Ignoring species availability biases occupancy estimates in single-scale occupancy models

Most applications of single-scale occupancy models do not differentiate between availability and detectability, even though species availability is rarely equal to one. Species availability can be estimated using multi-scale occupancy models; however, for the practical application of multi-scale occupancy models, it can be unclear what a robust sampling design looks like and what the statistical properties of the multi-scale and single-scale occupancy models are when availability is less than one. Using simulations, we explore the following common questions asked by ecologists during the design phase of a field study: (Q1) what is a robust sampling design for the multi-scale occupancy model when there are a priori expectations of parameter estimates? (Q2) what is a robust sampling design when we have no expectations of parameter estimates? and (Q3) can a single-scale occupancy model with a random effects term adequately absorb the extra heterogeneity produced when availability is less than one and provide reliable estimates of occupancy probability? Our results show that there is a tradeoff between the number of sites and surveys needed to achieve a specified level of acceptable error for occupancy estimates using the multi-scale occupancy model. We also document that when species availability is low (<0.40 on the probability scale), then single-scale occupancy models underestimate occupancy by as much as 0.40 on the probability scale, produce overly precise estimates, and provide poor parameter coverage. This pattern was observed when a random effects term was and was not included in the single-scale occupancy model, suggesting that adding a random-effects term does not adequately absorb the extra heterogeneity produced by the availability process. In contrast, when species availability was high (>0.60), single-scale occupancy models performed similarly to the multi-scale occupancy model. Users can further explore our results and sampling designs across a number of different scenarios using the RShiny app https://gdirenzo.shinyapps.io/multi-scale-occ/. Our results suggest that unaccounted for availability can lead to underestimating species distributions when using single-scale occupancy models, which can have large implications on inference and prediction, especially for those working in the fields of invasion ecology, disease emergence, and species conservation.