Estimating the proportion of uncatchable animals in a population by double-sampling

Estimates of population size obtained by capture-recapture methods refer solely to the catchable portion of a population. Given a population containing marked animals, two closed-form maximum likelihood estimators of the proportion of uncatchable animals are presented. They are based on twice sampling the proportion of marked animals in the population: the first sample is drawn from catchable animals only, the second from mixed catchable and uncatchable animals. If the individuals in the first sample are not available to the second sample, both samples must be taken from a representative subpopulation of known size. The quantities required may be obtained during a standard capture-recapture session, provided the sampling methods meet the relevant assumptions; the ensuing estimate of population size can then be corrected for uncatchability. The technique is illustrated for eider ducks, using data from Coulson (1984, Ibis 126, 525-543).