Background

Modeling and inference in metapopulation models has received considerable attention over the last 10 or 15 years. Much of the work has been on devising models of extinction and colonization, assuming the occupancy state was perfectly observable. The Markovian state model (absent spatial dynamics) was developed by Clark and Rosenzweig (1994). Hanski (1994), Day and Possingham (1995) and others have addressed spatial dynamics. Formalization of inference procedures has been addressed by Moilanen (1999); and O'Hara et al. (2002) and Ter Braak and Etienne (2003) provide a Bayesian treatment of the inference problem for occupancy models with temporal dynamics. These papers focus on the state process model and inference under that model supposing that the state-variable could be observed perfectly.

Several papers have considered the situation in which the state variable is subject to imperfect observation. Erwin et al. (1998) recognized the connection between these models and models for populations of individuals experiencing mortality and recruitment. The equivalence arises by equating a site or patch (or colony) with an individual. Thus, when detection is perfect, open population capture-recapture models can be used to obtain estimates of survival and recruitment. This work led to Barbraud et al. (2003), who continued to develop the analogy with capture-recapture, employing a 'multi-state' model under the 'robust design' (Pollock, 1982) to estimate colony survival and colonization in the presence of imperfect detection. The fundamental problem addressed by Barbraud et al. (2003) was, quoting directly from them (Barbraud et al., 2003, p. 116):

However, in studies of colony dynamics, interior 0's in a colony site detection history can indicate either that breeding individuals were present but not detected, or that breeding individuals were not present (locally extinct), yet recolonized at a later time. In this respect, the modeling of colony site detection history data is similar to the modeling of species detection history data in community studies (Nichols et al. 1998), and is similar also to the modeling of capture-recapture data in the presence of temporary emigration. The robust design (Pollock 1982) provides the information needed to estimate quantities of interest in the presence of temporary emigration (Kendall et al. 1997), and also provides a basis for estimating colony dynamics parameters from detection history data.

Previously, Moilanen (2002) also considered non-detection or observation error in the form of 'false zeros' as a result of non-detection. MacKenzie et al. (2003) gave a comprehensive treatment of the problem with formal inference based on conventional likelihood methods. Royle and Kery (2007) provided a fully-hierarchical formulation of the model that integrates the Markovian process model with the formal observation model allowing for non-detection.

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