Mark-Recapture Population Estimator

Population Estimate (N) uses the classic Lincoln-Petersen formula, N = MC/R: Marked in First Capture times Total Second Capture, divided by Recaptured Marked. Because R is a count of marked individuals found again — a subset that can never exceed either M or C by definition — this calculator clamps R to the smaller of the three values before running any math, so an entered figure that doesn't respect that real-world constraint (say, more "recaptured" than were ever marked or ever caught the second time) can't produce a nonsensical or undefined result. All three inputs move Population Estimate in a predictable direction: raising M or C raises it, while raising R lowers it, since a higher recapture proportion implies a smaller total population relative to your sample sizes.

Recapture Rate (R divided by C) and Marking Fraction (M divided by Population Estimate) look like two different metrics but reduce to the exact same value algebraically — substituting N = MC/R into M/N gives R/C, so they will always match. The Chapman Estimate applies the bias correction statistician Douglas Chapman published in 1951 (N_c = ((M+1)(C+1)/(R+1)) - 1), derived from properties of the hypergeometric distribution specifically to reduce the small-sample bias the plain Lincoln-Petersen formula carries when R is low, and the 95% confidence interval uses the classical Lincoln-Petersen variance approximation, which is known to widen quickly and become unstable when R is small — the Sampling Adequacy label exists specifically to flag when R is too low (below roughly 7) for the estimate to be trusted at face value, a well-documented limitation of the method rather than a quirk of this calculator.