Predicting the Number of New Species in Further Taxonomic Sampling

Abstract

In evaluating the effectiveness of further sampling in species taxonomic surveys, a practical and important problem is predicting the number of new species that would be observed in a second survey, based on data from an initial survey. This problem can also be approached by estimating the corresponding expected number of new species. A. R. Solow and S. Polasky recently proposed a predictor (or estimator), with the form of a sum of many terms, that was derived under the assumption that all unobserved species in the initial sample have equal relative abundances. We show in this paper that the summation can be expressed as only one term. We provide a direct justification for the simplified estimator and connect it to an extrapolation formula based on a special type of species accumulation curve. Using the proposed justification, we show that, for large sample sizes, the estimator is also valid under an alternative condition, i.e., species that are represented the same number of times in the initial sample have equal relative abundances in the community. This condition is statistically justified from a Bayesian approach, although the estimator exhibits moderate negative bias for predicting larger samples in highly heterogeneous communities. In such situations, we recommend the use of a modified estimator that incorporates a measure of heterogeneity among species abundances. An example using field data from the extant rare vascular plant species patterns in the southern Appalachians is presented to compare the various methods. Corresponding Editor: A. R. Solow

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