# 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. > Canonical page: https://elysiatools.com/en/tools/mark-recapture-estimator - **Category:** Health - **Keywords:** mark recapture, capture recapture, lincoln petersen, chapman estimator, petersen method, population size estimate, population ecology, wildlife census, seber standard error, ecology calculator, field biology, population estimation ## 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. ## Inputs - **First sample: marked and released (n₁)** (number): Animals caught in the first session, marked, and released back into the population. - **Second sample: total caught (n₂)** (number): Total animals caught in the second session (marked + unmarked). - **Marked animals recaptured (m₂)** (number): Animals in the second sample that carry a mark from the first session. - **Estimator** (select) ## 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 - Enter n₁ (marked and released), n₂ (total caught in the second session), and m₂ (recaptures that still carry a mark). - Choose Chapman (default, bias-corrected) or Lincoln–Petersen (simple N̂ = n₁n₂/m₂). - The tool returns N̂, Seber SE, 95% CI, approximate never-seen count, marked fraction in the second sample, and per-session capture probability. - Inputs 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. ## Frequently asked questions ### 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. ## Related tools - [Bioavailability Calculator (F = AUC_po · Dose_iv / AUC_iv · Dose_po)](https://elysiatools.com/en/tools/bioavailability-calculator): Calculate the absolute bioavailability F of an extravascular (typically oral) dose: F = (AUC_po · Dose_iv) / (AUC_iv · Dose_po), where AUC_po and AUC_iv are the areas under the concentration-time curve after oral and IV dosing, and the doses correct for any difference in amount administered. F is dimensionless and lies in \[0, 1\]; IV bioavailability is by definition 1, while oral F < 1 reflects incomplete absorption and/or first-pass metabolism. AUC can be in any consistent unit (e.g. mg·h/L) since it cancels out of the ratio. Valid only for linear pharmacokinetics, the same drug molecule, and doses within the linear range. 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