NERC, University of St Andrews. Statistics, University of St Andrews. School of Mathematics and Statistics, University of St Andrews. Marine Alliance for Science & Technology Scotland, University of St Andrews. Centre for Research into Ecological & Environmental Modelling, University of St Andrews. Sea Mammal Research Unit, University of St Andrews. Scottish Oceans Institute, University of St Andrews. School of Biology, University of St Andrews. St Andrews Sustainability Institute
Funding: part-funded by the UK Natural Environment Research Council to SMRU (Grant no. SMRU1001). 1. Grey seals (Halichoerus grypus) were the first mammals to be protected by an Act of Parliament in the UK and are currently protected under UK, Scottish, and EU conservation legislation. Reporting requirements under each of these statutes requires accurate and timely population estimates. Monitoring is principally conducted by aerial surveys of the breeding colonies; these are used to produce estimates of annual pup production. Translating these data to estimates of adult population size requires information about demographic parameters such as fecundity and sex ratio. 2. An age‐structured population dynamics model is presented, which includes density dependence in pup survival, with separate carrying capacities in each of the four breeding regions considered (North Sea, Inner Hebrides, Outer Hebrides, and Orkney). This model is embedded within a Bayesian state–space modelling framework, allowing the population model to be linked to available data and the use of informative prior distributions on demographic parameters. A computer‐intensive fitting algorithm is presented based on particle filtering methods. 3. The model is fitted to region‐level pup production estimates from 1984 to 2010 and an independent estimate of adult population size, derived from aerial surveys of hauled‐out seals in 2008. The fitted model is used to estimate total population size from 1984 to 2010. 4. The population in the North Sea region has increased at a near‐constant rate; growth in the other three regions began to slow in the mid‐1990s and these populations appear to have reached carrying capacity. The total population size of seals aged 1 year or older in 2010 was estimated to be 116 100 (95% CI 98 400–138 600), an increase of