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Our goal is to estimate the true number of classes in a population, called the species richness. We consider the case where multiple frequency count tables have been collected from a homogeneous population, and investigate a penalized maximum likelihood estimator under a negative binomial model. Because high probabilities of unobserved classes increase the variance of species richness estimates, our method penalizes the probability of a class being unobserved. Tuning the penalization parameter is challenging because the true species ri