Modeling abundance using hierarchical distance sampling

In this chapter, we provide an introduction to classical distance sampling ideas for point and line transect data, and for continuous and binned distance data. We introduce the conditional and the full likelihood, and we discuss Bayesian analysis of these models in BUGS using the idea of data augmentation, which we discussed in Chapter 7. We then extend the basic ideas to the problem of hierarchical distance sampling (HDS), where we have multiple point or transect sample units in space (or possibly in time). The benefit of HDS in practice is that it allows us to directly model spatial variation in population size among these sample units. This is a preeminent concern of most field studies that use distance sampling methods, but it is not a problem that has received much attention in the literature. We show how to analyze HDS models in both the unmarked package and in the BUGS language for point and line transects, and for continuous and binned distance data. We provide a case study of HDS applied to a survey of the island scrub-jay on Santa Cruz Island, California.