What can occupancy models gain from time-to-detection data?

The time taken to detect a species during site occupancy surveys contains information about the observation process. Accounting for the observation process leads to better inference about site occupancy. We explore the gain in efficiency that can be obtained from time-to-detection (TTD) data and show that this model type has a significant benefit for estimating the parameters related to detection intensity. However, for estimating occupancy probability parameters, the efficiency improvement is generally very minor. To explore whether TTD data could add valuable information when detection intensities vary between sites and surveys, we developed a mixed exponential TTD occupancy model. This new model can simultaneously estimate the detection intensity and aggregation parameters when the number of detectable individuals at the site follows a negative binomial distribution. We found that this model provided a much better description of the occupancy patterns than conventional detection/nondetection methods among 63 bird species data from the Karoo region of South Africa. Ignoring the heterogeneity of detection intensity in the TTD model generally yielded a negative bias in the estimated occupancy probability. Using simulations, we briefly explore study design trade offs between numbers of sites and surveys for different occupancy modeling strategies.