Capture Recapture Worksheets, Questions and Revision

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H13 Capture Recapture

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

A wildlife trust wants to estimate the number of great crested newts living in a pond, using the capture-recapture (Petersen) method. The population estimate is found using the formula

N = (n1 x n2) / m

where N is the estimated population size, n1 is the number caught and marked in the first catch, n2 is the number caught in the second catch, and m is the number in the second catch that are already marked.

(a)Write down what n1 and m represent in this formula.(1)

(b)On the first visit, 50 newts are caught, marked, and released back into the pond. On the second visit, 40 newts are caught, of which 8 already have marks from the first visit. Use the formula to work out an estimate for the number of newts in the pond.(2)

(c)Give one condition that must hold true for the population between the two visits for this estimate to be reliable.(1)

(Total for Question 1 is 4 marks)

2

An angling club wants to estimate the number of perch living in a small lake. In the first catch, 60 perch are caught, marked, and returned to the lake. In the second catch, 45 perch are caught, of which 12 are already marked.

(a)Use the capture-recapture formula to estimate the number of perch in the lake.(2)

(b)Give one reason why this value is only an estimate of the true number of perch in the lake, rather than an exact count.(1)

(Total for Question 2 is 3 marks)

3

Rangers at a nature reserve use capture-recapture to estimate the number of rabbits living there. The diagram shows the results of the two catches.

(a)Use the diagram to write down the value of m.(1)

(b)Use the values shown in the diagram to estimate the total rabbit population.(2)

(c)Explain what the overlapping region of the diagram represents.(1)

(Total for Question 3 is 4 marks)

4

For each statement about the capture-recapture method, write down whether it is True or False.

(i)Between the two catches, no individuals should be born, die, move into, or move out of the population.(1)

(ii)Marks used to identify captured individuals must not fade, rub off, or be lost before the second catch.(1)

(iii)Every individual in the population, whether marked or not, must be equally likely to be caught in the second catch.(1)

(iv)The formula only works correctly if exactly the same number of individuals are caught in the first catch and in the second catch (n1 must equal n2).(1)

(Total for Question 4 is 4 marks)

5

Which of the following is NOT an assumption needed for a reliable capture-recapture estimate?

A) The population is closed between visits (no births, deaths, immigration or emigration)
B) Every individual is equally likely to be captured
C) Marks remain visible and are not lost between visits
D) The two samples, n1 and n2, must always be equal in size

(Total for Question 5 is 1 mark)

6

Ecologists carry out capture-recapture surveys of water voles at three different sites. The table shows the results.

Site	n1 (marked in first catch)	n2 (caught in second catch)	m (marked recaptured)
Site A	80	60	12
Site B	45	50	15
Site C	96	40	8

(a)Work out the estimated water vole population at each of the three sites.(2)

(b)Write down which site has the largest estimated water vole population.(1)

(c)Give one reason why comparing these three estimates directly might not give a fair picture of which site truly has the most water voles.(1)

(Total for Question 6 is 4 marks)

7

A team estimates the number of otters along a stretch of river. In the first catch, 37 otters are marked. In the second catch, 52 otters are caught, of which 9 are already marked.

(a)Work out an estimate for the number of otters, giving your answer to the nearest whole number.(2)

(b)Explain why it makes sense to round your answer in part (a) to a whole number.(1)

(Total for Question 7 is 3 marks)

8

A team plans a capture-recapture survey of hedgehogs. In the first catch, 30 hedgehogs are marked. The team wants their final population estimate, N, to come out at 180, based on 5 marked hedgehogs being found in the second catch.

(a)Rearrange the formula N = (n1 x n2) / m to make n2 the subject.(1)

(b)Use your rearranged formula, with N = 180, n1 = 30 and m = 5, to work out how many hedgehogs, n2, would need to be caught in the second catch.(2)

(Total for Question 8 is 3 marks)

9

A park ranger estimates a squirrel population is 250, based on marking 100 squirrels in the first catch, and catching 50 squirrels in the second catch. Work out how many of the 50 squirrels caught in the second catch, m, must already have been marked for this estimate to be correct.

(Total for Question 9 is 2 marks)

10

Give two ways in which a research team could improve the reliability of a capture-recapture population estimate.

