Sample Size Calculation for Finding Unseen Species

Estimation of the number of species extant in a geographic region has been discussed in the statistical literature for more than sixty years. The focus of this work is on the use of pilot data to design future studies in this context. A Dirichlet-multinomial probability model for species frequency data is used to obtain a posterior distribution on the number of species and to learn about the distribution of species frequencies. A geometric distribution is proposed as the prior distribution for the number of species. Simulations demonstrate that this prior distribution can handle a wide range of species frequency distributions including the problematic case with many rare species and a few exceptionally abundant species. Monte Carlo methods are used along with the Dirichlet-multinomial model to perform sample size calculations from pilot data, e.g., to determine the number of additional samples required to collect a certain proportion of all the species with a pre-specified coverage probability. Simulations and real data applications are discussed