Exploring trees with treespace
We first load treespace, and the packages required for graphics:
The function treespace defines typologies of phylogenetic trees using a two-step approach:
perform pairwise comparisons of trees using various (Euclidean) metrics; by default, the comparison uses the Kendall and Colijn metric (Kendall and Colijn, 2016) which is described in more detail below; other metrics rely on tip distances implemented in adephylo (Jombart et al., 2010) and phangorn (Schliep 2011).
use Metric Multidimensional Scaling (MDS, aka Principal Coordinates Analysis, PCoA) to summarise pairwise distances between the trees as well as possible into a few dimensions; the output of the MDS is typically visualised using scatterplots of the first few Principal Components (PCs); this step relies on the PCoA implemented in ade4 (Dray and Dufour, 2007).
The function treespace performs both tasks, returning both the matrix of pairwise tree comparisons ($D), and the PCoA ($pco). This can be illustrated using randomly generated trees:
# generate list of trees
suppressWarnings(RNGversion("3.5.0"))
set.seed(1)
x <- rmtree(10, 20)
names(x) <- paste("tree", 1:10, sep = "")
# use treespace
res <- treespace(x, nf=3)
names(res)## [1] "D" "pco"## $D
## tree1 tree2 tree3 tree4 tree5 tree6 tree7 tree8 tree9
## tree2 26.00
## tree3 31.06 26.74
## tree4 42.85 42.12 44.44
## tree5 30.66 27.71 27.37 44.79
## tree6 36.50 31.18 30.18 41.81 31.59
## tree7 34.64 28.71 29.48 40.35 31.11 32.37
## tree8 28.97 26.29 24.45 43.74 23.47 30.41 29.00
## tree9 29.63 27.42 27.48 45.61 26.31 30.89 29.77 24.60
## tree10 34.87 30.00 29.44 44.97 34.06 31.05 34.41 31.54 32.59
##
## $pco
## Duality diagramm
## class: pco dudi
## $call: dudi.pco(d = D, scannf = is.null(nf), nf = nf)
##
## $nf: 3 axis-components saved
## $rank: 9
## eigen values: 142.1 76.52 62.69 49.88 41.07 ...
## vector length mode content
## 1 $cw 9 numeric column weights
## 2 $lw 10 numeric row weights
## 3 $eig 9 numeric eigen values
##
## data.frame nrow ncol content
## 1 $tab 10 9 modified array
## 2 $li 10 3 row coordinates
## 3 $l1 10 3 row normed scores
## 4 $co 9 3 column coordinates
## 5 $c1 9 3 column normed scores
## other elements: NULLPairwise tree distances can be visualised using adegraphics:
# table.value with some customization
table.value(res$D, nclass=5, method="color",
symbol="circle", col=redpal(5))
The best representation of these distances in a 2-dimensional space is given by the first 2 PCs of the MDS. These can be visualised using any scatter plotting tool; here we use the treespace function plotGroves, based on the adegraphics function scatter:
Alternatively, plotGrovesD3 creates interactive plots based on d3.js:
The functionality of treespace can be further illustrated using ape’s dataset woodmouse, from which we built the 201 trees supplied in woodmiceTrees using the neighbour-joining and bootstrapping example from the ape documentation.
data(woodmiceTrees)
wm.res <- treespace(woodmiceTrees,nf=3)
# PCs are stored in:
head(wm.res$pco$li)## A1 A2 A3
## 1 -0.9949 -1.363 -0.7918
## 2 -0.6137 -1.014 -0.6798
## 3 2.6667 4.219 -2.9293
## 4 -13.6081 1.854 1.0947
## 5 2.1980 4.176 -3.1960
## 6 3.6013 4.865 2.9853Packages such as adegraphics and ggplot2 can be used to make alternative plots, for example visualising the density of points within the space.
The treespace function multiDist simply performs the pairwise comparison of trees and outputs a distance matrix. This function may be preferable for large datasets, and when principal co-ordinate analysis is not required. It includes an option to save memory at the expense of computation time.