Two-stage sequential Bayesian study design for species estimation

A problem of interest for ecology and conservation is that of determining the best al-

location of survey effort in studies aimed at estimating the proportion of sites occupied

by a species. Many species are difficult to detect and often remain undetected during

surveys at sites where they are present. Hence, for the estimator of species occupancy

to be unbiased, detectability needs to be taken into account. In such studies there is a

trade-off between sampling more sites and expending more survey effort within each

site. This design problem has not been addressed to date with an explicit consideration

of the uncertainty in assumed parameter values. In this article we apply sequential and

Bayesian design techniques and show how a simple two-stage design can significantly

improve the efficiency of the study. We further investigate the optimal allocation of

survey effort between the two study stages, given a prior distribution for the parame-

ter values. We address this problem using asymptotic approximations and then explore

how the results change when the sample size is small, considering second-order approx-

imations and highlighting the value of simulations as a tool for study design. Given the

efficiency gain, we recommend following the sequential design approach for species

occupancy estimation. This article has supplementary material online.