Additionally, the x-axis can also be the estimated coverage of either abundance or number of samples. In standard rarefaction curves the x-axis is either the abundance (individual-based) or number of samples (sample-based). Analytic estimators for individual-based, sample-based, and coverage-based rarefaction on Hill numbers were derived by Chao et al. In the past, rarefaction curves have been estimated by repeated subsampling, but it is no longer necessary. Sample-based incidence data can be represented as a single matrix, with i=1 to R rows and j=1 to Sobs columns, and entries Wij=1 or Wij=0 to indicate the presence or absence of species j in sampling unit i. Within each of these sampling units, the presence (1) or absence (0) of each species are the required data, even though abundance data may have been collected. For sample-based (incidence) data, the reference sample consists of a set of R standardized sampling units, such as traps, plots, transect lines, etc. Individual-based data is represented as a single vector of length Sobs, the elements of which are the observed abundances Xi. For individual-based (abundance) data, the reference sample consists of n individuals drawn at random from N*, with Sobs species present, each represented by Xi individuals. In this complete assemblage, there are i=1 to S species and N* total individuals, with Ni individuals of species i. DetailsĬonsider a complete assemblage for which all species and their relative abundance are known. ValueĪ data frame with entries for sample-size (this refers either to number of individuals in individual-based rarefaction, or to number of sampling units in sample-based rarefaction) or coverage (in coverage-based rarefaction), and the corresponding Hill number. If not specified (default), rarefaction is calculated for all subsample sizes. Subsample size for rarefying community, either a single value or a vector.

Analytic rarefaction