The challenge problem was as follows.
Download the following two files:
Use the phytools function fitPagel to fit Pagel's model for correlated
binary-trait evolution on the tree. What do you find? Visualize the character data on
the tree. What does this tell you about the basis for your result?
First, let's load packages:
library(phytools)
## Loading required package: ape
## Warning: package 'ape' was built under R version 3.3.0
## Loading required package: maps
##
## # maps v3.1: updated 'world': all lakes moved to separate new #
## # 'lakes' database. Type '?world' or 'news(package="maps")'. #
Now load data & tree from file:
tree<-read.tree("fitPagel-challenge.tre")
X<-read.csv("fitPagel-challenge.csv",row.names=1)
Now, let's apply Pagel's (1994) method using fitPagel:
x<-setNames(X[,1],rownames(X))
y<-setNames(as.factor(X[,2]),rownames(X))
fitted.model<-fitPagel(tree,x,y)
fitted.model
##
## Pagel's binary character correlation test:
##
## Independent model rate matrix:
## a|0 a|1 b|0 b|1
## a|0 -0.1021196 0.0000000 0.1021196 0.0000000
## a|1 3.5809628 -3.6830823 0.0000000 0.1021196
## b|0 0.1021198 0.0000000 -0.1021198 0.0000000
## b|1 0.0000000 0.1021198 3.5809628 -3.6830825
##
## Dependent model rate matrix:
## a|0 a|1 b|0 b|1
## a|0 0.00000 0.00000 0.00000 0.00000
## a|1 18.34017 -36.69125 0.00000 18.35108
## b|0 0.00000 0.00000 -61.01172 61.01172
## b|1 0.00000 0.00000 60.99491 -60.99491
##
## Model fit:
## log-likelihood
## independent -47.46589
## dependent -24.95332
##
## Hypothesis test result:
## likelihood-ratio: 45.02514
## p-value: 3.928399e-09
##
## Model fitting method used was fitMk
Obviously, the more parameter rich “dependent” model fits better. But let's visualize our data on the tree to see if it tells us anything more:
dotTree(tree,X,fsize=0.6,ftype="i")
Now, we see that there is only one change in character one - but that change (or, rather, trait difference) defines a shift in rate or process for character 2.
This is essentially the result identified by Maddisson & Fitzjohn (2015).
Written by Liam J. Revell. Last updated 12 Mar. 2016.