Rarefaction Species Richness


Rarefied species richness for community ecologists.


rarefy(x, sample, se = FALSE, MARGIN = 1)
rrarefy(x, sample)
drarefy(x, sample)
rarecurve(x, step = 1, sample, xlab = "Sample Size", ylab = "Species",
          label = TRUE, col, lty, ...)
rareslope(x, sample)



Community data, a matrix-like object or a vector.


Margin for which the index is computed.


Subsample size for rarefying community, either a single value or a vector.


Estimate standard errors.


Step size for sample sizes in rarefaction curves.

xlab, ylab

Axis labels in plots of rarefaction curves.


Label rarefaction curves by rownames of x (logical).

col, lty

plotting colour and line type, see par. Can be a vector of length nrow(x), one per sample, and will be extended to such a length internally.


Parameters passed to nlm, or to plot, lines and ordilabel in rarecurve.


Function rarefy gives the expected species richness in random subsamples of size sample from the community. The size of sample should be smaller than total community size, but the function will work for larger sample as well (with a warning) and return non-rarefied species richness (and standard error = 0). If sample is a vector, rarefaction of all observations is performed for each sample size separately. Rarefaction can be performed only with genuine counts of individuals. The function rarefy is based on Hurlbert's (1971) formulation, and the standard errors on Heck et al. (1975).

Function rrarefy generates one randomly rarefied community data frame or vector of given sample size. The sample can be a vector giving the sample sizes for each row. If the sample size is equal to or smaller than the observed number of individuals, the non-rarefied community will be returned. The random rarefaction is made without replacement so that the variance of rarefied communities is rather related to rarefaction proportion than to the size of the sample.

Function drarefy returns probabilities that species occur in a rarefied community of size sample. The sample can be a vector giving the sample sizes for each row. If the sample is equal to or smaller than the observed number of individuals, all observed species will have sampling probability 1.

Function rarecurve draws a rarefaction curve for each row of the input data. The rarefaction curves are evaluated using the interval of step sample sizes, always including 1 and total sample size. If sample is specified, a vertical line is drawn at sample with horizontal lines for the rarefied species richnesses.

Function rareslope calculates the slope of rarecurve (derivative of rarefy) at given sample size; the sample need not be an integer.


A vector of rarefied species richness values. With a single sample and se = TRUE, function rarefy returns a 2-row matrix with rarefied richness (S) and its standard error (se). If sample is a vector in rarefy, the function returns a matrix with a column for each sample size, and if se = TRUE, rarefied richness and its standard error are on consecutive lines.

Function rarecurve returns invisible list of rarefy results corresponding each drawn curve.


Jari Oksanen


Heck, K.L., van Belle, G. & Simberloff, D. (1975). Explicit calculation of the rarefaction diversity measurement and the determination of sufficient sample size. Ecology 56, 1459–1461.

Hurlbert, S.H. (1971). The nonconcept of species diversity: a critique and alternative parameters. Ecology 52, 577–586.

See Also

Use specaccum for species accumulation curves where sites are sampled instead of individuals. specpool extrapolates richness to an unknown sample size.


S <- specnumber(BCI) # observed number of species
(raremax <- min(rowSums(BCI)))
Srare <- rarefy(BCI, raremax)
plot(S, Srare, xlab = "Observed No. of Species", ylab = "Rarefied No. of Species")
abline(0, 1)
rarecurve(BCI, step = 20, sample = raremax, col = "blue", cex = 0.6)

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