Mark–Recapture Calculator
A population estimate from a mark–recapture survey — the Lincoln–Petersen index, the less biased Chapman version, and a 95% confidence interval.
Catch and mark a sample, release it, and later catch a second sample: the proportion marked in the second catch estimates the proportion marked in the whole population, so N ≈ M × C ÷ R.
How the mark–recapture calculator works
Catch and mark a sample, release it, and later catch a second sample: the proportion marked in the second catch estimates the proportion marked in the whole population, so N ≈ M × C ÷ R. Chapman’s correction, (M + 1)(C + 1) ÷ (R + 1) − 1, removes the upward bias when few are recaptured. The method assumes a closed population, marks that do not affect survival or catchability, and mixing between catches.
Formula: N = M × C ÷ R; Chapman N = (M + 1)(C + 1) ÷ (R + 1) − 1
Worked examples
| Inputs | Population estimate (Chapman) | Note |
|---|---|---|
| 120 marked, 150 caught, 18 recaptured | 961 | about 961 (L–P 1,000) |
| 50 marked, 60 caught, 5 recaptured | 518 | about 518 — few recaptures |
| 200 marked, 200 caught, 40 recaptured | 984 | about 985 |
FAQFrequently asked questions
Why is Chapman’s version preferred?
Lincoln–Petersen overestimates on average, badly when recaptures are few, and is undefined with none. Chapman’s adds one to each count, which removes the bias and always gives a number.
What are the assumptions?
No births, deaths, immigration or emigration between catches; marks are permanent and do not change survival or catchability; marked animals mix fully; every animal is equally likely to be caught. Trap-happy or trap-shy animals bias the result.
How many should I mark?
Enough to get at least 7–10 recaptures — ideally 20 or more. Roughly, mark and recatch about 10–20% of the population you suspect; the confidence interval shows whether it was enough.
What about open populations?
Multi-session designs (Jolly–Seber, Schnabel) handle populations that change between samples. Lincoln–Petersen is for two samples close together in time.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- CSIRO — Australia's national science agency
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.