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 computerintensive 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 <1% on the previous year. 5. The modelling and fitting methods are widely applicable to other wildlife populations where diverse sources of information are available and inference is required for the underlying population dynamics.

1. Estimates of population size and trends are essential for effective conservation and management of wildlife populations. For harbour seals (Phoca vitulina), these data are required to fulfil statutory reporting obligations under national and international regulations.2. Aerial survey counts of harbour seals hauled out during their annual moult were used to estimate population sizes and trends at UK, regional (seal management unit, SMU) and local (Special Area of Conservation, SAC) scales.3. Results indicate that the current UK harbour seal population is similar to estimates from the late 1990s, but there were significant declines in some subpopulations and increases in others. 4. Fitted trends suggest that the UK harbour seal population can be divided into three geographically coherent groups: South-east populations (South-East and North-East England SMUs) have shown continuous increases punctuated by phocine distemper virus epidemics in 1988 and 2002; north-east populations (East Scotland, Moray Firth, North Coast and Orkney, and Shetland SMUs) have declined since the late 1990s; north-west populations (West Scotland, Western Isles, and South-West Scotland SMUs) have remained stable or increased. Similar geographical population substructure is evident in recent population genetics results. 5. Trends within SACs generally match SMU trends since 2002. Of the nine SACs designated for harbour seals, four declined (in East Scotland, Moray Firth, and North Coast and Orkney SMUs), four remained stable (in Shetland and West Scotland SMUs), and one increased (in South-East England SMU).6. Large changes in relative abundance have resulted from differences in regional trends. For example, in 1996-1997 the West Scotland and North Coast and Orkney SMUs each held~27% of the Great Britain population but now hold 50% and~4% respectively; in 1980, the South-East England SMU population was~50% that of the Wadden Sea population, but by 2016 it was equivalent to <20% of the Wadden Sea count.

Summary1. The annual cycle of many animals is characterized by the need to satisfy different life history priorities, often requiring seasonal movements. For such species, investigating carryover effects (such as the year-long drivers of breeding success) and managing protected areas effectively, relies on quantifying these movements. Here, we model the seasonal movements of the UK population of grey seals Halichoerus grypus and show how insights from the model can improve its management. 2. We fit a hidden process model to two types of information -regional population redistribution and individual movements -to estimate the seasonal transition probabilities of breeding female grey seals among four regions around the UK. 3. We found that between 21% and 58% of females used different regions for breeding and foraging. 4. For our study period, we detected an increase in the breeding performance of animals that foraged in the Hebrides and South-East Coast. 5. Grey seal Special Areas of Conservation (SACs) were designed to encompass a significant proportion of the UK breeding population:~40% of the breeding females in our study area. Of the females breeding on SACs, only 15% breed in Northern Scotland, but up to 50% forage there. Our results indicate that, by only considering the breeding distribution of females that breed in SACs, the impact of anthropogenic activities on nearby SACs may be overestimated, whereas impacts on remote SACs may be underestimated. 6. Synthesis and applications. By quantifying the link between the foraging and breeding distributions of grey seals, management of breeding populations can be focused on the foraging regions where the resources necessary for reproduction are acquired. The construction of marine developments is dependent on demonstrating that they will not have an adverse effect on the integrity of Special Areas of Conservation (SACs), and we have shown that this requires consideration of the seasonal transition probabilities estimated in this study. Our specific results provide support for management strategies that jointly consider SACs and Marine Protected Areas (MPAs). More generally, we prescribe combinations of data on population size, breeding performance and individual movement that can enable our framework to be applied to seasonally migrating species.

1. Estimates of both absolute abundance and trends in abundance are among the most basic pieces of information required for planning the conservation and management of wildlife populations. They are important for understanding both the current situation of species and potential risks to them.2. This study presents estimates of the size of the harbour seal (Phoca vitulina) population associated with the Orkney Islands, a part of northern Scotland that used to contain one of the largest concentrations of this species in Europe.3. The numbers of animals counted during aerial surveys of this area have decreased substantially over the period 2001-2010. ARGOS transmitters attached to flipper tags were used to rescale the counts into estimates of abundance and to confirm the rate of decline of this population.4. Females hauled out for more of the survey window (0.84; bootstrap 95% CI: 0.63-0.99) than males (0.61; bootstrap 95% CI: 0.34-0.86). The animals hauled out less during weekends (0.57; bootstrap 95% CI: 0.40-0.74) than during the week (0.76; bootstrap 95% CI: 0.58-0.91).5. The sex-ratios of this population is unknown. Assuming it was close to 1:1, then there were around 3586 (bootstrap 95% CI: 2970-4542) harbour seals in Orkney in 2010. A female-skewed sex-ratio would reduce the population estimate, and a changing sex-ratio might mean the counts understate the real decline.6. The mean annual rate of decline in the Orkney population of harbour seals, over the period 2001-2010, is estimated at 13% (95% CI: 10.8-14.8). Similar data for Arisaig, on the west coast of Scotland, shows an increase of around 2% (95% CI: 1.5-2.4) and, assuming an equal sex-ratio, 923 animals (95% CI: 765-1169) in 2007.

1. The population size of many species, particularly those in the aquatic environment, cannot be censused directly. Counts, during the breeding season, of one component of the population (e.g. breeding females) are often used as an index to allow investigation of trends. In species, such as grey seals (Halichoerus grypus), for which births are not tightly synchronous, single counts of pups represent an unknown proportion of the total number of pups born (pup production), and thus of breeding females (i.e. each pup born represents a breeding female).2. Grey seals pup at large colonies around the coast of the UK. Information on their populations is required under national and international legislation.3. In the UK, pup production has been monitored at some colonies since 1956. Currently, large colonies (~90% of UK pup production) are monitored either using ground (~10%; annually) or aerial surveys (~80%; annually until 2010, and thereafter biennially).4. Here, the model used to estimate pup production at aerially surveyed colonies from 1987 to 2010 is described; structured pup counts from multiple surveys are combined with knowledge of life-history parameters to model birth curves.5. The resulting trends in pup production up to 2010 (aerially surveyed colonies) and 2016 (ground surveyed colonies) are examined.6. In 2010, over 45,000 pups were estimated to be born in the UK. Pup production appeared to have reached an asymptote in the Inner Hebrides, Outer Hebrides and Orkney, whereas it is still increasing exponentially in the North Sea. Although density-dependent processes acting at sea are likely to be responsible for these regional trends, we suggest that the substantial variation in trends within regions are likely caused by processes acting at the colony level. Some long-established colonies, including Special Areas of Conservation, are exhibiting decreasing trends. 7. Special Areas of Conservation often serve as de facto monitoring sites and are the focus of management efforts. The observed temporal and spatial variability in patterns of colony growth rates highlight the potential risks of using such sites to develop wider management policies.