Impact of sampling with replacement in occupancy studies with spatial replication

Summary 1. The proportion of sites occupied by a species is a state variable commonly used in ecology. Replicate surveys at sampled sites can be used to address the problem of imperfect detection to obtain an asymptotically unbiased estimator of species occupancy. Replication can be achieved in various ways, including visiting a series of spatial subunits within each surveyed site. Depending on how these spatial subunits are sampled, bias can be induced in the estimator of site occupancy. 2. This paper explores and discusses the consequences of sampling with or without replacement when using spatial replication in occupancy studies and the species is absent from some of the replicates within occupied sites. Simulations are used to illustrate the findings, and results are compared with previously published recommendations. 3. The study shows that sampling without replacement does not induce bias in the estimator of site occupancy when each spatial subunit has a constant probability of occupancy, regardless of the occupancy status of other subunits within the same sampling site. 4. The study further demonstrates that sampling with replacement may in this case induce bias in the site occupancy estimator. It is thus argued that choosing to sample with or without replacement should be based on considerations of the system in question. 5. Synthesis and applications: In some occupancy studies, it may be convenient to obtain the replication required to account for imperfect detection by surveying various spatial subunits within each sampling site. Sampling with replacement has previously been recommended for this scenario. However, this sampling strategy can induce bias in the estimator of occupancy under realistic ecological conditions. The discussion provided here is of special interest for those involved in the design of occupancy studies.