(Total for Question 10 is 2 marks)

11

For each action, state whether it would IMPROVE, WORSEN, or have NO EFFECT on the reliability of a capture-recapture estimate.

(i)Increasing the sample sizes n1 and n2.(1)

(ii)Leaving several months between the two catches, for a species that breeds quickly.(1)

(iii)Recording the exact time of day of each catch, without changing anything else about how the survey is carried out.(1)

(iv)Using a marking method that makes animals easier for predators to spot.(1)

(Total for Question 11 is 4 marks)

12

In a capture-recapture survey of frogs, some of the marks used in the first catch fade and become hard to see before the second catch takes place.

(a)Explain why this would cause the value of m recorded in the second catch to be smaller than it should be.(1)

(b)Hence explain whether this fault would cause the capture-recapture method to overestimate or underestimate the true population.(2)

(Total for Question 12 is 3 marks)

13

Capture-recapture is an example of using a sample to estimate a feature of a whole population, in a similar way to other sampling techniques used in statistics.

(a)Give one reason why it would usually be impractical to find the exact size of an animal population by counting every individual (a census).(1)

(b)State one similarity between capture-recapture and other sampling methods (such as a survey of people) used to estimate a characteristic of a large population.(1)

(Total for Question 13 is 2 marks)

14

A team estimates the number of grasshoppers in a meadow by repeating the capture-recapture survey on three different days. The table shows the results.

Day	n1 (marked in first catch)	n2 (caught in second catch)	m (marked recaptured)
Day 1	40	30	8
Day 2	45	35	9
Day 3	50	25	10

(a)Work out the population estimate for each of the three days.(2)

(b)Work out the mean of these three estimates.(2)

(c)Explain why using the mean of several repeated surveys generally gives a more reliable estimate than using the result of a single survey.(1)

(Total for Question 14 is 5 marks)

15

A survey estimates the population of hares living in a 40-hectare field, using capture-recapture. In the first catch, 64 hares are marked. In the second catch, 50 hares are caught, of which 10 are already marked.

(a)Show that the capture-recapture estimate for this field is 320 hares.(2)

(b)Work out the estimated density of hares, in hares per hectare, for this field.(2)

(c)A neighbouring 25-hectare field has an estimated density of 6 hares per hectare, from a separate survey. Work out how many more hares are estimated to be in the first field compared with the second field.(2)

(Total for Question 15 is 6 marks)

16

A wildlife charity plans to investigate the size of the otter population along a 10 km stretch of river, using the capture-recapture method.

(a)Plan: Write a suitable statistical question the charity could investigate using capture-recapture.(1)

(b)Collect: Give one practical difficulty the charity might face when trying to catch and mark otters, and suggest how they could deal with it.(2)

(c)Process: In the first catch, 18 otters are caught, marked and released. In the second catch, 24 otters are caught, of which 6 are already marked. Work out an estimate for the otter population.(2)

(d)Interpret: Comment on how much confidence the charity should have in this estimate, given the sample sizes used, and suggest one way they could make the estimate more reliable.(2)

(Total for Question 16 is 7 marks)

17

Some species change their behaviour after first being caught. 'Trap-happy' individuals become easier to catch a second time (for example, if bait is used to catch them). 'Trap-shy' individuals become harder to catch a second time, because they learn to avoid the trap.

(a)If the animals in a study are trap-happy, explain the effect this has on the recorded value of m, and hence on the population estimate N.(2)

(b)If the animals in a study are trap-shy, state whether the population estimate N will tend to be an overestimate or an underestimate, giving a brief reason.(2)

(Total for Question 17 is 4 marks)

18

A researcher carries out a capture-recapture survey of adders (a type of snake). In the first catch, 60 adders are marked. In the second catch, 50 adders are caught.

(a)If 8 of the 50 adders caught in the second catch are marked, work out the population estimate.(2)

(b)The researcher later realises that one of the marked adders was miscounted as unmarked, so the true value of m should have been 7, not 8. Work out the new population estimate, giving your answer to the nearest whole number.(2)

(c)Comment on what this shows about the reliability of capture-recapture estimates when the value of m is small.(1)

(Total for Question 18 is 5 marks)

19

A team wants to find out whether the population of red squirrels in a woodland has grown after several years of conservation work. They carry out capture-recapture surveys before and after the project.

