What is the Lincoln-Petersen method?

It is a two-sample mark-recapture technique where animals caught in a first session are marked and released. A second session then captures a new sample, and the proportion of marked individuals in that sample is used to estimate total population size via N = M * C / R.

Why does R need to be at least 1?

If no marked animals are recaptured (R = 0) the estimator is undefined because division by zero occurs. In practice, a minimum of about 7-10 recaptures is recommended for meaningful precision.

How is the confidence interval calculated?

This tool uses the normal-approximation method on ln(N), which performs well when recaptures are reasonably large. For very small recapture counts, exact or bootstrap intervals are preferable.

What assumptions does this method make?

The population is closed (no births, deaths, immigration, or emigration between sessions); marks are not lost; marked and unmarked animals are equally catchable; and the second sample is random.

What is the Chapman correction?

The Chapman modification N = ((M+1)(C+1)/(R+1)) - 1 reduces bias when sample sizes are small. This tool offers both the classic and Chapman estimates.

Mark-Recapture Population Estimator

Estimate total animal population size from mark-recapture data using the Lincoln-Petersen method, with confidence interval.

Sample Data

M — First-capture marked animals

Total animals caught, marked, and released in session 1.

C — Second-capture total animals

All animals caught in session 2 (marked + unmarked).

R — Recaptured marked animals

Animals in session 2 that were already marked. Must be ≥1.

Confidence level

90% 95% 99%

Sample presets

Enter field counts and click
Estimate Population to see results.

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Summary

The Mark-Recapture Population Estimator uses the Lincoln-Petersen formula to calculate estimated population size (N) from three field counts: the number of animals marked in the first capture (M), the total caught in the second capture (C), and the number of recaptured marked animals (R). It also reports a 95% confidence interval so you can assess precision.

How it works

Enter the number of animals captured and marked in the first sampling session (M).
Enter the total number of animals captured in the second session (C).
Enter the number of animals in the second session that were already marked (R).
Click "Estimate Population" to compute N = (M * C) / R.
Review the estimated population, confidence interval, and capture probability.

Use cases

Estimating fish population in a lake for fisheries management.
Monitoring mammal abundance in wildlife surveys.
Teaching ecology students about population sampling methods.
Planning conservation interventions that require accurate census data.
Comparing population estimates across survey seasons.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu

Mark-Recapture Population Estimator

Sample Data

Lincoln-Petersen Estimate

Chapman Correction (small-sample bias reduction)

Summary

How it works

Use cases

Frequently Asked Questions

Mark-Recapture Population Estimator

Use the Mark-Recapture Population Estimator

Sample Data

Lincoln-Petersen Estimate

Chapman Correction (small-sample bias reduction)

Summary

How it works

Use cases

Frequently Asked Questions