Incomplete detection in enumeration surveys: Whither distance sampling?

This paper considers the problem of undercount or incomplete detection in enumeration surveys that are intended to estimate population counts or population abundance. The problem is widespread in ecology but also occurs in other surveys: the census undercount is a well-known example of the problem. After framing the problem in a general context, the paper focuses on line transect sampling and the distance sampling method which has been widely applied in surveys of ecological populations. It describes distance sampling data and presents a graphical derivation of the distance sampling estimator. The graphical analysis leads to a new expression for the distance sampling estimator which gives useful insights into the nature of the estimator. The paper discusses the uniformity assumption on which distance sampling depends and describes the properties of the distance sampling estimator when uniformity does not hold. It then explores the relationship between this and other evaluations of distance sampling and mentions briefly some statistical ideas for treating the general incomplete detection problem. The paper concludes with some reflections on general insights arising from the research.