Rarefy (version 1.1.1)

ser_functional: Functional Spatially-Explicit Rarefaction Curves

Description

The function calculates classic and spatially-explicit rarefaction curves using different indexes of functional diversity.

Usage

ser_functional(comm,dist_f=NULL,dist_xy,method=c("rao","chao","fun_div"), 
tau=NA,q=0,comparison=FALSE,resampling=99,fun_div=NULL,args=NULL,verbose=FALSE)

Value

An object of class data.frame with 3 columns is returned:

- Rarefaction: : mean of the values of the accumulation curves for all the sampling dimensions;

- IC_up: upper confidence interval;

- IC_low: lower confidence interval.

Arguments

comm

a community dataframe or matrix with N plots as rows, S species as columns. Only the abundances of species in plots are allowed as entries for the methods rao and chao. Plot names should be provided as row names.

dist_f

an object of class dist containing the pairwise functional distances among species. The distance matrix should be squared Euclidean or simply Euclidean.

dist_xy

an object of class dist containing the pairwise geographic distances among the plots or an object of class, an object of class vector containing the order of the sampling units along a gradient or an object of class matrix or data.frame where each column represents a gradient along which the sampling units are ordered. The names of the labels must be the same as the rows of comm. If dist_xy is not of class dist, then a distance matrix is calculated using the Euclidean distance coefficient.

method

the diversity index for the calculation of the rarefaction curve, one among "rao", "chao" or "fun_div". See details.

tau

threshold of functional distinctiveness between any two species for chao. See details.

q

parameter that determines the sensitivity of the measure to the relative abundance of the species for chao.

comparison

if TRUE, both non-spatially explicit and spatially explicit rarefactions are calculated.

resampling

number of times plots (rows) are randomly resampled from comm to calculate the mean accumulation curve for the non-spatially-explicit rarefaction.

fun_div

a string with the name of the user-defined function for the diversity index in the rarefaction. The function must calculate the value of the chosen diversity index per plot and return a numeric vector with the values calculated.

args

a list with the arguments for fun_div. The value NA should be given in place of the community matrix in the list. The names of the elements must correspond to the names of the arguments of the function passed.

verbose

if TRUE, the arguments of fun_div are inserted interactively by the user.

Author

Elisa Thouverai

with contributions of Sandrine Pavoine.

Details

The available methods are:

rao: Rao functional diversity is based on the quadratic entropy of Rao (1982) and incorporates both the relative abundances of species and a measure of the pairwise functional distances between species. It expresses the average difference between two randomly selected individuals with replacements. $$Q(\mathbf{p}_i,\mathbf{D})=\sum_{k=1}^S\sum_{l=1}^S p_{k}p_{l}d_{kl}$$ where \(p=(p1,...,p_k,...,S)\) is the vector of relative species abundances, \(S\) is the number of species, \(\mathbf{D}=(d_{kl})\) is the matrix of functional dissimilarities among species, and \(d_{kl}\) is the functional dissimilarity between species \(k\) and \(l\).

chao: Chao et al. (2018) functional beta-diversity index FD quantifies the effective number of equally-distinct functional groups in the considered plots at the distinctiveness tau threshold. Any two species with functional distance greater than or equal to tau, are treated as functionally equally-distinct and as belonging to different functional groups with distance tau. For each pair of species with functional distance lower than tau but different from zero, only a proportion of individuals is considered functionally equally-distinct, the other proportion of individuals is considered functionally indistinct. If the pairwise distance is equal to zero, the two species are treated as belonging to the same functional group. After dividing the set of species to form functionally indistinct groups, the contribution of every species is quantified and then the FD of order q is calculated using the Hill number of order \(q\): $$^{q}\textrm{FD}(\Delta(\tau))=\left ( \sum_{i=1}^{S} \nu_{i}(\tau)\left(\frac{a_i(\tau)}{n_{+}} \right )^{(1/1-q)} \right )$$ where \(a_{i}(\tau)\) is the combined abundance of all functionally-indistinct individuals from species \(i\), \(v_{i}(\tau)=n_{i}/a_{i}(\tau)\) represents the attribute contribution of species \(i\) for a threshold level tau (\(n_{i}\) is the abundance of species \(i\)), \(n_+\) is the total number of individuals in the community and \(q\) is the parameter that determines the sensitivity of the measure to the relative abundance of the species.

References

Botta-Dukat, Z. (2005) Rao's quadratic entropy as a measure of functional diversity based on multiple traits. Journal of Vegetation Science, 16, 533--540.

Chao, A., Chiu, C.-H., Villeger, S., Sun, I.F., Thorn, S., Lin, Y., Chiang, J.-M., B. Sherwin, W. (2018) An attribute-diversity approach to functional diversity, functional beta diversity, and related (dis)similarity measures. Ecological Monographs, 89, e01343.

Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24--43.

Ricotta, C., Pavoine, S., Bacaro, G., Acosta, A. (2012) Functional rarefaction for species abundance data. Methods in Ecology and Evolution, 3, 519--525.

See Also

rare_Rao

rare_alpha

Examples

if (FALSE) {
#Time consuming
require(ade4)
data(duneFVG)
data(duneFVG.xy)
data(duneFVG.tr8)
tr8_N<-duneFVG.tr8$traits.tot[,c(1,3,4)]
tr8_D<-data.frame(duneFVG.tr8$traits.tot[,2])
tr8_Q<-duneFVG.tr8$traits.tot[,5:15]
tr8dist<-dist.ktab(ktab.list.df(list(tr8_N,tr8_D,tr8_Q)),type=c('N','D','Q'))
tr8dist<-cailliez(tr8dist) 
dist_sp<-dist(duneFVG.xy$tot.xy,'euclidean')
## Rao index
## Take care that the following scripts may be time-consuming 
rare<-ser_functional(duneFVG$total,tr8dist,dist_sp,method='rao',comparison=TRUE)
plot(rare [,1], ylab="Rao QE", xlab="Number of plots", type="l", ylim=range(rare, na.rm=TRUE))
lines(rare[,2], lty=2)
lines(rare[,3], lty=2)
lines(rare[,4 ], col=2)
lines(rare[,5], lty=2, col=2)
lines(rare[,6], lty=2, col=2)
legend("bottomright",  legend=c("spatially-explicit rarefaction", "classic rarefaction"),
lty=1, col=1:2)
# dashed lines represent the confidence interval
## Chao index
rareC<-ser_functional(duneFVG$total,tr8dist,dist_sp,method='chao',tau=0.6,q=2,comparison
=TRUE)
plot(rareC [,1], ylab="Chao", xlab="Number of plots", type="l", ylim=range(rareC, na.rm
=TRUE))
lines(rareC[,2], lty=2)
lines(rareC[,3], lty=2)
lines(rareC[,4 ], col=2)
lines(rareC[,5], lty=2, col=2)
lines(rareC[,6], lty=2, col=2)
legend("bottomright",  legend=c("spatially-explicit rarefaction", "classic rarefaction"),
lty=1, col=1:2)
# dashed lines represent the confidence interval
}