# Trees with a root edge

#### Richel Bilderbeek

#### 2023-08-21

This document intends to display a feature of the nLTT package: if a
stem is added to a phylogeny, the begin of that stem is set as the most
recent common ancestor.

Here I create a random phylogeny:

```
set.seed(42)
tree1 <- ape::rcoal(2)
tree1$edge.length <- tree1$edge.length / tree1$edge.length[1] # nolint ape variable name
```

I copy that same phylogeny and add a stem:

```
tree2 <- tree1
tree2$root.edge <- 1 # nolint ape variable name
```

Here is how the stemless phylogeny looks like:

```
ape::plot.phylo(tree1, root.edge = TRUE)
ape::add.scale.bar() #nolint
```

I set `root.edge`

to `TRUE`

, just show it is
absent.

Here is how the phylogeny with stem looks like:

```
ape::plot.phylo(tree2, root.edge = TRUE)
ape::add.scale.bar() #nolint
```

When overlaying their nLTT plots, one can expect two things:

- it is assumed that the phylogeny without a root is leading, and the
other phylogeny has its root removed
- it is assumed that the phylogeny with a root is leading, and the
other phylogeny is assumed to have a root of length zero

The nLTT package does the latter:

```
nLTT::nltt_plot(tree1, xlim = c(0, 1), ylim = c(0, 1))
nLTT::nltt_lines(tree2, col = "red")
```

When looking at the nLTT plot, one can eyeball that the nLTT
statistic (the surface between the two curves) is around about one
quarter.

When calculating the nLTT statistic, one needs to explicitly set to
take the stems into account:

`print(nLTT::nLTTstat_exact(tree1, tree2, ignore_stem = FALSE))`

`## [1] 0.25`

When ignoring the stems, the phylogenies are equal, thus have an nLTT
statistic of zero:

`print(nLTT::nLTTstat_exact(tree1, tree2, ignore_stem = TRUE))`

`## [1] 0`