PEM-functions: Phylogenetic Eigenvector Maps
In MPSEM: Modeling Phylogenetic Signals using Eigenvector Maps

Description Usage Arguments Details Value Functions Author(s) References See Also Examples

Functions to calculate and manipulate Phylogenetic Eigenvector Maps (PEM).

PEMInfluence(x, mroot = TRUE)

PEMweights(d, a = 0, psi = 1)

PEM.build(
  x,
  d = "distance",
  sp = "species",
  a = 0,
  psi = 1,
  tol = .Machine$double.eps^0.5
)

PEM.updater(object, a, psi = 1, tol = .Machine$double.eps^0.5)

PEM.fitSimple(
  y,
  x,
  w,
  d = "distance",
  sp = "species",
  lower = 0,
  upper = 1,
  tol = .Machine$double.eps^0.5
)

PEM.forcedSimple(
  y,
  x,
  w,
  d = "distance",
  sp = "species",
  a = 0,
  psi = 1,
  tol = .Machine$double.eps^0.5
)

getGraphLocations(tpall, targets)

getAncGraphLocations(x, tpall)

Locations2PEMscores(object, gsc)

`x`	A `graph-class` object containing a phylogenetic graph.
`mroot`	Boolean (TRUE or FALSE) specifying whether multiple rooting is allowed.
`d`	The name of the member of `x$edge` where the phylogenetic distances (edge lengths) can be found.
`a`	The steepness parameter describing whether changes occur, on average, progressively long edges (a close to 0) or abruptly at vertices (a close to 1).
`psi`	Relative evolution rate along the edges (default: 1). This parameter is only relevant when multiple values are assigned to different portions of the phylogeny.
`sp`	Name of the member of `x$vertex` where a `logical` vertex property specifying which vertices are species can be found. (see `graph-class`).
`tol`	Eigenvalue threshold to regard eigenvectors as usable.
`object`	A `PEM-class` object containing a Phylogenetic Eigenvector Map.
`y`	One or many response variable(s) in the form of a numeric vector or a `matrix`, respectively.
`w`	A `graph-class` object containing a phylogenetic graph.
`lower`	Lower limit for the L-BFGS-B optimization algorithm as implemented in `optim`.
`upper`	Upper limit for the L-BFGS-B optimization algorithm as implemented in `optim`.
`tpall`	Parameter of function `getGraphLocations`: Phylogenetic tree object of class ‘phylo’ (package ape) containing all species (model and target) used in the study.
`targets`	Name of the target species to extract using the `tpall`.
`gsc`	The output of `getGraphLocations`.

Functions PEMInfluence and PEMweights are used internally by PEM.build to create a binary matrix referred to as an ‘influence matrix’ and weight its columns. That matrix has a row for each vertex of graph ‘x’ and a column for each of its edges. The elements of the influence matrix are 1 whenever the vertex associated with a row is located in the tree either directly or indirectly downward the edge associated with a column. That function is implemented in C language using recursive function calls. Although PEMInfluence allows one to use multiple roots as its default parameter, it is called within PEM.build with mroot = FALSE. User must therefore ensure that the graph provided to PEMap is single-rooted.

Function PEM.build is used to produce a phylogenetic eigenvector map, while function PEM.updater allows one to re-calculate a PEM-class object with new weighting function parameters. Function PEM.fitSimple performs a maximum likelihood estimation of a and psi assuming single values for the whole tree whereas function PEM.forcedSimple allows one the force parameters a and psi to a PEM-class object while adding the same computational details as those PEM.fitSimple would have produced (and which are necessary to make predictions).

Functions getGraphLocations returns the coordinates of a species in terms of its position with respect to the influence matrix while function Locations2PEMscores transforms these coordinates into sets of scores that can be used to make predictions. Function getAncGraphLocations produce the same output as getGraphLocations, but of the ancestral species (i.e. the nodes of the phylogeny) in order to estimate ancestral trait values.

Function PEMInfluence returns the influence matrix of graph x and function PEMweights returns weights corresponding to the distances. Functions PEM.build, PEM.fitSimple, PEM.forcedSimple returns a PEM-class object. Function getGraphLocations returns a list whose first member is an influence coordinates matrix whose rows refer to the target species and columns refer to the edges and second member is the lengths of the terminal edges connecting each target species to the rest of the phylogeny. Function Locations2PEMscores returns a list whose first member is a PEM score matrix whose rows refer to the target species and columns refer to the eigenvectors and second member is the variance associated with the terminal edges connecting the target species to the phylogeny.

PEMInfluence: Calculate the influence matrix of a phylogenetic graph.
PEMweights: Calculates the edge weights to be used in PEM calculation.
PEM.build: Calculates a PEM with parameters given by arguments a and psi.
PEM.updater: Update a PEM with new parameters given by arguments a and psi.
PEM.fitSimple: Fit a PEM with a single “a” parameter value for the whole phylogeny (assumes psi = 1).
PEM.forcedSimple: Calculates a PEM while forcing a single value for parameter “a” for the whole phylogeny (assumes psi = 1).
getGraphLocations: Get the location of species on a phylogenic graph.
getAncGraphLocations: Get the location of an ancestral species on the phylogenetic graph.
Locations2PEMscores: Calculates the PEM scores on phylogenetic graph locations.

