Designing studies to detect differences in species occupancy: power analysis under imperfect detection

1. Studies aimed at estimating species site occupancy while accounting for imperfect detection are common in ecology and conservation. Often there is interest in assessing whether occupancy differs between two samples, for example, two points in time, areas or habitats. To ensure that meaningful results are obtained in such studies, attention has to be paid to their design, and power analysis is a useful means to accomplish this. 2. We provide tools for conducting power analysis in studies aimed at detecting occupancy differences under imperfect detection and explore associated design trade-offs. We derive a formula in closed form that conveniently allows determining the sample size required to detect a difference in occupancy with a given power. Because this formula is based on asymptotic approximations, we use simulations to assess its performance, at the same time comparing that of different significance tests. 3. We show that the closed-formula performs well in a wide range of scenarios, providing a useful lower sample size bound. For the simulated scenarios, a Wald test on the probability scale was the most powerful test among those evaluated. 4. We found that choosing the number of repeat visits based on existing recommendations for single-season studies will often be a good approach in terms of minimizing the effort required to achieve a given power. 5. We demonstrate that our results and discussion are applicable regardless of whether independence or Markovian dependence is assumed in the occupancy status of sites between seasons, and illustrate their utility when designing to detect a trend in multiple-season studies. 6. Assessing differences in species occupancy is relevant in many ecological and conservation applications. For the outcome of these monitoring efforts to be meaningful and so to avoid wasting the often limited resources, survey design has to be carefully addressed to ensure that the relevant differences can be indeed detected and that this is achieved in the most efficient way. Here, we provide guidance and tools of immediate practical use for the design of such studies, including code to conduct power analysis.