Before the project: n1 = 40, n2 = 30, m = 10
After the project: n1 = 54, n2 = 36, m = 9

(a)Work out the estimated red squirrel population before and after the conservation project.(3)

(b)The team concludes: 'The conservation project has definitely increased the red squirrel population.' Comment on whether this conclusion is fully justified, given that both figures are estimates.(2)

(Total for Question 19 is 5 marks)

20

On a small, fully enclosed island, a capture-recapture survey of tortoises uses n1 = 42, n2 = 28 and m = 14. Rangers later manage to carry out a complete count (a census) of every tortoise on the island, and find there are actually 91 tortoises.

(a)Show that the capture-recapture estimate for the tortoise population is 84.(2)

(b)Work out the percentage error of the capture-recapture estimate, compared with the true census figure of 91, giving your answer correct to 1 decimal place.(3)

(c)Suggest one possible reason why the capture-recapture estimate might have been lower than the true population figure.(1)

(Total for Question 20 is 6 marks)

21

A wildlife survey of badgers uses capture-recapture. In the first catch, 45 badgers are marked. In the second catch, 52 badgers are caught, of which 9 are already marked. Of the 52 badgers caught in the second catch, 13 show signs of mange (a skin condition).

(a)Work out the estimated total badger population.(2)

(b)Assuming the second catch is representative of the whole population, estimate the total number of badgers in the population with signs of mange.(3)

(c)State the extra assumption needed for your answer to part (b) to be a valid estimate.(1)

(Total for Question 21 is 6 marks)

22

Two teams plan separate capture-recapture surveys of the same species of butterfly in neighbouring meadows.

Team X: catches and marks 20 butterflies in the first catch, and catches 15 in the second catch, both on the same day.
Team Y: catches and marks 80 butterflies in the first catch, and catches 60 in the second catch, one week later.

(a)Give one reason why Team Y's sample sizes are likely to produce a more reliable population estimate than Team X's.(1)

(b)Give one reason why waiting a week between catches, as Team Y did, rather than surveying on the same day like Team X, could reduce the reliability of the estimate.(1)

(c)Suggest a survey design that would avoid both of these problems.(1)

(Total for Question 22 is 3 marks)

Mark scheme · H13 Capture Recapture

Question 1

(a) B1 n1 = the number caught and marked in the first catch, and m = the number in the second catch that are already marked (both needed), oe
(a) Answer: n1 = number marked in the first catch; m = number of marked individuals found in the second catch
(b) M1 (50 x 40) / 8, oe
(b) A1 250 cao
(b) Answer: 250
(c) B1 any valid condition, e.g. no newts enter, leave, are born or die between the two visits (the population is closed), oe
(c) Answer: e.g. no newts enter, leave, are born or die between the two visits

Question 2

(a) M1 (60 x 45) / 12, oe
(a) A1 225 cao
(a) Answer: 225
(b) B1 valid reason, e.g. the method relies on catching and marking only a sample of the fish, rather than counting every fish in the lake, so it can only give an approximate figure, oe
(b) Answer: e.g. it is based on catching a sample of fish, not counting every fish in the lake

Question 3

(a) B1 14 cao
(a) Answer: 14
(b) M1 (70 x 56) / 14, oe
(b) A1 280 cao
(b) Answer: 280
(c) B1 the rabbits that were marked in the first catch and were also caught again in the second catch (the recaptured marked rabbits), oe
(c) Answer: the rabbits marked in the first catch that were caught again (recaptured) in the second catch

Question 4

(i) B1 True cao
(i) Answer: True
(ii) B1 True cao
(ii) Answer: True
(iii) B1 True cao
(iii) Answer: True
(iv) B1 False cao
(iv) Answer: False

