For decades, statisticians have studied the species problem: how to estimate the total number of species, observed plus unobserved, in a population. This problem dates at least as far back as 1943, to a paper by R.A. Fisher. These methods have found many applications in general ecology, but their importance has grown considerably in recent years, driven by the introduction of high-throughput DNA sequencing into microbial ecology. We examine the state of the art in terms of estimating the total number of taxa in a microbial population from a sample of sequences. We focus mainly on estimating the number of species within a single population (α-diversity), but we also briefly consider statistical inference for comparing the numbers of species across populations (β-diversity). We discuss the full range of statistical techniques, parametric and nonparametric as well as frequentist and Bayesian, and specific implications of their use in microbial diversity studies. We conclude with some recommendations for theoretical investigation and computational tool development.


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