An Approximate Bayesian Method Applied to Estimating the Trajectories of Four British Grey Seal (Halichoerus grypus) Populations from Pup Counts

For British grey seals, as with many pinniped species, population monitoring is implemented by aerial surveys of pups at breeding colonies. Scaling pup counts up to population estimates requires assumptions about population structure; this is straightforward when populations are growing exponentially but not when growth slows, since it is unclear whether density dependence affects pup survival or fecundity. We present an approximate Bayesian method for fitting pup trajectories, estimating adult population size and investigating alternative biological models. The method is equivalent to fitting a density-dependent Leslie matrix model, within a Bayesian framework, but with the forms of the density-dependent effects as outputs rather than assumptions. It requires fewer assumptions than the state space models currently used and produces similar estimates. We discuss the potential and limitations of the method and suggest that this approach provides a useful tool for at least the preliminary analysis of similar datasets. 1. Introduction Complete censuses are not practical for most animal populations. Instead, abundances usually have to be estimated by scaling up from partial counts. This process is complicated when the components of a population differ in their detectability. Pinnipeds such as grey seals (Halichoerus grypus), where young pups remain ashore and the rest of the population spends the majority of its time at sea, are an extreme example of this problem. In these cases, population estimation can effectively come down to scaling up from observations of pups. This process needs to be done efficiently, and also evaluate the population estimates’ precision. This paper presents a way of simplifying the computations and reducing the assumptions underlying such models. It produces similar results to the, more complicated, methods currently used to produce the estimates on which decisions about the conservation and management of British grey seal populations are based. These simplifications can release resources and data for the examination of environmental and other effects on the populations. In this particular study, they have removed the need for maximum fecundity and survival to be considered equal everywhere. Grey seals are colonial breeders. Females mature at around six years of age and give birth to a single pup in the autumn. The pups are born on land and remain ashore for several weeks. This behaviour, along with their neonatal white coats, makes them relatively easy to observe. Counting the other components of these populations is much less