Sequential stopping rules for species accumulation

Identifying and counting the total number of biological species observed to date, and plotting versus a measure of the effort used to record them, gives rise to a species accumulation curve. Interest typically is concerned with estimating the total number of species in the area of study, having observed only the accumulation curve, having no information on species frequencies. This article considers the problem of optimally stopping the sampling process. We use a sequential procedure with a fixed maximum horizon for accumulation. A utility function based on the number of new species to be observed and the effort saved from the maximum horizon is adopted, and a workable algorithm based on backward induction is obtained. An example in accumulation of bat species is also presented.