You can do this on your own data, or on included data here.

##Continuous data

library(geiger)
library(pic)
tree.primates <- read.tree(text="((((Homo:0.21,Pongo:0.21):0.28,Macaca:0.49):0.13,Ateles:0.62):0.38,Galago:1.00);") #using examples from ape ?pic
X <- c(4.09434, 3.61092, 2.37024, 2.02815, -1.46968)
Y <- c(4.74493, 3.33220, 3.36730, 2.89037, 2.30259)
names(X) <- names(Y) <- c("Homo", "Pongo", "Macaca", "Ateles", "Galago")
pic.X <- pic(X, tree.primates)
pic.Y <- pic(Y, tree.primates)

Now, positivitize the contrasts and do a regression through the origin.

##Discrete data

require("corHMM")
?corHMM
data(primates)
ls()
print(primates)
require(phytools)

Just to make this a better dataset for our exercise, I’m going to change some of the states (I want to have all four trait combinations present). For actual analyses, of course, DO NOT INVENT YOUR DATA.

First, a review of discrete state models:

primates$trait[which(grepl("Hylobates",primates$trait[,1])),2]<-1

trait1<-primates$trait[,2]
names(trait1)<-primates$trait[,1]
plotSimmap(make.simmap(primates$tree, trait1), pts=FALSE, fsize=0.8)
rate.mat.er<-rate.mat.maker(rate.cat=1, hrm=FALSE, ntraits=1, nstates=2, model="ER")
print(rate.mat.er)

What does this matrix mean?

pp.er<-corHMM(primates$tree,primates$trait[,c(1,2)],rate.cat=1,rate.mat=rate.mat.er,node.states="marginal")
print(pp.er)

What do these results mean?

rate.mat.ard<-rate.mat.maker(rate.cat=1, hrm=FALSE, ntraits=1, nstates=2, model="ARD")
print(rate.mat.ard)

And these?

pp.ard<-corHMM(primates$tree,primates$trait[,c(1,2)],rate.cat=1,rate.mat=rate.mat.ard,node.states="marginal")
print(pp.ard)

which model is better?

Now let’s look at multiple traits.

This is a matrix with four states

rate.mat.er.4state<-rate.mat.maker(rate.cat=1, hrm=FALSE, ntraits=1, nstates=4, model="ER")
print(rate.mat.er.4state)

Convert the two binary traits into a single four character state

fourstate.trait<-rep(NA,Ntip(primates$tree))
for(i in sequence(Ntip(primates$tree))) {
    if(primates$trait[i,2]==0 && primates$trait[i,3]==0) {
        fourstate.trait[i]<-0
    }   
    if(primates$trait[i,2]==0 && primates$trait[i,3]==1) {
        fourstate.trait[i]<-1
    }   
    if(primates$trait[i,2]==1 && primates$trait[i,3]==0) {
        fourstate.trait[i]<-2
    }   
    if(primates$trait[i,2]==1 && primates$trait[i,3]==1) {
        fourstate.trait[i]<-3
    }   
}
fourstate.data<-data.frame(Genus_sp=primates$trait[,1], T1=fourstate.trait)

print(rayDISC(primates$tree, fourstate.data, ntraits=1, model="ER", node.states="marginal"))
print(rayDISC(primates$tree, fourstate.data, ntraits=1, rate.mat=rate.mat.er.4state, node.states="marginal", model="ARD"))
rate.mat.ard.4state<-rate.mat.maker(rate.cat=1, hrm=FALSE, ntraits=1, nstates=4, model="ARD")
print(rate.mat.ard.4state)

Now let’s make the equivalent of a GTR matrix:

rate.mat.gtr.4state<-rate.mat.ard.4state
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(1,4))
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(2,6))
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(3,8))
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(4,6))
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(5,7))
rate.mat.gtr.4state<-rate.par.eq(rate.mat.gtr.4state, c(6,7))
print(rate.mat.gtr.4state)

print(rayDISC(primates$tree, fourstate.data, ntraits=1, rate.mat= rate.mat.gtr.4state, node.states="marginal", model="ARD"))

Now make a model like Pagel 1994

print(rate.mat.maker(rate.cat=1, hrm=FALSE, ntraits=2, nstates=2, model="ARD"))
rate.mat.pag94<-rate.par.drop(rate.mat.ard.4state, drop.par=c(3,5,8,10))
print

Now that you have some introduction, there are two routes:

##Route 1

Construct a model to test if state 1 can never be lost

Experiment with the effects of frequencies at the root.

Create and use a model to see if transitions from 00 go to 11 only via 01.

##Route 2

Maddison and FitzJohn (2015) pretty convincingly show (to me) that Pagel (1994) is just not a good method. Ok. So work on a fix. They point to Read and Nee (1995) as a low power but possible solution. Look at their appendix, especially, and write an implementation.