Functions to calculate and manipulate Phylogenetic Eigenvector
Maps (PEM), which are sets of eigenfunctions describing the structure of a
phylogenetic graph. Each computation function is briefly described in
section Functions below.
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)
Function PEMInfluence returns the influence matrix of
graph x and function PEMweights returns weights
corresponding to the distances. Functions PEM.build,
PEM.fitSimple and PEM.forcedSimple return a
PEM-class object. Function getGraphLocations
returns a list whose first member is an influence coordinate matrix whose rows refer to the target species and columns refer to the edges. The second member contains 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. The second member contains the variance associated
with the terminal edges connecting the target species to the phylogeny.
A graph-class object containing a phylogenetic graph.
Boolean (TRUE or FALSE) specifying whether multiple roots are allowed.
The name of the member of x$edge where the phylogenetic
distances (edge lengths) can be found.
The steepness parameter describing whether changes occur, on average: progressively long edges (a close to 0) or abruptly at vertices (a close to 1).
Relative evolution rate along the edges (default: 1). This parameter is only relevant when multiple values are assigned to different portions of the phylogeny.
Name of the member of x$vertex where a logical
vertex property can be found, specifying which vertices are species (see
graph-class).
Eigenvalue threshold indicating that eigenvectors as usable.
A PEM-class object containing a Phylogenetic
Eigenvector Map.
One or many response variable(s) in the form of a single numeric
vector or a matrix, respectively.
A graph-class object containing a phylogenetic graph.
Lower limit for the L-BFGS-B optimization algorithm
implemented in optim.
Upper limit for the L-BFGS-B optimization algorithm
implemented in optim.
First parameter of function getGraphLocations:
Phylogenetic tree object with class ‘phylo’ (package ape)
containing all species (model and target) used in the study.
Name of the target species to extract using the tree
tpall.
The output of getGraphLocations.
PEMInfluence(): Influence Matrix
Calculates the influence matrix of a phylogenetic graph. The influence matrix is a binary matrix whose rows and columns correspond to the vertices and edges of the phylogenetic graph, respectively, and whose elements describe whether a given edge had been taken by any ancestors of a vertex (representing extinct of extant species) during evolution (value = 1) or not (value = 0).
PEMweights(): PEM Weighting
A power function to obtain the edge weights used during PEM calculation.
PEM.build(): PEM Building
Calculates a PEM with parameters given by arguments a and psi.
PEM.updater(): PEM Update
Update a PEM with new parameters given by arguments a and psi.
PEM.fitSimple(): Fitting a PEM to Data while Estimating Global Steepness
Fits a PEM to a data set estimating the selection (steepness) parameter using gradient descent. The selection and evolution rate (psi = 1) are assumed to be homogeneous for the whole phylogenetic network.
PEM.forcedSimple(): Fitting a PEM to Data while Forcing Global Steepness
Fits a PEM to a data set forcing a user-provided selection (steepness) parameter. The selection and evolution rate (psi = 1) are assumed to be homogeneous for the whole phylogenetic network.
getGraphLocations(): Get Phylogenetic Graph Locations
Takes a phylogenetic tree and a list of species to be removed, and produce a phylogenic graph without these species together with the locations of the removed species on that graph (i.e., the location where the removed species would be found should they be inserted again in the phylogenetic graph).
getAncGraphLocations(): Get Ancestral Species Location
Get the location on the phylogenetic graph of the immediate ancestors for a list of species. The species of the list remain in the resulting phylogenetic graph. This function is useful for estimating the ancestral state of a trait.
Locations2PEMscores(): PEM Score Calculation
Calculates the scores of an extant or ancestral species on a phylogenetic eigenvector map (i.e., its value on the eigenvectors of the map) from its location on the phylogenetic graph used to build that map.
tools:::Rd_package_author("MPSEM") -- Maintainer: tools:::Rd_package_maintainer("MPSEM")
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 (or node) 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
argument, it is called within PEM.build with mroot = FALSE.
User must therefore make sure 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 parameters a and psi assuming single
values for the whole tree, whereas function PEM.forcedSimple
allows one to impose values to arguments a and psi of a
PEM-class object, while making the function produce the same
details as PEM.fitSimple would have produced; these details 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 produces the same output as
getGraphLocations, but for the ancestral species (i.e. the
nodes of the phylogeny) in order to estimate ancestral trait values.
