Variation in rank abundance replicate samples and impact of clustering

Calculating a single-sample rank abundance curve by using the negative-binomial distribution provides a way to investigate the variability within rank abundance replicate samples and yields a measure of the degree of heterogeneity of the sampled community. The calculation of the single-sample rank abundance curve is used in combination with the negative-binomial rank abundance curve-fit model to analyse the principal effect of clustering on the species-individual (S-N) curve and the species-area curve. With the usual plotting of S against log N or log area, assuming that N is proportional to area, S-N curves and species-area curves are the same curves with only a shifted horizontal axis. Clustering results in a lower recorded number of species in a sample and stretches the S-N curve and species-area curve over the horizontal axis to the right. In contrast to what is suggested in the literature, we surmise that the effect of clustering on both curves will gradually fade away with increasing sample size. Since the slopes of the curves are not constant, they cannot be used as species diversity indices or site discriminant. S-N curves and species-area curves cannot be extrapolated.