A state-space model for estimating pinniped pup production from serial counts at breeding colonies

Estimating pinniped abundance is difficult because they are highly mobile and widely distributed, and spend the majority of time at sea. Abundance estimates are typically based on counts on land or ice. In species that breed colonially, such as the grey seal (Halichoerus grypus), monitoring is largely focused on the breeding season, and pup production (number of pups born in a season) is used as an index of the total population size. At any one colony, grey seals give birth over several months, so not all pups are present at the colony at any one time. Pups are born white and moult into an adult-like coat before leaving the colony. At most key UK breeding colonies, over the course of a breeding season, a series of digital photographic aerial surveys are conducted and analysts count the numbers of white and moulted seal pups photographed. We developed a flexible state-space model to estimate pup production using these count data. The model is comprised of a deterministic process model for birth, moult, and leaving, and a stochastic observation model that allows for imperfect detection and classification. We implemented this model in Template Model Builder (TMB) and fit it using maximum likelihood. We show that our model performs well on simulated and real datasets. This model could be applied to other taxa for which successive counts of different life stages are collected, and used to investigate key ecological questions including, for example, the impact of climate change on phenology.