Efficiency and robustness in distance sampling

Distance sampling is a technique for estimating the abundance of animals or other objects in a region, allowing for imperfect detection. The impact of uncertainty about the detection parameters on the precision of the estimated abundance is important, both for deciding on the appropriate sample size and determining whether to use distance sampling or an alternative method. This paper derives the asymptotic penalty due to this uncertainty, and tabulates it for a variety of models. The penalty is typically between 2 and 4 but can be much higher, particularly for steeply declining detection rates where distance sampling is typically most strongly recommended. The asymptotic results are confirmed in a simulation study which also examines model-averaging, mis-specified detection function and simple strip expansion. The paper shows that distance sampling needs larger sample sizes than is commonly supposed, and so should not be regarded as the only acceptable approach to abundance estimation.