Thursday, November 1, 2012

Visualizing the posterior density of a binary character on the tree

A phytools user recently asked:

is it possible to use the simmap function also on 1000 trees and plot a summary of the 1000 maps on the tree?

Now, I'm pretty sure what he wants to do is plot the posterior probabilities for internal nodes based on the mappings for those nodes. (Actually, states are only mapped on branches, but any mapping implies a set of states at internal nodes.) This requires a few tricks, but is not too hard. It occurred to me, however, that (at least for a binary character) we could represent the probability density of being in each state along all the edges of the tree based on our set of mappings. We can do this by integrating information from all stochastic maps into a probability for each part of each branch in the tree.

I just wrote a function to do this. Right now it will only allow a binary character with states "0" & "1", and it only maps probability on a blue→red scale. I will probably incorporate this into the phytools function fancyTree, just to minimize the proliferation of plotting functions within phytools. For now, though, it is a stand-alone function called densityMap (direct link to code here). Note that it uses a new version of plotSimmap, so you may want to download that too if you want to try it (direct link here).

Let's try it:

> source("densityMap.R")
> source("plotSimmap.R")
> # simulate tree
> tree<-pbtree(n=100,scale=1)
> # simulate stochastic history & binary state on tree
> Q<-matrix(c(-2,2,2,-2),2,2,dimnames=list(c(0,1),c(0,1)))
> tree<-sim.history(tree,Q)
> # generate stochastic maps
> trees<-make.simmap(tree,tree$states,nsim=100)
> # now map posterior density
> densityMap(trees,res=1000)
sorry - this might take a while; please be patient
>

I don't know. . . . I think that's pretty cool.

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