A diversity and richness analysis method based on the Preston (1948) log-normal distribution.
Preston.dist(counts, start = 0.2, cex.octave = 1, cex.legend = 1, cex.pt = 1, ...)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.
Vector of counts for species in a community dataset.
Starting value for non-linear least squares estimation of a in \(n = n_0 \times e^{-aR^2}\).
Character expansion for octave labels.
Character expansion for legend.
Character expansion for symbols.
Additional arguments from plot.
Ken Aho
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.
Preston, F.W. (1948) The commonness and rarity of species. Ecology 29, 254-283.
data(BCI.count)
BCI.ttl<-apply(BCI.count,2,sum)
Preston.dist(BCI.ttl)
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