Sequential sampling in the search for new shared species

In microbial sciences, as well as other disciplines, it is often valuable to sample communities in a sequential or group sequential manner, in order to determine their structure or their similarity. We develop sequential sampling procedures to accomplish this by first assuming that one observation is drawn with replacement from each population at a time. Suppose that the sampling is terminated after n pairs of observations and k shared species were discovered, and assume that we receive payoff h(k)−cn, where h(k) is non-decreasing and the sampling cost c is non-negative. Similar to Rasmussen and Starr (1979), we show that an optimal stopping rule exists if h(k+1)−h(k) is non-increasing. An analogous result holds for group sequential sampling. This leads to using an estimate of the probability of discovering new shared species as a stopping indicator for comparing two populations with respect to the similarity index. We show by simulation and real examples that this is a feasible approach which can help to reduce the sample size.