gm.prcomp: Principal components analysis of shape data

Description

Function performs PCA on Procrustes shape coordinates

Usage

gm.prcomp(A, phy = NULL, ...)

Arguments

A 3D array (p x k x n) containing Procrustes shape variables for a set of aligned specimens

phy

An optional phylogenetic tree of class phylo

...

Other arguments passed to scale

Value

An object of class "gm.prcomp" contains a list of results for each of the PCA approaches implemented. Each of these lists includes the following components:

Principal component scores for all specimens.

anc.x

Principal component scores for the ancestors on the phylogeny.

The singular values of the decomposed VCV matrix.

rotation

The matrix of variable loadings, i.e. the eigenvectors of the decomposed matrix.

shapes

A list with the shape coordinates of the extreme ends of all PC axes.

ancestors

The matrix of estimated ancestral shapes, if a phylogeny is used.

Details

The function performs a principal components analysis of shape variation. It also allows a phylomorphospace approach, where the user can provide a phylogeny and obtain a graph with estimated ancestral shape values and the tree projected into PCA space.

PLOTTING: Contrary to previous geomorph implementations, gm.prcomp does not produce plots. For plotting options of gm.prcomp class objects combine plot.gm.prcomp and picknplot.shape following the examples below. Note that trying to plot the full result of gm.prcomp will give an error. Choose a specific PCA method to be plotted, by pointing to one of the components of the list returned by gm.prcomp.

Examples

Run this code

# NOT RUN {
 data(plethspecies) 
 Y.gpa <- gpagen(plethspecies$land)    #GPA-alignment
 
 ### PCA 
 pleth.raw <- gm.prcomp(Y.gpa$coords)
 summary(pleth.raw)
 
 ### PCA with phylogeny (result is same as above, but with additional components)
 pleth.phylo <- gm.prcomp(Y.gpa$coords, phy = plethspecies$phy)
 summary(pleth.phylo)
 
 #### Plotting
 plot(pleth.raw)
 gps <- as.factor(c(rep("gp1", 5), rep("gp2", 4))) # Two random groups
 par(mar=c(2, 2, 2, 2))
 plot(pleth.raw, pch=22, cex = 1.5, bg = gps) # Modify options as desired
 #  Add things as desired using standard R plotting
 text(par()$usr[1], 0.1*par()$usr[3], labels = "PC1 - 45.64%", pos = 4, font = 2)
 text(0, 0.95*par()$usr[4], labels = "PC2 - 18.80%", pos = 4, font = 2)
 legend("topleft", pch=22, pt.bg = unique(gps), legend = levels(gps))
 
 ### Phylomorphospace plot
 plot(pleth.phylo, pch=21, bg=1:nrow(pleth.phylo$x), phylo = TRUE,
      phylo.par = list(edge.color="grey", node.cex=0)); title(main="phylomorphospace")
 text(pleth.phylo$x, labels = labels(pleth.phylo$x)[[1]],
      pos = 2, font = 4) 
 text(pleth.phylo$anc.x, labels = 1:nrow(pleth.phylo$anc.x),
      adj = c(-0.1, -0.1), font = 2) 
 
 ### Visualize shape variation using picknplot.shape Because picknplot requires 
 ### user decisions, the following example
 ### is not run (but can be with removal of #).
 ### For detailed options, see the picknplot help file
 # picknplot.shape(plot(pleth.phylo))
 

# }