A critique of the use of jackknife and related non-parametric techniques to estimate species richness

Species richness in an assemblage is frequently used as a measure of biological diversity. However, observed species richness is strongly dependent on sample size. If more samples are collected, then more species are observed. Non-parametric species richness estimators, such as the jackknife 1 and 2 and the Chao 1 and 2, are indicated in the literature as potential solutions to the problem of dependence of observed species richness on sampling effort. These methods are intended to estimate the total species richness in an area or assemblage with small sampling effort. Non-parametric estimators are based on the number of species observed, and the number of rare species in a sample, i.e., that occurred in one and/or two sampling units, or with one and/or two individuals. High estimates are produced when samples contain large proportions of rare species. Using a range of real datasets, I show that estimates produced by non-parametric methods are generally dependent on observed species richness. An implicit assumption of these non-parametric techniques is that the rare species curve should present high values at small sample sizes and decreasing values as sampling effort is increased. This assumption was observed in only one out of eight datasets presented. Instead, the rare species curve generally flattens off around a constant value as sampling effort increases. I conclude that non-parametric estimators are not reliable to estimate species richness in an assemblage when the rare species curve does not show a decreasing trend. Comments are made on the possibilities of using non-parametric estimators in the comparison of species assemblages