| fourthcorner {ade4} | R Documentation |
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.
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)
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 |
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:
modeltype=1): Permute values for each species independently (i.e., permute within each column of table L)
modeltype=2): Permute values of sites (i.e., permute entire rows of table L)
modeltype=3): Permute values for each site independently (i.e., permute within each row of table L)
modeltype=4): Permute values of species (i.e., permute entire columns of table L)
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)
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.
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.
Stephane Dray dray@biomserv.univ-lyon1.fr
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.
rlq
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$traits,nrepet=99,modeltype=4) four.comb<-combine.4thcorner(four2,four4) plot(four.comb, type = "G")
> library(ade4)
> ### Name: fourthcorner
> ### Title: Functions to compute the fourth-corner statistic
> ### Aliases: fourthcorner fourthcorner2 print.4thcorner summary.4thcorner
> ### plot.4thcorner combine.4thcorner
> ### Keywords: multivariate
>
> ### ** Examples
>
> data(aviurba)
> four1<-fourthcorner(aviurba$mil,aviurba$fau,aviurba$traits,nrepet=99)
> print(four1,varR=2,varQ=3)
Fourth-corner Statistics
------------------------
------------------------
Permutation method 1 ( 99 permutations)
call: fourthcorner(tabR = aviurba$mil, tabL = aviurba$fau, tabQ = aviurba$traits, nrepet = 99)
breeding and small.bui :
---------------------------
Chi2 = 27.79316 Prob(Chi2) = 0.01
N. less than Chi2 obs = 99 N. equal to Chi2 obs = 1
Min(Chi2) = 0.1190478 Max(Chi2) = 27.79316 Mean(Chi2) = 3.047718
G = 36.98892 Prob(G) = 0.01
N. less than G obs = 99 N. equal to G obs = 1
Min(G) = 0.1191480 Max(G) = 36.98892 Mean(G) = 3.161991
D(ground,yes)=1 D(ground,no)=59
Min 1 36
Max 24 59
Mean 15 45
Pr. 0.01 0.01
Pr. adj. 0.08 0.08
N.LT 0 99
N.EQ 1 1
D(building,yes)=128 D(building,no)=300
Min 84 289
Max 139 344
Mean 109.13 318.87
Pr. 0.04 0.04
Pr. adj. 0.16 0.16
N.LT 96 2
N.EQ 2 2
D(scrub,yes)=20 D(scrub,no)=101
Min 20 78
Max 43 101
Mean 31.42 89.58
Pr. 0.01 0.01
Pr. adj. 0.08 0.08
N.LT 0 99
N.EQ 1 1
D(foliage,yes)=38 D(foliage,no)=107
Min 26 95
Max 50 119
Mean 36.6 108.4
Pr. 0.4 0.4
Pr. adj. 0.8 0.8
N.LT 60 32
N.EQ 8 8
> summary(four1)
Fourth-corner Statistics
Permutation method 1 ( 99 permutations)
---
Var. R Var. Q Stat. Value Prob.
farms / feed.hab Chi2 4.36429 0.11
farms / feed.strat Chi2 4.29285 0.11
farms / breeding Chi2 3.2343 0.29
farms / migratory Chi2 3.19878 0.08 .
small.bui / feed.hab Chi2 5.57482 0.07 .
small.bui / feed.strat Chi2 13.5964 0.01 **
small.bui / breeding Chi2 27.7932 0.01 **
small.bui / migratory Chi2 0.987997 0.42
high.bui / feed.hab Chi2 3.11706 0.21
high.bui / feed.strat Chi2 8.13102 0.03 *
high.bui / breeding Chi2 12.4354 0.01 **
high.bui / migratory Chi2 0.629089 0.39
industry / feed.hab Chi2 2.05616 0.35
industry / feed.strat Chi2 1.6009 0.44
industry / breeding Chi2 22.2859 0.01 **
industry / migratory Chi2 0.987534 0.34
fields / feed.hab Chi2 14.0114 0.02 *
fields / feed.strat Chi2 7.89491 0.02 *
fields / breeding Chi2 38.339 0.01 **
fields / migratory Chi2 5.39284 0.01 **
grassland / feed.hab Chi2 1.27967 0.57
grassland / feed.strat Chi2 2.1178 0.36
grassland / breeding Chi2 16.6997 0.02 *
grassland / migratory Chi2 0.0977542 0.79
scrubby / feed.hab Chi2 2.87647 0.22
scrubby / feed.strat Chi2 5.17033 0.11
scrubby / breeding Chi2 7.93878 0.06 .
scrubby / migratory Chi2 3.40197 0.12
deciduous / feed.hab Chi2 2.56302 0.29
deciduous / feed.strat Chi2 4.27795 0.11
deciduous / breeding Chi2 36.3742 0.01 **
deciduous / migratory Chi2 0.00146756 0.96
conifer / feed.hab Chi2 0.677739 0.70
conifer / feed.strat Chi2 3.27694 0.22
conifer / breeding Chi2 8.13156 0.03 *
conifer / migratory Chi2 0.181774 0.67
noisy / feed.hab Chi2 8.04038 0.02 *
noisy / feed.strat Chi2 6.75501 0.03 *
noisy / breeding Chi2 22.8175 0.01 **
noisy / migratory Chi2 0.992204 0.35
veg.cover / feed.hab Chi2 29.4893 0.02 *
veg.cover / feed.strat Chi2 78.3169 0.01 **
veg.cover / breeding Chi2 118.24 0.01 **
veg.cover / migratory Chi2 9.14415 0.33
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 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")
> > > > >