A Bayesian state-space model for estimating pup production in an asynchronous breeder: the grey seal (Halichoerus grypus)

For wide-ranging or cryptic species, abundance estimation often relies on counts when individuals aggregate during breeding or migration. When these events are asynchronous, counts represent an unknown proportion of the focal component of the population. Grey seals (Halichoerus grypus), colonial breeders with protracted pupping seasons, typify this challenge: a single survey corresponds to an unknown proportion of total pup production (number of pups born in a season). Pups are born with white pelage before moulting and leaving, allowing a time series of counts of white and moulted pups to be derived from serial aerial photography. Current maximum likelihood approaches have limited flexibility to incorporate model extensions or test alternative parameterizations. We developed a Bayesian state-space model that explicitly incorporates mortality and examines effects of misspecifying moult and leave timing. Via simulation, we demonstrate biases from omitting mortality, misspecifying leave timing, and misparametrizing the observation and process models. Incorporating platform-specific (drone and fixed-wing surveys) observation error from Farne Island colonies surveyed in 2023, we refine detection rates and fit the model to these data. This framework has potential to improve abundance estimates for other asynchronously breeding species and be extended to include temporal and spatial variation in survival and phenology.