Optimal Allocation of Sampling Effort in Depletion Surveys

We consider the problem of designing a depletion or removal survey as part of estimating animal abundance for populations with imperfect capture or detection rates. In a depletion survey, animals are captured from a given area, counted, and withheld from the population. This process is then repeated some number of times at the same location and the decreasing catches of the local population inform jointly local abundance and the capture or detection rate, which we call catchability. The aim of such a survey may be to learn about the catchability process, and this information may then be applied to a broader survey of the population so as to accurately estimate total abundance. In this manuscript we consider the problem of how to optimally allocate sampling effort at the depletion sites. Allocating sampling effort involves determining how many times to repeat the depletion process at a given site versus how many different sites to include in the sampling. By maximizing the Fisher information of the parameter describing catchability as a function of the survey design, we attempt to estimate the optimal number of depletions per site, which depends on the catchability value itself. We also discuss other aspects of depletion sampling apparent from the derivation of Fisher information, including the difficulties of sampling with low catchability values (e.g. below 0.15), and we consider our results with respect to the annual Chesapeake Bay blue crab abundance survey conducted by the Maryland Department of Natural Resources.