapture method?

This method is used when you want to estimate the size of a population
It is used when it is impossible or time-consuming to count the whole population

How do I use the capture-recapture method?

Let N be the size of the population
Take a first sample (the capture) of size M
- Tag them with a mark or label
- Release them back into the population
- Give them some time to mix with the rest of the population
Take a second sample (the recapture) of size n
- Let m be the number of them that have been recaptured (previously been tagged)
Form an equation by assuming that the proportion of the second sample that have been tagged is equal to the proportion of the population that has been tagged
- $\frac{m}{n} = \frac{M}{N}$
- In words this is $\frac{Number of " recaptured "}{Size of second sample} = \frac{Size of first sample}{Size of population}$
Rearrange this equation to find an estimate for the population size N
- $N = \frac{n}{m} \times M$

Worked Example

Roger captures 50 rabbits from Lopital Woods and marks them by putting a safe tag on their ears. Roger then releases the rabbits back into the woods. One week later, Roger captures 100 rabbits and finds that 8 of the rabbits have the tag in their ears.

Use the capture-recapture method to estimate the size of the population of rabbits in Lopital Woods.

Let N be the size of the population.

Write down the fraction of the population that have the tag: $\frac{50}{N}$

Write down the fraction of the second sample that have the tag: $\frac{8}{100}$

Form an equation by making the two fractions equal: $\frac{8}{100} = \frac{50}{N}$

Cross multiply: $8 N = 5000$

Divide both sides by 8: $N = \frac{5000}{8} = 625$

Write your answer: There are aound 625 rabbits in Lopital Woods

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AQA GCSE Maths

Revision Notes

9.9.2 Capture - Recapture

Capture - Recapture

What is the capture-recapture method?

How do I use the capture-recapture method?

Worked Example

Author: Daniel

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