## Tuesday, April 16, 2013

### CI on LTT plot from a sample of trees

Today, someone posted the following query to R-sig-phylo:

Does anyone know of a good implementation of an LTT plot that can draw a Confidence Interval or HPD interval from a set of trees? I've seen things like `ltt` in phytools that can draw one line for each tree in the sample. However, this can look a bit messy, and I'd ideally love to just plot the 95% CI or HPD of the ages/lineages in the trees. Has anyone seen anything like this?

Dave Bapst promptly responded that there is a function in his paleotree that can do this. For example:

> require(phytools)
> require(paleotree)
> trees<-pbtree(n=50,t=log(50)-log(2),method="direct", nsim=200,quiet=T)
> multiDiv(trees,(log(50)-log(2))/100,plotLogRich=TRUE)

This is pretty cool.

It occurred to me that there are two different CIs that we might be interested in: the CI(lineages), given a time in the past; or the CI(time) given a number of lineages. The former, CI(n|t), can be read as the (say) 95% CI of the number of lineages alive at time t; whereas the latter, CI(t|n), is the 95% CI on the timing of the nth speciation event.

Even before Dave responded, especially because phytools was mentioned in the query, I'd already started working on this. Here's a link to a function that does this, and also computes the mean (rather than median), and returns the result invisibly. So, for instance:

trees<-pbtree(n=50,t=log(50)-log(2),method="direct",nsim=200,quiet=T)
> # same as paleotree
> XX<-ltt95(trees,log=TRUE)
> # here is the object returned
> XX
time low(lineages) lineages high(lineages)
[1,] 0.00000000             1      1.0              1
[2,] 0.03218876             2      2.0              3
[3,] 0.06437752             2      2.0              3
[4,] 0.09656627             2      2.0              3
[5,] 0.12875503             2      2.0              4
[6,] 0.16094379             2      2.0              4
[7,] 0.19313255           ...

Now on time with the mode changed to "mean":

> # now on time + mode="mean"
> ltt95(trees,log=TRUE,method="times",mode="mean")

It also works for trees with varying total length or number of tips (although in the latter case, only for method="lineages". So, for instance:

> treesN<-pbtree(n=50,nsim=200)
> ltt95(treesN,log=TRUE,method="lineages",mode="mean")

Or:
> treesT<-pbtree(t=log(50)-log(2),nsim=200)
> ltt95(treesT,log=TRUE,method="lineages",mode="mean")

Finally, we can set an arbitrary α level. For instance:

> XX<-ltt95(trees,alpha=0.1,mode="mean",log=FALSE)

Basically, you get the idea. Please note that the version of pbtree that I'm using in the above simulations is in a non-CRAN phytools update (phytools 0.2-46).

1. Thanks Liam, very useful. Any chance to add the expectation to the plot too?

1. For a fixed t & N the expectation under pure-birth is just exponential growth at rate of (log(N)-log(2))/t. To add this curve, just do:

ltt95(trees,...) # ... = any other options of ltt95
x<-0:100/100*t
y<-2*exp(((log(N)-log(2))/t)*x)
lines(x,y,...) # ... = any other options of lines

Let us know if that works. Liam

2. Thanks Liam! This is very helpful. I am wondering if there is a way to reverse the time axis?

3. This comment has been removed by the author.

4. Hi Liam and yhank you fot this useful function, please can you tell me if you have the way to reverse the time axis, I try it wit xaxis="negative" but i have the same resulte as before.
thank

Note: due to the very large amount of spam, all comments are now automatically submitted for moderation.