Maximum likelihood estimation for model Mt,α for capture-recapture data with misidentification

We investigate model Mt,α  for abundance estimation in closed-population capture-recapture studies, where animals are identified from natural marks such as DNA profiles or photographs of distinctive individual features. Model Mt,α  extends the classical model Mt  to accommodate errors in identification, by specifying that each sample identification is correct with probability α and false with probability 1-α. Information about misidentification is gained from a surplus of capture histories with only one entry, which arise from false identifications. We derive an exact closed-form expression for the likelihood for model Mt,α  and show that it can be computed efficiently, in contrast to previous studies which have held the likelihood to be computationally intractable. Our fast computation enables us to conduct a thorough investigation of the statistical properties of the maximum likelihood estimates. We find that the indirect approach to error estimation places high demands on data richness, and good statistical properties in terms of precision and bias require high capture probabilities or many capture occasions. When these requirements are not met, abundance is estimated with very low precision and negative bias, and at the extreme better properties can be obtained by the naive approach of ignoring misidentification error. We recommend that model Mt,α  be used with caution and other strategies for handling misidentification error be considered. We illustrate our study with genetic and photographic surveys of the New Zealand population of southern right whale (Eubalaena australis).