Question 5

B1 D cao
Answer: D) The two samples, n1 and n2, must always be equal in size

Question 6

(a) M1 correct method shown for at least one site, e.g. (80 x 60)/12, oe
(a) A1 400, 150 and 480 all correct
(a) Answer: Site A = 400, Site B = 150, Site C = 480
(b) B1 Site C cao, ft from part (a)
(b) Answer: Site C
(c) B1 valid reason, e.g. the surveys may have been carried out under different conditions at each site (different weather, time of year, effort, or time between catches), so the estimates may not be equally reliable or directly comparable, oe
(c) Answer: e.g. the three surveys may not have used the same conditions or level of effort, so the estimates may not be directly comparable

Question 7

(a) M1 (37 x 52)/9, oe (= 213.7...)
(a) A1 214 cao (awrt)
(a) Answer: 214
(b) B1 valid explanation, e.g. you cannot have a fraction of an otter, so the population estimate must be a whole number of animals, oe
(b) Answer: e.g. you cannot have a fraction of an otter; the population must be a whole number

Question 8

(a) B1 n2 = (N x m) / n1, oe
(a) Answer: n2 = (N x m) / n1
(b) M1 (180 x 5)/30, oe
(b) A1 30 cao
(b) Answer: 30

Question 9

M1 (100 x 50)/250, oe
A1 20 cao
Answer: 20

Question 10

B1 any valid method, e.g. use larger sample sizes for n1 and/or n2, oe
B1 any different valid method, e.g. reduce the time between the two catches so fewer births, deaths, or movements can occur; repeat the survey and average several estimates; use a marking method that does not affect behaviour or survival, oe
Answer: e.g. use larger sample sizes; reduce the time between the two catches; repeat the survey and average the estimates (any two)

Question 11

(i) B1 Improve cao
(i) Answer: Improve
(ii) B1 Worsen cao
(ii) Answer: Worsen
(iii) B1 No effect cao
(iii) Answer: No effect
(iv) B1 Worsen cao
(iv) Answer: Worsen

Question 12

(a) B1 valid explanation, e.g. some frogs that are actually marked will not be recognised as marked because their mark has faded, so they get wrongly counted as unmarked, oe
(a) Answer: e.g. faded marks mean some truly marked frogs are wrongly recorded as unmarked
(b) B1 overestimate identified
(b) B1 correct reasoning, e.g. since m is in the denominator of N = (n1 x n2)/m, a smaller recorded value of m makes N come out larger than it should be, oe
(b) Answer: Overestimate

Question 13

(a) B1 valid reason, e.g. animals move around and may hide, or the population or area involved may be too large to check every individual with certainty, oe
(a) Answer: e.g. animals move and hide, and populations can be too large to count every individual directly
(b) B1 valid similarity, e.g. both use information from a smaller sample to make an estimate about a whole population, because examining every member of the population directly is impractical, oe
(b) Answer: e.g. both use a smaller sample to estimate something about the whole population, because a full count is impractical

Question 14

(a) M1 correct method shown for at least one day, e.g. (40 x 30)/8, oe
(a) A1 150, 175 and 125 all correct
(a) Answer: Day 1 = 150, Day 2 = 175, Day 3 = 125
(b) M1 (150 + 175 + 125) / 3, oe (or ft from part a)
(b) A1 150 cao
(b) Answer: 150
(c) B1 valid explanation, e.g. a single survey's estimate can be strongly affected by chance in exactly which individuals happen to be caught; averaging several surveys reduces the effect of this random variation on the overall estimate, oe
(c) Answer: e.g. averaging reduces the effect of chance variation between individual surveys

Question 15

(a) M1 (64 x 50)/10, oe
(a) A1 320 confirmed cao
(a) Answer: 320
(b) M1 320 / 40, oe
(b) A1 8 cao
(b) Answer: 8 hares per hectare
(c) M1 25 x 6 (= 150), oe
(c) A1 170 cao (320 - 150)
(c) Answer: 170

Question 16

(a) B1 any suitable question linking otters and this stretch of river, e.g. 'How many otters live along this 10 km stretch of river?', oe
(a) Answer: e.g. How many otters live along this 10 km stretch of river?
(b) B1 valid difficulty, e.g. otters are shy, nocturnal, or hard to trap, oe
(b) B1 valid solution linked to the difficulty, e.g. use humane traps set overnight near known otter paths or holts, oe
(b) Answer: e.g. otters are hard to trap because they are nocturnal; use humane traps set overnight near known otter holts
(c) M1 (18 x 24)/6, oe
(c) A1 72 cao
(c) Answer: 72
(d) B1 valid comment, e.g. the samples of 18 and 24 are quite small, so a small error in catching or counting could change the estimate a lot, giving fairly low confidence, oe
(d) B1 valid improvement, e.g. repeat the survey with larger samples, or on several different days, and compare or average the results, oe
(d) Answer: e.g. confidence is fairly low because the samples are small; repeating the survey with larger samples would improve reliability

