Accounting for missing data when assessing availability in animal population surveys: an application to ice-associated seals in the Bering Sea

Population ecologists often use telemetry to estimate the probability that an animal is available for sampling (availability probability). Such estimates are paramount for generating reliable estimates of animal abundance and are sometimes of biological interest in their own right (e.g. for characterizing pinniped haul-out behaviour or landbird singing frequency). We consider the estimation of availability probability from telemetry data when there are missing records. When records are missing-completely-at-random (i.e. not influenced by whether an animal is available for sampling or other covariates), approaches that censor missing records result in unbiased estimates of availability probability. However, censoring such records can result in bias when data are not missing-completely-at-random. We present a novel Bayesian temporal availability model that can be used to explicitly account for the process by which missing data arise. Our approach couples an underlying model for the partially observed availability process together with an observation model that allows state-dependent probabilities of missingness. This approach provides relatively unbiased estimates of availability probability even in the face of violations of the missing-at-random assumption. A new R package, TempOcc, is introduced to automate estimation. We demonstrate the utility of our approach by analysing both simulated data and hourly satellite telemetry records for 157 ice-associated seals in the Bering Sea, for which 27% of records were missing. In this case, we were interested in generating unbiased estimates of haul-out probabilities. Such probabilities are necessary when estimating abundance from aerial survey counts and assessing possible changes in seal phenology. Our analysis indicates that the missing-at-random assumption is indeed violated in telemetry studies of phocid seals in the Bering Sea. However, estimates of availability probability do not depend critically on this assumption. We recommend that ecologists routinely consider the implications of violating the missing-at-random assumption when estimating availability probabilities. Where possible, the modelling framework articulated in this study can be used to diagnose and correct for violations of the missing-at-random assumption.