Capture Recapture - Worksheets, Questions and Revision

18 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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6.13 Capture Recapture

EDEXCEL 1MA1 · Calculator allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
The capture-recapture method is used to estimate the size of a population of animals.
(Total for Question 1 is 1 mark)
2
For each statement, write True or False.
(i) The capture-recapture method assumes the population does not change between the two samples (no births, deaths, immigration or emigration).
(ii) A larger second sample will always give a less reliable estimate than a smaller one.
(iii) If marks fall off some animals before the second sample is caught, the population estimate will tend to be too high.
(iv) The formula for capture-recapture is N = n1 + n2 - m.
(Total for Question 2 is 4 marks)
3
Which of the following best describes the capture-recapture method for estimating population size?
  • A) Counting every individual in the population directly
  • B) Catching a sample, marking it and releasing it, then using the proportion of marked individuals found in a second sample to estimate the total population size
  • C) Measuring the area of the habitat and multiplying by an average density figure from a textbook
  • D) Asking local residents to estimate how many animals they have seen
(Total for Question 3 is 1 mark)
4
Match each label to its correct description.
Labels: n1, n2, m, N
Descriptions:
1. The number of individuals caught and marked in the first sample
2. The number of individuals caught in the second sample
3. The number of marked individuals found in the second sample
4. The estimated total population size
(Total for Question 4 is 4 marks)
5
A gamekeeper wants to estimate the number of pheasants on his estate.
On Monday he catches 60 pheasants, rings each one, then releases them.
On Thursday he catches 90 pheasants and finds that 18 of them are ringed.
(Total for Question 5 is 2 marks)
6
An ecologist is estimating the number of newts in a pond.
She catches 35 newts, marks them, and releases them back into the pond.
The next day she catches 42 newts. 5 of these are marked.
(Total for Question 6 is 3 marks)
7
A marine biologist tags 40 crabs in a rock pool and releases them. Later, she catches a second sample of 64 crabs, of which 16 are tagged.
Show that this gives an estimate of 160 crabs living in the rock pool.
(Total for Question 7 is 2 marks)
8
In a wood, an ecologist estimates there are 260 squirrels in total. She marked 30 squirrels in the first sample.
(Total for Question 8 is 3 marks)
9
State three assumptions that must be made for the capture-recapture method to give a reliable estimate of population size.
(Total for Question 9 is 3 marks)
10
A marine biologist tags 80 turtles in a bay. Two months later, she takes a second sample of 60 turtles and finds that 15% of them are tagged.
(a)Work out the number of tagged turtles in the second sample.(1)
(b)Use your answer to part (a) to estimate the total number of turtles in the bay. Give your answer to the nearest whole number.(2)
(Total for Question 10 is 3 marks)
11
Two students each estimate the number of woodlice under a log using the capture-recapture method.
Student A: catches and marks 20 woodlice, then a second sample of 20 woodlice contains 4 marked.
Student B: catches and marks 60 woodlice, then a second sample of 60 woodlice contains 36 marked.
(a)Show that both students obtain the same estimate for the population.(2)
(b)Explain why Student B's estimate is likely to be more reliable than Student A's estimate.(1)
(Total for Question 11 is 3 marks)
12
A nature reserve covers 5 hectares. To estimate its hare population, 45 hares are caught and tagged in a first sample. In a second sample of 60 hares, 9 are found to be tagged.
(a)Estimate the total number of hares in the reserve.(2)
(b)Work out the population density of hares, in hares per hectare.(1)
(Total for Question 12 is 3 marks)
13
A researcher estimates there are 420 mice in a barn. She marked 35 mice in the first sample. She wants her second sample to contain exactly 5 marked mice.
(Total for Question 13 is 2 marks)
14
In a capture-recapture study, some of the marks put on animals in the first sample fall off before the second sample is taken.
(Total for Question 14 is 2 marks)
15
A pond snail population is estimated using capture-recapture. In the first sample, 52 snails are marked. In the second sample of 38 snails, 7 are marked.
(a)Calculate an estimate for the population of snails, giving your answer to 3 significant figures.(2)
(b)Explain why it would not be appropriate to report the final population estimate as a decimal.(1)
(Total for Question 15 is 3 marks)
16
A wildlife survey estimates the population of red squirrels in a forest in two consecutive years using capture-recapture.
Year 1: 60 squirrels tagged in the first sample; second sample of 50, of which 12 are tagged.
Year 2: 80 squirrels tagged in the first sample; second sample of 70, of which 14 are tagged.
(a)Calculate the population estimate for Year 1 and for Year 2.(2)
(b)Work out the percentage change in the population estimate from Year 1 to Year 2.(2)
(Total for Question 16 is 4 marks)
17
A reservoir management team wants to estimate the number of pike in a reservoir with a surface area of 8 hectares.
In April, they catch and tag 72 pike, then release them. Two weeks later, they catch a second sample of 90 pike, and find that 15 are tagged.
In September, they repeat the survey: they tag 60 pike in a first sample, and in a second sample of 80 pike, 10 are found to be tagged.
(a)Estimate the number of pike in the reservoir in April.(2)
(b)Work out the population density of pike in April, in pike per hectare.(1)
(c)Calculate the population estimate for September.(2)
(d)The team claims that the pike population increased by exactly 10% between April and September. Determine, showing your working, whether this claim is correct.(2)
(Total for Question 17 is 7 marks)
18
The capture-recapture formula assumes that the proportion of marked animals found in the second sample is the same as the proportion of marked animals in the whole population.
(Total for Question 18 is 3 marks)
Mark scheme · 6.13 Capture Recapture

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18