## Introduction

Estimating and interpreting patterns of occupancy lie at the heart of many questions in ecology and problems in conservation. For example, metapopulation theory often explores variation in patch occupancy in fragmented landscapes (Hanski 1994). Species distribution models, which are widely used in guiding conservation and management decisions, frequently rely on observed patterns of detection and non-detection (Guisan *et al.* 2006). Additionally, occupancy can provide valuable information on population trends when more detailed demographic or abundance estimates are not practical (Bailey, Simons & Pollock 2004).

Traditional approaches to occurrence estimation, such as logistic regression or Incidence Function Models (Hanski 1994), assume perfect detection of species. Recently, these approaches have been criticized because even modest amounts of false absences (i.e. modelling a species as absent when it is in fact present) can bias parameter estimates in metapopulation models and predicted habitat relationships (Moilanen 2002; Tyre *et al.* 2003; Gu & Swihart 2004; Martin *et al.* 2005).

Because of the bias introduced by non-detection errors, several recent investigations have focused on how to model occupancy, given imperfect detection (Geissler & Fuller 1987; Azuma, Baldwin & Noon 1990; MacKenzie *et al.* 2002; Tyre *et al.* 2003; Stauffer, Ralph & Miller 2004). Of these new techniques, MacKenzie & Royle (2005) suggest that the approach of MacKenzie *et al.* (2002) is the most flexible and that other approaches are special cases of their general model. This approach has provided significant improvements over traditional approaches, which is reflected in a recent surge in occupancy studies (Marsh & Trenham 2008).

To estimate detection probability, MacKenzie *et al.*’s (2002, 2006) occupancy-modelling approach requires multiple surveys at each site. Detection probability is then estimated from the pattern of detections and non-detections that arise from these multiple surveys. A necessary assumption for estimating and accounting for detectability is that sites are closed to changes in occupancy between surveys, which has been described as the ‘closure assumption’. The term ‘closure’ reflects the assumption that if a site is occupied during at least one survey, it is assumed to have been occupied during all surveys, and any non-detection during a survey is considered a ‘false zero’ or a ‘false negative’.

A commonly used sampling approach for occupancy studies is to visit a site multiple times and conduct a single survey during each site visit (e.g. Bailey, Simons & Pollock 2004; Ball, Doherty & McDonald 2005). We will refer to this approach as a *standard occupancy* sampling protocol. Site visits are frequently separated by periods of weeks or months, and sites are assumed to be closed during these time periods. Violations of this assumption may lead to biased estimates of occupancy. However, little work has been carried out to assess how violations of the closure assumption may affect occupancy estimates, and MacKenzie *et al.* (2006) have only inferred the strength and direction of these biases from Kendall’s (1999) evaluation of capture–recapture models. Although MacKenzie *et al.* (2006) provide useful suggestions for reducing the problem of closure, no formal framework has been developed to explicitly test the closure assumption.

Here, we address the closure assumption for occupancy estimation by advocating the use of Pollock’s (1982) robust design over short time intervals, wherein an observer conducts multiple surveys during each site visit. We show that this approach permits estimation of transitions in site occupancy (i.e. local colonization and extinction) and formal statistical tests of closure between site visits. Using two data sets on bird distributions, we test the likelihood of closure over time-scales typical of many wildlife occupancy investigations. Finally, using simulations, we assess how sensitive occupancy models are to violations of the closure assumption and evaluate the power of likelihood-ratio tests to identify these violations.