ade4 (version 1.5-2)

fourthcorner: Functions to compute the fourth-corner statistic

Description

These functions allow to compute the fourth-corner statistic for abundance or presence-absence data. The fourth-corner statistic has been developped by Legendre et al (1997) and extended in Dray and Legendre (2008). The statistic measures the link between three tables: a table L (n x p) containing the abundances of p species at n sites, a second table R (n x m) with the measurements of m environmental variables for the n sites, and a third table Q (p x s) describing s species traits for the p species.

Usage

fourthcorner(tabR, tabL, tabQ, modeltype = 1, nrepet = 999, tr01 = FALSE)
fourthcorner2(tabR, tabL, tabQ, modeltype = 1, nrepet = 999, tr01 = FALSE)
## S3 method for class '4thcorner':
print(x, varQ = 1:nrow(x$tabG), varR = 1:ncol(x$tabG),...)
## S3 method for class '4thcorner':
summary(object,...)
## S3 method for class '4thcorner':
plot(x, type=c("D","D2","G"), alpha=0.05,...)
combine.4thcorner(four1,four2)

Arguments

tabR

a dataframe with the measurements of m environmental variables (columns) for the n sites (rows).

tabL

a dataframe containing the abundances of p species (columns) at n sites (rows).

tabQ

a dataframe describing s species traits (columns) for the p species (rows).

modeltype

an integer (0-5) indicating the permutation model used in the testing procedure (see details).

nrepet

the number of permutations

tr01

a logical indicating if data in tabL must be transformed to presence-absence data (FALSE by default)

object

an object of the class 4thcorner

x

an object of the class 4thcorner

varR

a vector with indices for variables in tabR

varQ

a vector with indices for variables in tabQ

type

a character to specify if results should be plotted for cells (D and D2) or variables (G)

alpha

a value of significance level

four1

an object of the class 4thcorner

four2

an object of the class 4thcorner

...

further arguments passed to or from other methods

Value

• For the fourthcorner function, a list where: tabD, tabDmin, tabDmax, tabDmoy, tabDNEQ, tabDNLT, tabDProb, tabDNperm are dataframes with observed statistic; minimum, maximum, average statistics obtained by the permutation procedure; number of simulated values equal to the observed statistic; number of simulated values less than the observed statistic; P-values; and number of permutations. Results are given for cells of the fourth-corner (homogeneity for quant./qual.). tabG, tabGmin, tabGmax, tabGmoy, tabGNEQ, tabGNLT, tabGProb, tabGNperm are dataframes with observed statistic; minimum, maximum, average statistics obtained by the permutation procedure; number of simulated values equal to the observed statistic; number of simulated values less than the observed statistic; P-values; and number of permutations. Results are given for variables (Pearson's Chi2 for qual./qual.). tabD2, tabD2min, tabD2max, tabD2moy, tabD2NEQ, tabD2NLT, tabD2Prob, tabD2Nperm are dataframes with observed statistic; minimum, maximum, average statistics obtained by the permutation procedure; number of simulated values equal to the observed statistic; number of simulated values less than the observed statistic; P-values; and number of permutations. Results are given for cells of the fourth-corner (Pearson r for quant./qual.). tabG2, tabG2min, tabG2max, tabG2moy, tabG2NEQ, tabG2NLT, tabG2Prob, tabG2Nperm are dataframes with observed statistic; minimum, maximum, average statistics obtained by the permutation procedure; number of simulated values equal to the observed statistic; number of simulated values less than the observed statistic; P-values; and number of permutations. Results are given for variables (G for qual./qual.)

  The fourthcorner2 function returns a list where:

  tabG, tabGmin, tabGmax, tabGmoy, tabGNEQ, tabGNLT, tabGProb, tabGNperm are dataframes with observed statistic; minimum, maximum, average statistics obtained by the permutation procedure; number of simulated values equal to the observed statistic; number of simulated values less than the observed statistic; P-values; and number of permutations. Results are given for variables. It returns also the list trRLQ with results for the multivariate statistic.

Details

For the fourthcorner function, the link is measured by a Pearson correlation coefficient for two quantitatives variables (trait and environmental variable), by a Pearson Chi2 and G statistic for two qualitative variables and by a Pseudo-F and Pearson r for one quantitative variable and one qualitative variable. The fourthcorner2 function offers a multivariate statistic (equal to the sum of eigenvalues of RLQ analysis) and measures the link between two variables by a square correlation coefficient (quant/quant), a Chi2/sum(L) (qual/qual) and a correlation ratio (quant/qual). The significance is tested by a permutation procedure. Different models are available:

• model 1 (modeltype=1): Permute values for each species independently (i.e., permute within each column of table L)
• model 2 (modeltype=2): Permute values of sites (i.e., permute entire rows of table L)
• model 3 (modeltype=3): Permute values for each site independently (i.e., permute within each row of table L)
• model 4 (modeltype=4): Permute values of species (i.e., permute entire columns of table L)
• model 5 (modeltype=5): Permute values of species and after (or before) permute values of sites (i.e., permute entire columns and after (or before) entire rows of table L)

Note that the last model is strictly equivalent to permuting simultaneously the rows of tables R and Q, as proposed by Doledec et al. (1996).

The function summary returns results for variables (G). The function print returns results for cells (D and D2). In the case of qualitative variables, Holm's corrected pvalues are also provided.

The function plot produces a graphical representation of the results (white for non siginficant, light grey for negative sgnificant and dark grey for positive suignficant relationships). Results can be plotted for variables (G) or for cells (D and D2). In the case of qualitative / quantitative association, homogeneity (D) or correlation (D2) are plotted.

The function combine.4thcorner combines the outputs of two fourth-corner objects as described in Dray and Legendre (2008). It returns an object of the class 4thcorner. The function simply creates a new 4th.corner object where pvalues are equal to the maximum of pvalues of the two arguments.

References

Doledec, S., Chessel, D., ter Braak, C.J.F. and Champely, S. (1996) Matching species traits to environmental variables: a new three-table ordination method. Environmental and Ecological Statistics, 3, 143--166.

Legendre, P., R. Galzin, and M. L. Harmelin-Vivien. (1997) Relating behavior to habitat: solutions to the fourth-corner problem. Ecology, 78, 547--562.

Dray, S. and Legendre, P. (2008) Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology, 89, 3400--3412.

See Also

rlq

Examples

data(aviurba)
four1<-fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99)
print(four1,varR=2,varQ=3)
summary(four1)
plot(four1, type = "G")

## Procedure to combine the results of two models proposed in Dray and Legendre (2008)
four2<-fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99,modeltype=2)
four4<-fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99,modeltype=4)
four.comb<-combine.4thcorner(four2,four4)
plot(four.comb, type = "G")