Effects of taxon abundance distributions on expected numbers of sampled taxa

Question: Holding both the true number of taxa and their evenness constant, what is the effect of the shape of the abundance distribution on the number of sampled taxa? Method: We examine the effects of three types of abundance distribution (geometric, log-normal and Zipf) on the expected number of sampled taxa using Hurlbert's equation (1971, equation 14). First, we examine the differences in the number of sampled taxa for the three distributions given the same true number of taxa and true evenness. Second, we determine the sample sizes needed to find more taxa from a taxon-rich, low-evenness collection than found in a taxon-poor, high-evenness collection with the same model distribution. Conclusions: Independently of the true number of taxa and evenness, the shape of the abundance distribution affects the number of taxa expected in a sample. Given moderate to large sample sizes, a Zipf distribution will yield the most taxa, whereas a geometric distribution will yield the fewest. When comparing collections with the same model distributions, it takes the smallest sample sizes to recognize that a taxon-rich, low-evenness Zipf distribution has more taxa than does a taxon-poor, high-evenness Zipf distribution. It requires the largest sample sizes to do this when both are geometric distributions. A necessary implication of these results is that no simple evenness metric can predict the same number of sampled taxa given the same true number of taxa, true evenness and sample size but different model distributions.