Mark-resight abundance estimation under incomplete identification of marked individuals

Often less expensive and less invasive than conventional mark-recapture, so-called 'mark-resight' methods are popular in the estimation of population abundance. These methods are most often applied when a subset of the population of interest is marked (naturally or artificially), and non-invasive sighting data can be simultaneously collected for both marked and unmarked individuals. However, it can often be difficult to identify marked individuals with certainty during resighting surveys, and incomplete identification of marked individuals is potentially a major source of bias in mark-resight abundance estimators. Previously proposed solutions are ad hoc and will tend to underperform unless marked individual identification rates are relatively high (>90%) or individual sighting heterogeneity is negligible. Based on a complete data likelihood, we present an approach that properly accounts for uncertainty in marked individual detection histories when incomplete identifications occur. The models allow for individual heterogeneity in detection, sampling with (e.g. Poisson) or without (e.g. Bernoulli) replacement, and an unknown number of marked individuals. Using a custom Markov chain Monte Carlo algorithm to facilitate Bayesian inference, we demonstrate these models using two example data sets and investigate their properties via simulation experiments. We estimate abundance for grassland sparrow populations in Pennsylvania, USA when sampling was conducted with replacement and the number of marked individuals was either known or unknown. To increase marked individual identification probabilities, extensive territory mapping was used to assign incomplete identifications to individuals based on location. Despite marked individual identification probabilities as low as 67% in the absence of this territorial mapping procedure, we generally found little return (or need) for this time-consuming investment when using our proposed approach. We also estimate rookery abundance from Alaskan Steller sea lion counts when sampling was conducted without replacement, the number of marked individuals was unknown, and individual heterogeneity was suspected as non-negligible. In terms of estimator performance, our simulation experiments and examples demonstrated advantages of our proposed approach over previous methods, particularly when marked individual identification probabilities are low and individual heterogeneity levels are high. Our methodology can also reduce field effort requirements for marked individual identification, thus, allowing potential investment into additional marking events or resighting surveys.