Capture–recapture

Objective. Estimate populations and evaluate model assumptions.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Capture–recapture estimates the size of a population too large to count directly, by marking a sample, releasing it, then recapturing a second sample and seeing what proportion is marked. The key relation is (marked in second sample ÷ second sample size) = (first sample size ÷ total population), rearranged to estimate total population. This relies on assumptions such as no births, deaths or migration between captures, and marked individuals mixing randomly. If 50 fish are tagged, then a later catch of 40 fish contains 8 tagged ones, population ≈ 50 × 40 ÷ 8 = 250. Always state the model's assumptions when asked to evaluate reliability.

Worked example

In a capture–recapture study, 60 animals are tagged initially. Later, a sample of 45 animals is caught, of which 9 are tagged. Estimate the total population.

1 $Use population \approx (first sample \times second sample) \div tagged recaptured$
2 $Population \approx (60 \times 45) \div 9$
3 $Population \approx 2700 \div 9$
4 $Population \approx 300$

Answer: 300

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Students often invert the capture–recapture ratio, multiplying instead of dividing appropriately, giving a population estimate smaller than the actual sample sizes used, which is clearly impossible.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard