An important problem in ecological research is the design of efficient data collection methods such that the cost of time and money is minimized while the amount of information collected is sufficiently maximized. This is particularly challenging for the study of rare species, which are often of conservation concern and may be vulnerable to decline and extinction. For studies involving populations of rare and clustered individuals, adaptive cluster sampling (ACS) can increase efficiency and reduce variance in comparison to designs such as simple random sampling. The ACS design involves first the collection of an initial set of units from the population according to a probability sampling scheme (e.g., simple random sampling), and then if an initial unit satisfies a given criterion, its neighbors that are directly adjacent are sampled. If one of those neighoring units satisfies the criterion, its neighbors are sampled and so on, until no additional neighboring units satisfy the criterion. A major disadvantage of ACS, however, is that the final sample size is unknown at the initiation of sampling. We propose a restricted ACS design, where the number of sampled units neighboring any primary unit is limited (to 12 in our study but the limit is flexible). To illustrate this design and its properties, we present an example where occupancy of native cacti is the primary variable and criterion for adaptive sampling. Our goal is to estimate the fraction of area occupied by the cacti as well as by two cactus-feeding insects, the native moth Melitara prodenialis, and the invasive moth, Cactoblastis cactorum, at our study sites in northeastern Florida.
Results/Conclusions
When units are selected according to restricted ACS, the Horvitz-Thompson estimator of the mean, which is unbiased for unrestricted adaptive cluster sampling, is biased for the criterion-based variable but has desirable properties for secondary variables such as the estimation of the fraction of area occupied by the cactus-feeding insects. We recommend some bias correction techniques and show that bias is decreased for all variables of interest.