Guénard, G., Legendre, P., and Peres-Neto, P. 2013. Phylogenetic eigenvector maps: a framework to model and predict species traits. Methods in Ecology and Evolution. 4: 1120--1131
Makarenkov, V., Legendre, L. & Desdevise, Y. 2004. Modelling phylogenetic relationships using reticulated networks. Zoologica Scripta 33: 89--96
Blanchet, F. G., Legendre, P. & Borcard, D. 2008. Modelling directional spatial processes in ecological data. Ecological Modelling 215: 325--336
PEM-class
### Synthetic example
## This example describes the phyogeny of 7 species (A to G) in a tree with 6
## nodes, presented in Newick format, read by function
## read.tree of package ape.
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=""))
t1 # Summary of the structure of the tree
summary(t1)
x <- Phylo2DirectedGraph(t1)
## Calculate the (binary) influence matrix; E1 to E12 are the tree edges
## Edge E12 comes from the tree origin
PEMInfluence(x)
PEMInfluence(x)[x$vertex$species,]
## Building phylogenetic eigenvector maps
PEM1 <- PEM.build(x)
PEM2 <- PEM.build(x, a = 0.2)
PEM3 <- PEM.build(x, a = 1)
PEM4 <- PEM.updater(PEM3,a=0.5)
## Print summary statistics about PEM1
print(PEM1)
## Extract the eigenvectors (species A--G, 6 eigenvectors)
as.data.frame(PEM4)
## Example of a made up set of trait values for the 7 species
y <- c(A=-1.1436265,B=-0.3186166,C=1.9364105,D=1.7164079,E=1.0013993,
F=-1.8586351,G=-2.0236371)
## Estimate a 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$optim # Optimisation results
## Force neutral evolution over the whole tree
PEMfrc1 <- PEM.forcedSimple(y=y,x=NULL,w=x,d="distance",sp="species",a=0)
PEMfrc1$x$edge$a # Steepness parameter forced on each individual edge
## Graph locations for target species X, Y, and Z not found in the original
## data set
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=""))
tpAll
summary(tpAll) # Summary of the structure of the tree
grloc <- getGraphLocations(tpAll, c("X","Y","Z"))
grloc
PEMfs2 <- PEM.fitSimple(y=y, x=NULL, w=grloc$x, d="distance", sp="species",
lower=0, upper=1)
PEMfs2
## Same as for PEMfs1$optim
PEMfs2$optim
## Get the PEM scores from the species graph locations:
PEMsc1 <- Locations2PEMscores(PEMfs2, grloc)
lm1 <- lm(y ~ V_2 + V_3 + V_5, data=PEMfs2)
## Making prdictions for the species in locations `grloc`
## using linear model `lm1`:
ypred <- predict(object=PEMfs2, targets=grloc, lmobject=lm1, interval="none")
## Removing species X, Y, and Z from the tree in `tpAll`:
tpModel <- drop.tip(tpAll, c("X","Y","Z"))
## Plot the results
layout(t(c(1,1,2)))
par(mar=c(6,2,2,0.5)+0.1)
plot(tpModel, show.tip.label=TRUE, show.node.label=TRUE, root.edge = TRUE,
srt = 0, adj=0.5, label.offset=0.08, font=1, cex=1.5, xpd=TRUE)
edgelabels(paste("E", 1:nrow(tpModel$edge), sep=""),
edge=1:nrow(tpModel$edge), bg="white", font=1, cex=1)
points(x=0.20,y=2.25,pch=21,bg="black")
lines(x=c(0.20,0.20,0.65), y=c(2.25,0.55,0.55), xpd=TRUE, lty=2)
text("X",x=0.69, y=0.55, xpd=TRUE, font=1, cex=1.5)
points(x=0.35, y=4.5,pch=21,bg="black")
lines(x=c(0.35,0.35,0.6), y=c(4.5,5.47,5.47), xpd=TRUE, lty=2)
text("Y", x=0.64, y=5.47, xpd=TRUE, font=1, cex=1.5)
points(x=0.35, y=3, pch=21, bg="black")
lines(x=c(0.35,0.35,0.55), y=c(3,3.5,3.5), xpd=TRUE, lty=2)
text("Z", x=0.59, y=3.5, xpd=TRUE, font=1, cex=1.5)
text(c("NX","NY","NZ"), x=c(0.20,0.35,0.35), y=c(2.25,4.5,3)+0.3*c(1,-1,-1),
font=1, cex=1)
add.scale.bar(length=0.1, cex=1.25)
par(mar=c(3.75,0,2,2)+0.1)
plot(x=y, y=1:7, ylim=c(0.45,7), xlim=c(-4,4), axes=FALSE, type="n", xlab="")
axis(1, label=c("-4","-2","0","2","4"), at=c(-4,-2,0,2,4))
abline(v=0)
## Plot the observed values
points(x=y, y=1:7, xlim=c(-2,2), pch=21, bg="black")
text("B)", x=-3.5, y=7, cex=1.5, xpd=TRUE)
text("Trait value", x=0, y=-0.5, cex=1.25, xpd=TRUE)
## Plot the predicted values
points(x=ypred, y=c(0.5,5.5,3.5), pch=23, bg="white", cex=1.25)
## Estimate the ancestral trait values
ANCloc <- getAncGraphLocations(x)
PEMfsAnc <- PEM.fitSimple(y=y, x=NULL, w=ANCloc$x, d="distance",
sp="species", lower=0, upper=1)
PEMfsAnc$optim
## Get the PEM scores from the species graph locations:
PEManc1 <- Locations2PEMscores(PEMfsAnc, ANCloc)
## Making predictions for the ancestral species whose locations are found in
## `ANCloc` using the linear model `lm1`:
y_anc <- predict(object=PEMfsAnc, targets=ANCloc, lmobject=lm1,
interval="confidence")
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