Practice question

The Lincoln–Petersen estimator uses N ≈ MC/R. The initial marked release is M = 80 rats, the second capture contains C = 100 rats, and R = 20 of those are marked. Therefore N = 80 × 100/20 = 400 rats. Since marked animals constitute one-fifth of the recapture sample, the marked cohort is inferred to represent one-fifth of the whole population; five times 80 gives the same estimate. The method assumes that the population is effectively closed during the month, all animals have equal capture probability, marks remain visible and do not affect survival or behavior, and marked rats mix randomly with unmarked rats before recapture. Births, deaths, immigration, or emigration can change the marked proportion and bias the estimate. Behavioral responses to trapping are especially relevant for mammals: trap-shy animals reduce marked recaptures and inflate N, while trap-happy animals do the reverse. The numerical result is a model-based estimate, not an exact census, and uncertainty should normally be reported with adequate replication.