adiv (version 1.2)

crossdpcoa: Crossed-DPCoA

Description

Crossed-DPCoA typically analyze the phylogenetic or functional compositions of communities according to two factors affecting the communities (e.g. space and time; habitat and region)

The function crossdpcoa_maineffect obtains the space of DPCoA (the double principal coordinate analysis) where species are placed according to their functional traits or phylogeny and communities are placed at the center of their species. Next, levels of each factor are placed at the center of their communities. The function crossdpcoa_maineffect determines the principal axes of the positions of the levels of one of the factors in this space and project species' points on these principal axes. The main effect of the factor named facA is analysed by this process (Pavoine et al. 2013).

The function crossdpcoa_version1 performs version 1 of the crossed DPCoA in Pavoine et al. (2013) where the effect of factor facA on the diversity of communities, given factor facB, is analysed.

The function crossdpcoa_version2 performs version 2 of the crossed DPCoA in Pavoine et al. (2013) where the effect of factor facA on the diversity of communities, given factor facB, is also analysed.

Usage

crossdpcoa_maineffect(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)
crossdpcoa_version1(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)
crossdpcoa_version2(df, facA, facB, dis = NULL, 
scannf = TRUE, nf = 2, w = c("classic", "independence"), 
tol = 1e-07)

Arguments

df

a data frame or a matrix of 0/1 or nonnegative values (e.g. a communities x species data frame or matrix)

facA

a factor with the same length as the number of rows in df

facB

another factor with the same length as the number of rows in df

dis

an object of class dist that contains the distances among species (e.g. functional or phylogenetic distances). If NULL equidistances are used among species. The distances must have Euclidean properties. Distances are integrated in the Euclidean Diversity Index (Champely and Chessel 2002), which corresponds to a particular formulation of Rao (1982) quadratic entropy. For example the diversity within a community i is \(EDI=\sum_{k=1}^S\sum_{l=1}^S p_{k|i}p_{k|j}\frac{d_{kl}^2}{2}\), where S is the number of species, \(p_{k|i}\) is the relative abundance of species k within community i; \(d_{kl}\) is the (phylogenetic or functional) dissimilarity between species k and l.

scannf

a logical value indicating whether the screeplot (with eigenvalues) should be displayed.

nf

if scannf is FALSE, an integer indicating the number of kept axes.

w

either a character or a numeric vector of positive values that indicates how the rows of df (e.g. the communities) should be weighted. If w="classic", the weights are defined from the sum of the values in each row (e.g. sum of all species abundances within a community). If w="independence", then the weight attributed to a row of df (e.g. a community) is the product of the weight attributed to a level of factor A with the weight attributed to a level of factor B. If a vector of characters is given, only the first one is retained. If numeric, values in w must be in the same order as the rows of df (see Pavoine et al. 2013 for details on the definition of these weights).

tol

a numeric tolerance threshold: a value between -tol and tol is considered as null.

Value

The functions crossdpcoa_maineffect, crossdpcoa_version1 and crossdpcoa_version2 return a list containing the following information used for computing the crossed-DPCoA:

l1

coordinates of the columns of df (e.g. the species).

l2

coordinates of the levels of factor A.

l3

(for functions crossdpcoa_version1 and crossdpcoa_version2 only) coordinates of the rows of df (e.g. the communities).

eig

the eigenvalues.

lX

the weights attributed to the columns of df (e.g. species).

lA

the weights attributed to the levels of factor A.

lB

the weights attributed to the levels of factor B.

lC

the weights attributed to the rows of df (e.g. communities).

div

a numeric vector with the apportionment of Rao's quadratic diversity (APQE).

call

the call function.

References

Pavoine, S., Blondel, J., Dufour, A.-B., Gasc, A., Bonsall, M.B. (2013) A new technique for analysing interacting factors affecting biodiversity patterns: crossed-DPCoA. PloS One, 8, e54530.

Examples

# NOT RUN {
data(birdData)
phy <- read.tree(text=birdData$tre)
phydis <- sqrt(distTips(phy, method="nNodes")+1)

fau <- birdData$fau[, phy$tip.label]
facA <- birdData$facA
facB <- birdData$facB

#Here factor B is put first to analyze 
#the main effect of the strata:
cd_mainB <- crossdpcoa_maineffect(fau, facB, facA, phydis, w=rep(1/30, 30), scannf = FALSE)
barplot(cd_mainB$eig)
cd_mainB$eig[1:2]/sum(cd_mainB$eig)

#Positions of the levels of factor B on its principal axes:
s.label(cd_mainB$l2)
# The "d" value on graphs indicates the length of the edge of a grid cell (scale of the graphic). 

#The coordinates of the species on the same axes 
#can be displayed in front of the phylogeny:
mainBl1.4d <- phylo4d(phy, as.matrix(cd_mainB$l1))
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(mainBl1.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE)
par(mar=parmar)

#If factor A is put first, the analysis focus 
#on the main effect of the region:
cd_mainA <- crossdpcoa_maineffect(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
barplot(cd_mainA$eig)
cd_mainA$eig[1:2]/sum(cd_mainA$eig)

#Positions of the levels of factor A on its principal axes:
s.label(cd_mainA$l2)
# The "d" value on graphs indicates the length of the edge of a grid cell (scale of the graphic). 

#The coordinates of the species on the same axes 
# can be displayed in front of the phylogeny:
mainAl1.4d <- phylo4d(phy, as.matrix(cd_mainA$l1))
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(mainAl1.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE)
par(mar=parmar)

#Crossed DPCoA Version 1
cd_v1 <- crossdpcoa_version1(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
#Proportion of SS(A) expressed by the two first axes:
cd_v1$eig[1:2]/sum(cd_v1$eig)
#To view the positions of the locations on the first two axes, write:
s.label(cd_v1$l2)
#To view the positions of all communities on the first two axes, write:
s.label(cd_v1$l3)
#To view the positions of the species on the first two axes in front of the phylogeny, write:
v1l1.4d <- phylo4d(phy, as.matrix(cd_v1$l1))
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(v1l1.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE)
par(mar=parmar)

#Crossed DPCoA Version 2
#Crossed DPCoA version 2 can now be performed as follows:
cd_v2 <- crossdpcoa_version2(fau, facA, facB, phydis, w=rep(1/30, 30), scannf = FALSE)
#Proportion of variation among levels of factor A 
#in the subspace orthogonal to the principal axes of B
#expressed by the two first axes:
cd_v2$eig[1:2]/sum(cd_v2$eig)
#To view the positions of the locations on the first two axes, write:
s.label(cd_v2$l2)
#To view the positions of all communities on the first two axes, write:
s.label(cd_v2$l3)
#To view the positions of the species on the first two axes in front of the phylogeny, write:
v2l1.4d <- phylo4d(phy, as.matrix(cd_v2$l1))
parmar <- par()$mar
par(mar=rep(.1,4))
table.phylo4d(v2l1.4d, show.node=FALSE, symbol="squares", center=FALSE, scale=FALSE)
par(mar=parmar)
# }