Maths: Population Estimation Using Capture-Recapture

Capture-recapture offers a neat way to estimate a population you cannot count directly: mark a first sample, release it, then see how many marked individuals turn up in a second sample. The estimate N = (marked in first catch × total in second catch) ÷ (marked in second catch) works because the proportion of marked fish recaptured should mirror the proportion of the whole population that was originally marked. That logic only holds under strict conditions. The population must stay closed — no births, deaths, or migration between catches — and every fish must be equally catchable, so neither sample is biased. The mark itself must not change behaviour, survival, or recapture chances. When these assumptions break down, the formula quietly misfires: if marked fish die faster, too few are recaptured, and the estimate inflates. Understanding these mechanisms is what separates a reliable population estimate from a misleading one.