Incorporating Temporal Correlation in Seal Abundance Data with MCMC
Common or harbour seals (Phoca vitulina L.) are semi-aquatic mammals that spend time onshore at terrestrial sites where they haul-out to rest, breed, moult, engage in social activity, and escape predation (Fig.23.1).
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Incorporating Temporal Correlation in Seal Abundance Data with MCMC A.A. Saveliev, M. Cronin, A.F. Zuur, E.N. Ieno, N.J. Walker, and G.M. Smith
23.1 Introduction Common or harbour seals (Phoca vitulina L.) are semi-aquatic mammals that spend time onshore at terrestrial sites where they haul-out to rest, breed, moult, engage in social activity, and escape predation (Fig. 23.1). Over one-third of harbour seals in Ireland use haul-out sites in the southwest region (Cronin et al., 2007). Most of the haul-out sites in this region are located within Bantry Bay and the Kenmare River. Special Areas of Conservation (SACs) have been designated at each of these sites in accordance with the EU Habitats Directive. Assessing the year round changes in harbour seal abundance within SACs contributes to the monitoring obligations under the Habitats Directive and to the understanding of national population trends. Between April 2003 and November 2005, regular standardised haul-out count surveys of both bays were carried out by boat. Counts of seals at each haul-out site were carried out independently and simultaneously by two observers, initially from a distance of approximately 200 m from the haul-out site and at progressively closer ranges whilst minimising disturbance to the seals. Surveys were carried out at least monthly all year-round and weekly during the summer and autumn, weather permitting. Surveys were scheduled to occur within two hours either side of low tide and during daylight hours. In the original analysis of these data, Cronin (2007) used additive mixed modelling techniques. Residual auto-correlation structures and residual heterogeneity structures were included, albeit in the context of a Gaussian distribution. In this chapter, we do a similar statistical analysis, but replace the Gaussian distribution with a Poisson distribution because the response variable is a count (the number of seals). However, current software for generalised linear mixed modelling do not easily allow incorporating temporal correlation, and therefore, we use Markov
A.A. Saveliev (B) Kazan State University, Kazan, 420008, Russia
A.F. Zuur et al., Mixed Effects Models and Extensions in Ecology with R, Statistics for Biology and Health, DOI 10.1007/978-0-387-87458-6 23, C Springer Science+Business Media, LLC 2009
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Fig. 23.1 Mother and pup hauling out. The photo was taken by Michelle Cronin
Chain Monte Carlo (MCMC) techniques to fit a model that contains a temporal correlation structure. MCMC is based on Bayesian statistics: Something not every reader will be familiar with. Providing an introduction to Bayesian statistics is challenging and including one in a 20-page case study is near impossible. We could have simply dropped this chapter, but considered it important to include a final chapter showing there is life beyond the mixed modelling techniques discussed in earlier chapters. So, although we cannot give a detailed introduction to Bayesian statistics or MCMC, we can discuss salient points and recomme
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