Guillaume Guenard, with contribution from Pierre Legendre Maintainer: Guillaume Guenard <guillaume.guenard@gmail.com>

Guénard, G., Legendre, P., and Peres-Neto, P. 2013. Phylogenetic eigenvector maps (PEM): a framework to model and predict species traits. Meth. Ecol. Evol. 4: 1120–1131

Makarenkov, V., Legendre, L. & Desdevise, Y. 2004. Modelling phylogenetic relationships using reticulated networks. Zool. Scr. 33: 89–96

Blanchet, F. G., Legendre, P. & Borcard, D. 2008. Modelling directional spatial processes in ecological data. Ecol. Model. 215: 325–336

graph-class.

t1 <- read.tree(text=paste(
            "(((A:0.15,B:0.2)N4:0.15,C:0.35)N2:0.25,((D:0.25,E:0.1)N5:0.3,",
            "(F:0.15,G:0.2)N6:0.3)N3:0.1)N1;",sep=""))
x <- Phylo2DirectedGraph(t1)

## Calculates the (binary) influence matrix
PEMInfluence(x)
PEMInfluence(x)[x$vertex$species,]

## Building phylogenetic eigenvector maps
PEM1 <- PEM.build(x)
print(PEM1)
PEM2 <- PEM.build(x, a = 0.2)
PEM3 <- PEM.build(x, a = 1)
PEM4 <- PEM.updater(PEM3,a=0.5)

## Extracts the eigenvectors
as.data.frame(PEM4)

## Example of an hypothetical set of trait values
y <- c(A=-1.1436265,B=-0.3186166,C=1.9364105,D=1.7164079,E=1.0013993,
       F=-1.8586351,G=-2.0236371)

## Estimate single steepness parameter for the whole tree.
PEMfs1 <- PEM.fitSimple(y=y,x=NULL,w=x,d="distance",sp="species",lower=0,upper=1)
PEMfs1$optim       # Results of the optimization.

## Force neutral evolution for the whole tree.
PEMfrc1 <- PEM.forcedSimple(y=y,x=NULL,w=x,d="distance",sp="species",a=0)
PEMfrc1$x$edge$a   # Steepness parameter forced for each individual edge.

## Get graph locations for target species X, Y, and Z
tpAll <- read.tree(text=paste("((X:0.45,((A:0.15,B:0.2)N4:0.15,",
                              "(C:0.25,Z:0.2)NZ:0.1)N2:0.05)NX:0.2,",
                              "(((D:0.25,E:0.1)N5:0.05,Y:0.25)NY:0.25,",
                              "(F:0.15,G:0.2)N6:0.3)N3:0.1)N1;",sep=""))
grloc <- getGraphLocations(tpAll, c("X","Y","Z"))

PEMfs2 <- PEM.fitSimple(y=y, x=NULL, w=grloc$x, d="distance", sp="species",
                        lower=0,upper=1)

## Same as for PEMfs1$optim
PEMfs2$optim

PEMsc1 <- Locations2PEMscores(PEMfs2, grloc)
lm1 <- lm(y~V_2+V_3+V_5,data=PEMfs2)

ypred <- predict(object=PEMfs2,targets=grloc,lmobject=lm1,interval="none")

tpModel <- drop.tip(tpAll,c("X","Y","Z"))

## Plotting the results:
layout(t(c(1,1,2)))
par(mar=c(6,2,2,0.5)+0.1)
plot(tpModel,show.tip.label=TRUE,show.node.label=TRUE,root.edge = TRUE,
     srt = 0,adj=0.5,label.offset=0.08,font=1,cex=1.5,xpd=TRUE)
edgelabels(paste("E",1:nrow(tpModel$edge),sep=""),
           edge=1:nrow(tpModel$edge),bg="white",font=1,cex=1)
points(x=0.20,y=2.25,pch=21,bg="black")
lines(x=c(0.20,0.20,0.65),y=c(2.25,0.55,0.55),xpd=TRUE,lty=2)
text("X",x=0.69,y=0.55,xpd=TRUE,font=1,cex=1.5)
points(x=0.35,y=4.5,pch=21,bg="black")
lines(x=c(0.35,0.35,0.6),y=c(4.5,5.47,5.47),xpd=TRUE,lty=2)
text("Y",x=0.64,y=5.47,xpd=TRUE,font=1,cex=1.5)
points(x=0.35,y=3,pch=21,bg="black")
lines(x=c(0.35,0.35,0.55),y=c(3,3.5,3.5),xpd=TRUE,lty=2)
text("Z",x=0.59,y=3.5,xpd=TRUE,font=1,cex=1.5)
text(c("NX","NY","NZ"),x=c(0.20,0.35,0.35),y=c(2.25,4.5,3)+0.3*c(1,-1,-1),
     font=1,cex=1)
add.scale.bar(length=0.1,cex=1.25)
par(mar=c(3.75,0,2,2)+0.1)
plot(x=y,y=1:7,ylim=c(0.45,7),xlim=c(-4,4), axes=FALSE, type="n", xlab="")
axis(1,label=c("-4","-2","0","2","4"),at=c(-4,-2,0,2,4))
abline(v=0)

## Observed values:
points(x=y,y=1:7,xlim=c(-2,2),pch=21,bg="black")
text("B)",x=-3.5,y=7,cex=1.5,xpd=TRUE) ; text("Trait value",x=0,y=-0.5,
     cex=1.25,xpd=TRUE)

## Predicted values:
points(x=ypred,y=c(0.5,5.5,3.5),pch=23,bg="white",cex=1.25)

## Estimating ancestral trait values:
ANCloc <- getAncGraphLocations(x)
PEMfsAnc <- PEM.fitSimple(y=y,x=NULL,w=ANCloc$x,d="distance",sp="species",
                          lower=0,upper=1)
PEMfsAnc$optim

PEManc1 <- Locations2PEMscores(PEMfsAnc, ANCloc)
y_anc <- predict(object=PEMfsAnc,targets=ANCloc,lmobject=lm1,
                 interval="confidence")