Mark-Recapture Population Estimate Calculator
Estimate a total wildlife population from a mark-recapture study using both the Lincoln-Petersen index and the less-biased Chapman estimator.
How it works
Lincoln-Petersen: N = (M × C) / R · Chapman (less biased): N = (M+1)(C+1) / (R+1) − 1 · where M = first-capture marks, C = second sample, R = marked recaptures
Mark-recapture estimates a population you cannot count directly. You mark M animals, release them, then take a second sample of C animals and count how many R carry marks. If the marked animals mix evenly, the recapture fraction R/C mirrors the marked fraction M/N, giving N = MC/R. The simple Lincoln-Petersen index is biased upward with small samples, so the Chapman estimator adds +1 corrections and is preferred, especially when few animals are recaptured.
Worked example
You tag 40 fish, release them, then net 50 fish of which 8 are tagged. Lincoln-Petersen: N = 40 × 50 / 8 = 250. Chapman: (41 × 51)/9 − 1 = 231. The lake holds roughly 230–250 fish.
Sources: Mark and recapture — Wikipedia
Frequently asked questions
Why use the Chapman estimator instead of Lincoln-Petersen?
The plain Lincoln-Petersen ratio overestimates the population when samples are small, and it blows up if no marked animals are recaptured. The Chapman estimator adds +1 to each term, removing most of that bias and staying defined at R = 0.
What assumptions does mark-recapture rely on?
A closed population (no births, deaths, immigration or emigration between samples), marks that do not fall off or affect survival, and equal catchability so marked and unmarked animals mix and are caught with the same probability.
What if I recapture zero marked animals?
Lincoln-Petersen divides by R and is undefined at R = 0, so the calculator falls back to the Chapman estimate, which stays finite. A zero recapture usually means the population is large or mixing is incomplete.
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This calculator is for educational purposes. Double-check important results before acting on them.