ABSTRACT
In recent years there has been an explosion in the application of Bayesian methods within the field of statistical ecology. This is evidenced by the huge increase in the number of publications that use (and develop) Bayesianmethods for analyzing ecological data in both statistical and ecological journals. In addition, in recent years there have been a number of books published that focus solely on the use of Bayesianmethods within statistical ecology (King et al., 2009; Link and Barker, 2009; McCarthy, 2007; Royle and Dorazio, 2008). One reason why the Bayesian approach has enjoyed a significant increase in its application to ecology is the particularly complex data that are collected on a typical population under study. This can make standard frequentist analyses difficult to implement, often resulting in simplifying assumptions being made. For example, typical issues that can arise relate to complex distributional assumptions for the observed data; intractable likelihood expressions; and large numbers of biologically plausible models. Within a Bayesian framework it is possible to make use of standardMarkov chainMonte Carlo (MCMC) tools, such as data augmentation techniques, so that these simplifications do not need to be made. The analysis of ecological data is often motivated by the aim of understanding the
given system and/or of conservation management. This is of particular interest in recent years with the potential impact of climate change. Identifying relationships between demographic parameters (such as survival probabilities, productivity rates, and migrational behavior) and environmental conditions may provide significant insight into the potential impact of changing climate on agiven system. Inparticular, thedifferent biological processes are often separated into individual components (Buckland et al., 2004), allowing a direct interpretation of the processes and explicit relationships with different factors to be expressed. An area of particular recent interest in statistical ecology relates to the use of hidden Markov models (or state-space models) to separate the different underlying processes. For example, Newman et al. (2006) describe how these models can be applied to data relating to animal populations within a Bayesian framework. Royle (2008) uses a state-space formulation to separate the life history of the individuals (i.e. survival process) with the observation of the individuals (recapture process) in the presence of individual heterogeneity. The appeal of this type of approach is its conceptual simplicity, along with the readily available computational tools for fitting these models. The typical linear and normal assumptions can also be relaxed within this framework, permitting more realistic population models to be fitted. These methods have been applied to a number of areas, including fisheries models (Millar andMeyer, 2000), species richness (Dorazio et al., 2006),
occupancy models (Royle and Kéry, 2007). It is anticipated that the use of these methods will continue to increase within these, and additional, areas as a result of the more complex statistical analyses that can be performed and an increase in the number of relatively easy-to-use programs particularly using WinBUGS (or OpenBUGS). For example, Brooks et al. (2000, 2002, 2004), Gimenez et al. (2009), King et al. (2009), O’Hara et al. (2009), Royle (2008), and Royle et al. (2007) all provide WinBUGS code for different ecological examples. Within this chapter we focus on two forms of common ecological data: ring-recovery data and count data. We consider a number of issues related that typically arise when analysing such data, including mixed effects models, model selection, efficient MCMC algorithms, and integrated data analyses, extending themodels previously fitted to the data considered by Besbeas et al. (2002), Brooks et al. (2004), and King et al. (2008b). The individual models described canbefitted inWinBUGS; however, the lengthof the computer simulationsmakes the analysis for the count data prohibitive in this case.
