Mark-Recapture Population Estimate (Lincoln–Petersen & Chapman)

Mark-Recapture Population Estimate (Lincoln–Petersen & Chapman) | Online Free Tool | Elysia Tools

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.

Examples

1. Small-mammal grid: 60 marked, 100 caught, 15 recaptures

Field biologist

Background

A two-night live-trap grid on a closed plot yielded 60 animals marked and released, then 100 captures of which 15 were already marked.

Problem

Need a closed-population size with SE and 95% CI rather than a raw ratio.

How to use

Enter n₁ = 60, n₂ = 100, m₂ = 15 and keep the Chapman estimator.

{"n1":60,"n2":100,"m2":15,"estimator":"chapman"}

Outcome

Chapman N̂ = 384.06 (SE 73.59, 95% CI 239.83–528.29); Lincoln–Petersen = 400; about 324 animals were never seen.

2. Butterfly survey: 250 marked, 180 caught, 54 recaptures

Insect monitoring technician

Background

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.

{"n1":250,"n2":180,"m2":54,"estimator":"chapman"}

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Small-mammal grid: 60 marked, 100 caught, 15 recaptures

2. Butterfly survey: 250 marked, 180 caught, 54 recaptures

FAQ

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