Question 17

(a) B1 m tends to be higher than it should be, because marked animals are recaptured more easily than unmarked ones
(a) B1 since m is in the denominator of N = (n1 x n2)/m, a higher recorded m makes N smaller than it should be, so the population is underestimated
(a) Answer: m is too high, so N is an underestimate
(b) B1 overestimate cao
(b) B1 correct reason, e.g. trap-shy marked animals are recaptured less often than expected, so the recorded m is lower than it should be, which makes N larger than it should be, oe
(b) Answer: Overestimate

Question 18

(a) M1 (60 x 50)/8, oe
(a) A1 375 cao
(a) Answer: 375
(b) M1 (60 x 50)/7, oe (= 428.5...)
(b) A1 429 cao (awrt)
(b) Answer: 429
(c) B1 valid comment, e.g. when m is small, a change of just one animal makes a large difference to the estimate (54 more adders here), so the method becomes less reliable and more sensitive to small counting errors when few marked animals are recaptured, oe
(c) Answer: e.g. when m is small, one miscounted animal changes the estimate a lot (here by 54), so the method is less reliable with small m

Question 19

(a) M1 correct method shown for at least one, e.g. (40 x 30)/10, oe
(a) A1 120 cao (before)
(a) A1 216 cao (after)
(a) Answer: Before: 120; After: 216
(b) B1 valid comment on direction, e.g. the estimates do suggest an increase, from 120 to 216, oe
(b) B1 valid caveat, e.g. both figures are only estimates based on samples, each with their own possible error, so the true populations could be closer together than the estimates suggest, oe
(b) Answer: e.g. the estimates suggest growth (120 to 216), but as both are only estimates with their own possible error, the true increase may not be this large, and the conclusion is not completely certain

Question 20

(a) M1 (42 x 28)/14, oe
(a) A1 84 confirmed cao
(a) Answer: 84
(b) M1 (91 - 84) / 91, oe
(b) M1 their answer x 100
(b) A1 7.7% awrt cao
(b) Answer: 7.7%
(c) B1 valid reason, e.g. some tortoises may have been trap-shy and harder to catch a second time, or some genuinely unmarked tortoises may have been mistakenly recorded as marked, increasing m, oe
(c) Answer: e.g. some tortoises may have been trap-shy, or m may have been slightly overcounted

Question 21

(a) M1 (45 x 52)/9, oe
(a) A1 260 cao
(a) Answer: 260
(b) M1 13/52, oe
(b) M1 their 13/52 x their 260 (ft)
(b) A1 65 cao
(b) Answer: 65
(c) B1 valid assumption, e.g. the proportion of badgers with mange in the second catch (13 out of 52) is assumed to be representative of the proportion in the whole population, oe
(c) Answer: e.g. the 13 out of 52 with mange is assumed to represent the true proportion across the whole population

Question 22

(a) B1 valid reason, e.g. Team Y uses much larger sample sizes (n1 and n2), which generally makes the estimate less sensitive to small counting errors, oe
(a) Answer: e.g. Team Y's larger samples make the estimate less sensitive to small counting errors
(b) B1 valid reason, e.g. over a longer time gap there is more chance of births, deaths, or migration in or out of the meadow, or marks being lost, which breaks the assumptions the formula relies on, oe
(b) Answer: e.g. a longer gap gives more chance of births, deaths, migration, or lost marks, breaking the formula's assumptions
(c) B1 valid design, e.g. use large sample sizes (like Team Y) but with a short time gap between catches (like Team X), so the population stays closed but the estimate is not too sensitive to small errors, oe
(c) Answer: e.g. use large samples with a short time gap between catches

Capture Recapture (GCSE Statistics) - Worksheets, Questions and Revision

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H13 Capture Recapture

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