Capture-Recapture

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#14681

Capture-Recapture 

Total = original number tagged × total recaptured ÷ number tagged on recapture

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#18856

The capture-recapture technique was used to estimate the population of penguins in 2013. 50 penguins were caught and tagged and then released. Later 110 penguins were captured and 20 of these were tagged. The estimated population of penguins in 2013 is 13% less than in 2012. What was the estimated population for 2012?

Total = 50 × 110 ÷ 20

= 275

hence the estimated population of 2013 is 275
since this is 13% lower than 2012 that means that 275 = 87% × x
where x is the population in 2013 and 100% reduced by 13% is 87%

x = 275 ÷ 87%
x = 316
hence the estimated population in 2012 is 316

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#18857

50 animals are caught and tagged and released. Later, 220 animals are caught and it is noted that 35 of these animals are tagged. What would be the total population estimate?
Total = 50 × 220 ÷ 35 = 314.28	original = 50 recaptured = 220 tagged = 35 so we can say approximately 314
	A more formal approach:
$$\frac{50}{x}=\frac {35}{220}$$	This means that 50 out of the entire population (x) was tagged, then 35 out of the 220 that were caught were tagged. As the proportion should be the same, we set them equal to each other and solve for x
$$\frac{x}{50}=\frac {220}{35}$$	First job is to ‘flip’ both fractions so the x is on the top left, making it easier to solve
$$x=\frac{220}{35} \times 50$$	Multiply by sides by 50
x = 314.28	round to the nearest whole number
x = 314

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#18858

A biologist catches 100 deer in a forest, tags them and releases them back into the forest. A year later he catches 90 deer, of which 12 have tags. Estimate the total population of deer.
Total = 100 × 90 ÷ 12 = 750
	A more formal approach:
$$\frac{100}{x}=\frac {12}{90}$$	This means that 50 out of the entire population (x) was tagged, then 35 out of the 220 that were caught were tagged. As the proportion should be the same, we set them equal to each other and solve for x
$$\frac{x}{100}=\frac {90}{12}$$	First job is to ‘flip’ both fractions so the x is on the top left, making it easier to solve
$$x=\frac{90}{12} \times 100$$	Multiply by sides by 100
x = 750	round to the nearest whole number

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