Mark and Recapture Population Calculator (Lincoln-Petersen)
Enter the number marked, the second sample size and the recaptures to estimate the population.
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Mark and Recapture Population Calculator (Lincoln-Petersen) by TheCalcTools
How the Mark and Recapture Population Calculator (Lincoln-Petersen) works
If marked animals mix evenly back into the population, the share marked in the second sample matches the share marked in the whole population: N ≈ M × C ÷ R.
Chapman’s version adds 1 to each count and subtracts 1, which reduces bias when recaptures are few. The interval uses the normal approximation to Chapman’s variance.
The formula
Worked example
Using the default values shown in the calculator:
| Animals marked in the first sample | 60 |
|---|---|
| Animals caught in the second sample | 50 |
| Marked animals recaptured | 12 |
- 60 × 50 ÷ 12 = 250 (Lincoln-Petersen).
- Chapman: 61 × 51 ÷ 13 − 1 = 238.
Result:
| Population estimate (Chapman) | 238 |
|---|---|
| Lincoln-Petersen estimate | 250 |
| 95% interval, low | 142 |
| 95% interval, high | 334 |
Frequently asked questions
What assumptions matter most?
A closed population (no births, deaths or migration between samples), marks that do not fall off or change behaviour, and equal catchability of all animals.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.