asbio (version 1.2-5)

Preston.dist: Preston diversity analysis

Description

A diversity and richness analysis method based on the Preston (1948) log-normal distribution.

Usage

Preston.dist(counts, start = 0.2, cex.octave = 1, cex.legend = 1, cex.pt = 1, ...)

Arguments

counts

Vector of counts for species in a community dataset.

start

Starting value for non-linear least squares estimation of a in $n = n_0 \times e^{-aR^2}$.

cex.octave

Character expansion for octave labels.

cex.legend

Character expansion for legend.

cex.pt

Character expansion for symbols.

...

Additional arguments from plot.

Value

• Graph of the Preston log-normal distribution for a dataset given by "counts", and a summary of the analysis including the fitted Gaussian equation, the estimated number of species, and an estimate for the percentage of sampling that was completed i.e. [length(counts)/Est.no.of.spp]*100.

Details

Preston (1948) proposed that after a log$_2$ transformation species abundances, grouped in bins representing a doubling of abundance (octaves), would be normally distributed. Thus, after this transformation most species in a sample would have intermediate abundance, and there would be relatively few rare or ubiquitous species. The Preston model is based on the Gaussian function: $n = n_0 \times e^{-aR^2}$, where, $n_0$ is the number of species contained in the modal octave, n is the number of species contained in an octave R octaves from the modal octave, and a is an unknown parameter. The parameter a is estimated using the function nls, using a starting value, 0.2, recommended by Preston. The area under Preston curve provides an extrapolated estimate of richness and thus an indication of the adequacy of a sampling effort. Preston called a line placed at the 0th octave the veil line. He argued that species with abundances below the veil line have not been detected due to inadequate sampling.

References

Preston, F.W. (1948) The commonness and rarity of species. Ecology 29, 254-283.

See Also

dnorm, nls

Examples

data(BCI.count)
BCI.ttl<-apply(BCI.count,2,sum)
Preston.dist(BCI.ttl)