Estimating population size is an essential component of understanding population ecology and plays a key role in conservation and management. Currently, a number of approaches for estimating population size incorporate some form of imperfect detection (e.g., distance sampling, capture-recapture, double sampling, etc.). There are generally considered to be three components of detection probability: probability of presence during a survey, probability of availability given presence, and probability of detection given availability; however, most sampling and analytical methods only deal with one or two of these components. We present a hierarchal model to separate these three components of detection using spatially and temporally replicated distance-sampling surveys augmented with time-to-detection data. Separation of detection components allowed density estimation for multiple population levels, including the densities of individuals available for detection, individuals present in the sampling plot, and the superpopulation of individuals that use the plot. We conducted a simulation study to test the validity of the model and applied the model to a case study of Island Scrub-jays.
Simulation results indicated <4% relative bias of density estimates for the available and present populations when detection, presence, and availability were as low as 0.25, 0.75, 0.75, respectively. Superpopulation density estimates were more variable with relative bias >9% and accurate estimation often requiring detection probability >0.50. In the case study on Island Scrub-jays, the resulting median probabilities of presence, availability, and detection were 0.75, 0.92, and 0.26, respectively. Density estimates for available and present individuals were relatively similar (0.85-0.95 individuals/ha) due to high probability of availability. Superpopulation density was noticeably higher (1.09 individuals/ha), indicating a lack of geographical closure between surveys. Density estimates from the full hierarchical model were similar to reduced models that used only one or two of the sampling protocols, but reduced models only estimated a subset of densities.