Capture–Recapture Worksheet Generator
Six mark–release–recapture surveys of invented populations — snails in a pond, woodlice under a log pile — each giving the number marked, the size of the second catch and how many in it were marked. Pupils estimate the population with the Lincoln–Petersen index, the Chapman version or both. The second catch is actually drawn from a population of known size, so the answer page can show the estimate next to the real number and pupils see how far a fair survey can miss.
What this generator does
Gives population-estimate questions whose numbers behave like real survey data — the recapture count varies from survey to survey — and an answer key that reports both the estimate and what it was estimating.
How to use this tool
- Choose a small or large population and the estimate pupils should use.
- Leave 'Allow a survey where no marked animal is recaught' off for a first lesson; turn it on to discuss why Lincoln–Petersen then fails.
- Press Make six surveys, open an answer to check it, and print: questions on page one, answers with the true sizes on page two.
Understanding the controls
- Population size
- Small (40–150 animals, samples of 10–30) or large (200–1,000, samples of 30–100).
- Estimate to use
- Lincoln–Petersen, Chapman, or both side by side on the answer page.
- Allow zero recaptures
- When on, a survey may recatch no marked animals; the answer then explains why Lincoln–Petersen cannot be used.
- Paper and seed
- Paper size and density for printing; a seed rebuilds the same six surveys while the generator is unchanged.
Worked examples
- Seed 'meadow', small, survey 1
- 25 pond snails marked, 29 caught later, 9 of them marked: Lincoln–Petersen gives about 81 and Chapman 77. The invented pond really had 88.
- Same seed, survey 2
- 21 newts marked, 18 caught later, 3 marked: Lincoln–Petersen gives 126 and Chapman about 104. The pond really had 95 — few recaptures make a wide miss more likely.
Common use cases
- Practising the Lincoln index before or after fieldwork
- Showing that a correct calculation can still miss the true population
- Comparing Lincoln–Petersen with Chapman when recaptures are few
How this generator works
For each survey a true population size is chosen, then two samples are drawn from numbered animals, each subset equally likely. The recapture count is the overlap of the two samples, not a number picked to make the sum come out neatly. The answer key applies N ≈ M × C ÷ R (Lincoln–Petersen) or N ≈ (M + 1)(C + 1) ÷ (R + 1) − 1 (Chapman), rounded to whole animals, and each recapture count is re-counted from the drawn animals before the sheet appears.
Randomness and fairness
Population sizes and both samples are drawn with the browser's cryptographically secure generator, or from one seeded draw when a seed is typed. Recapture counts come from the drawn samples, so they vary as real ones would under the method's assumptions. Seeded sheets are deterministic, not cryptographic.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The populations are invented and meet the method's assumptions exactly: every animal equally catchable, nothing born, dying or moving between catches, no marks lost. Real surveys break these, usually by more than sampling error.
- Estimates are rounded to whole animals; some courses round differently or keep a decimal.
- No confidence intervals are given; the true size is printed instead, so the miss can be discussed directly.
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