Sequential adaptive sampling designs to estimate abundance in rare populations

A sampling design is a procedure by which a sample is selected and estimator is derived in order to estimate a characteristic of the population. The basic problem of sampling is to estimate some characteristic of a population by observing only part of the population. This study is concerned with the problem of designing sampling schemes for rare populations that exhibit patterns of clustering or patchiness related to habitat availability or intrinsic factors. Recent developments, such as adaptive cluster sampling (Thompson, 1990) have been shown to be a useful application for rare, clustered populations. However, in his design the use of it requires the decision of initial sample size. And the common estimators are not optimal in the sense of having the smallest variance among a set of possible estimators. Further, the design has very low efficiency relative to comparable conventional designs when the population is neither rare nor highly clustered (Christman, 1997). There is a positive probability that a sample will result in an estimate of zero abundance. Brown (1994) modified adaptive cluster sampling in which selection of units for the initial sample continues until a fixed final sample size is reached. This controls the sample size but at the cost of introducing bias into estimation of the population total. This study explores the methodologies and applications of sequential adaptive sampling. Unbiased estimators of the population total are attained under the positive aspects of the adaptive sampling and sequential selection of the initial sampling units by controlling the number of clusters sampled in the population. Several sampling designs are described. They incorporate an adaptive component. For each design, estimators and measures of their accuracy will be obtained. Comparisons of the mean squared errors are conducted to find the optimal estimator. These comparisons are analytic where the equations allow and through simulations otherwise.