Optimal sampling design and the accuracy of occupancy models

We present general theoretical limits on the possible accuracy (mean squared error or MSE) of occupancy estimates for a large range of occupancy study designs with imperfect detection and confirm our theoretical results via a simulation study. In particular, we show that for a given total survey effort, the best possible MSE is driven by two design-related factors: the fraction of visits made at occupied sites (regardless of whether that occupancy status is known or not) and the number of visits made to each site with unknown occupancy status (ie, sites with no detections). The limits reveal that there is very little room for improvement over optimal implementations of the three existing occupancy design paradigms: standard design (visit S sites K times each), removal design (visit S sites up to K times each, halting visits to each site following a positive detection), and conditional design (visit S sites once, then resurvey sites with a positive detection an additional K-1 times). For the small portion of the occupancy-detection parameter space where improvement can be achieved, we introduce a new hybrid survey design with accuracy closer to the theoretical limit, which we illustrate by reanalyzing an existing coyote (Canis latrans) camera trap dataset. Our results provide new clarity and intuition regarding key factors of occupancy study design.