Mark-Recapture Population Estimate (Lincoln–Petersen & Chapman)
Closed-population size from n₁ marked, n₂ caught, m₂ recaptured: Lincoln–Petersen and Chapman estimates with SE and 95% CI.
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Tool usage guide
Learn when to use this tool, what it supports, and how real users apply it.
Key facts
Category
Health
Input types
number, select
Output type
json
Sample coverage
4
API ready
Yes
Overview
Estimate the size of a closed population from a two-session mark–recapture census. Enter animals marked and released in the first sample (n₁), total animals caught in the second sample (n₂), and marked recaptures (m₂) to obtain Lincoln–Petersen and Chapman estimates of N̂ with Seber standard error and a 95% confidence interval.
When to use
You have completed two capture sessions on a closed population and know n₁, n₂, and m₂.
You need both the simple Lincoln–Petersen ratio and the bias-corrected Chapman estimator plus SE and 95% CI.
You want a quick field-biology check of never-seen individuals, marked proportion, and capture probability.
How it works
1Enter n₁ (marked and released), n₂ (total caught in the second session), and m₂ (recaptures that still carry a mark).
2Choose Chapman (default, bias-corrected) or Lincoln–Petersen (simple N̂ = n₁n₂/m₂).
3The tool returns N̂, Seber SE, 95% CI, approximate never-seen count, marked fraction in the second sample, and per-session capture probability.
4Inputs with m₂ = 0 or m₂ larger than min(n₁, n₂) are rejected; with m₂ < 10 the interval is only indicative.
Use cases
Wildlife census of a closed small-mammal, bird, or herpetofauna population after two trapping sessions.
Insect or butterfly monitoring where a known number of individuals were marked, released, and later recaptured.
Teaching or reporting a Petersen-method estimate with Chapman correction, SE, and confidence interval.
A single closed meadow was sampled twice; 250 butterflies were marked and released, 180 were caught later, and 54 still carried marks.
Problem
Produce a bias-corrected N̂ and a reasonably tight interval given a larger recapture count.
How to use
Enter n₁ = 250, n₂ = 180, m₂ = 54 and select Chapman.
FAQ
What numbers do I need?
n₁ (first-session animals marked and released), n₂ (second-session total catch), and m₂ (marked animals among those n₂).
How do Chapman and Lincoln–Petersen differ?
Lincoln–Petersen is N̂ = n₁n₂/m₂. Chapman is N̂ = (n₁+1)(n₂+1)/(m₂+1) − 1 and reduces small-sample bias; both are reported with Seber SE and 95% CI.
What assumptions does the estimate require?
A closed population (no births, deaths, immigration, or emigration between sessions), marks that do not fall off or change survival or catchability, and equal catchability of marked and unmarked animals.
What happens if m₂ is zero or very small?
m₂ = 0 (or m₂ > min(n₁, n₂)) is rejected. When m₂ is under 10 the 95% CI is only a rough guide.
What else is shown besides N̂?
Seber standard error, 95% CI, Lincoln–Petersen value when Chapman is selected, approximate never-seen individuals, marked proportion, and capture probability.