Observed distributions are fitted to classical RAC's.

RAClnorm(Ns, CheckArguments = TRUE)
RACgeom(Ns, CheckArguments = TRUE)
RAClseries(Ns, CheckArguments = TRUE)
RACbstick(Ns, CheckArguments = TRUE)

## Arguments

Ns

A numeric vector containing species abundances.

CheckArguments

Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time when the arguments have been checked elsewhere.

## Details

SpeciesDistribution or integer vectors can be used to fit classical rank-abundance curves (RAC) of classical distributions: "RAClnorm" for log-normal (Preston, 1948), "RAClseries" for log-series (Fisher et al., 1943), "RACgeom" for geometric (Motomura, 1932) or "RACbstick" for broken stick (MacArthur, 1957). method returns the estimated parameters of the fitted distribution. The broken stick has no parameter, so the maximum abundance is returned.

## Note

Fisher's alpha is estimated to fit the log-series distribution. The estimation is done by the fisher.alpha function of package vegan. It may differ substantially from the estimation returned by optimal.theta from package untb.

## Value

A list (the parameters of distributions are returned only if the distribution has been fit):

Rank

A numeric vector. The ranks of species in the fitted RAC.

Abundance

The abundance of species in the fitted RAC.

mu

The expectation of the log-normal distribution

sigma

The standard deviation of the log-normal distribution

alpha

Fisher's alpha in the log-series distribution

prob

The proportion of ressources taken by successive species in the geometric distribution

max

The maximum abundance in the broken-stick distribution

## Author

Eric Marcon <Eric.Marcon@agroparistech.fr>, Bruno Herault <Bruno.Herault@cirad.fr>

## References

Fisher R.A., Corbet A.S., Williams C.B. (1943) The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population. Journal of Animal Ecology 12: 42-58.

MacArthur R.H. (1957) On the Relative Abundance of Bird Species. PNAS 43(3): 293-295.

Motomura I. (1932) On the statistical treatment of communities. Zoological Magazine 44: 379-383.

Preston, F.W. (1948). The commonness, and rarity, of species. Ecology 29(3): 254-283.

rgeom, rlnorm, rCommunity, plot.SpeciesDistribution

## Examples

# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ns is the total number of trees per species
Ns <- as.AbdVector(Paracou618.MC$Ns) # Fitted parameters RACln <- RAClnorm(Ns) RACln$mu
#> [1] 0.9519812
RACln$sigma #> [1] 1.011383 RACgeom(Ns)$prob
#> [1] 0.01417454
RAClseries(Ns)$alpha #> [1] 86.94339 RACbstick(Ns)$max
#> [1] 29.51418