Capture–recapture and sampling assumptions
3 exam-style questions. Answers and the mark for each step are on the last page.
- Question 1
Scientists catch 40 fish from a lake, tag them and release them. A week later they catch 50 fish; 8 of them are tagged.
(a) Work out an estimate for the number of fish in the lake.
- Question 2
A capture-recapture survey marks 40 insects. In a second sample of 50, 9 are recognised as marked.
(a) Estimate the population. Give your answer to the nearest whole number.
(b) A proposed estimate is twice your unrounded model estimate. What recapture count would produce it with the same sample sizes?
(c) If this required recapture count is not an integer, what does that mean?
- Question 3
In a nature reserve, 60 birds are ringed and released. 5 of the ringed birds are later found to have died before the second sample. In the second sample of 72 birds, 9 are ringed.
(a) Work out an estimate of the number of birds in the reserve at the time of the second sample.
(b) Explain why using 60 in the calculation would give an overestimate.
Answers and marks
Question 1
(a) 250
- M1 or an equivalent proportion.
- A1 Correct answer: 250.
Question 2
(a)
- M1 Use marked first sample times second sample divided by marked recaptures.
- A1 Correct answer:
(b)
- M1 The estimate varies inversely with the marked recapture count.
- A1 Correct answer:
(c) With fixed sample sizes, no actual integer recapture count could give exactly that proposed doubled estimate.
- C1 Correct conclusion with supporting reasoning: With fixed sample sizes, no actual integer recapture count could give exactly that proposed doubled estimate.
Question 3
(a) 440
- P1 Using 55 ringed birds.
- P1 .
- A1 Correct answer: 440.
(b) It assumes more ringed birds were available to catch than there really were.
- C1 Using 60 overstates the ringed birds available, making too large.