Fish Population Estimate Calculator

This calculator estimates a fish population from mark-recapture data using the Chapman modification of the classic Lincoln-Petersen estimator: N̂ = ((M+1)(C+1)/(R+1)) − 1, where M is the number marked and released, C is the size of the second capture, and R is how many of those were marked recaptures. This is the estimator D.G. Chapman introduced in 1951 ("Some properties of the hypergeometric distribution with applications to zoological sample censuses"). The plain Lincoln-Petersen formula (N = M×C/R) is intuitive — if a known fraction of the population was marked, the same fraction should reappear in a second sample — but it's biased upward when recapture counts are small, so this calculator always applies Chapman's +1 adjustment in numerator and denominator, which is standard practice in fisheries science for exactly that reason.

It also computes the Chapman variance estimator to build a 95% confidence interval around the point estimate, since a single population number without an uncertainty range is easy to over-trust. From the population estimate, the calculator derives density (fish per hectare, using the survey area you provide) and the raw recapture rate (R/C as a percentage). That recapture rate matters beyond being a reported output: as a rule of thumb, estimates become unreliable when R/C drops much below 0.05, because too few recaptures make the variance — and therefore the confidence interval — extremely wide. The method's core assumptions are that the population is closed (no births, deaths, immigration, or emigration between samples), marking doesn't affect catchability or survival, and marked fish mix randomly back into the population before the second capture — violations of any of these will bias the estimate.