Add internal node to phylogenetic tree

I need to add an internal node in a phylogenetic tree, along one of the trees branches.

For example, let's say that I have the following tree:

library(ape)
library(phytools)

tree <- rtree(4)
plot(tree,no.margin=T,label.offset=0.1)
nodelabels()
tiplabels()
edgelabels()

I would like to insert a new node along branch 5 at time (edge.length) t, for example:

How could I do that?

You'll need to update the tree$edge table and the tree$edge.length vectors. You can find information on how these elements work in a "phylo" object here.

Here's a quick function that should help you do do that on any tree:

#@param tree a phylo object
#@param element.IDs the numbers before and after the internal node
#@param edge.length the added edge length
add.internal.node <- function(tree, element.IDs, edge.length) {

    ## Find the edge in the edge table
    tree_edge <- tree$edge
    old_edge <- which(apply(tree_edge, 1, function(x, IDs) all(x == IDs), IDs = element.IDs))
    if(length(old_edge) == 0) {
        stop("edge not found")
    }

    ## Add the new edge
    tree_edge <- rbind(tree_edge[-old_edge, ], c(element.IDs[1], "new"), c("new", element.IDs[2]))

    ## Adding a new edge length
    if(!is.null(tree$edge.length)) {
        new_edge_lengths <- c(tree$edge.length, edge.length)
    }

    ## Re-ordering node labels for the new edge table
    ## (element IDs need to be ordered in phylo objects)
    #1- name the new node (should be ID+1)
    tree_edge <- gsub("new", paste0("new", element.IDs[1]+1), tree_edge)
    #2- update all the nodes after ID+1
    update.nodes <- function(x, ID) {
        if(!is.na(as.integer(x))) {
            ## Is not NA so it's a node (update the value if it's higher than the ID)
            return(ifelse(as.integer(x) > ID, as.integer(x)+1, x))
        } else {
            ## Is NA so it's the new node (leave it be for now)
            return(x)
        }
    }
    ## Update all nodes
    tree_edge <- apply(tree_edge, c(1,2), update.nodes, ID = element.IDs[1])
    ## Remove the "new" bit and make everything integers again
    tree_edge <- gsub("new", "", tree_edge)
    tree_edge <- apply(tree_edge, c(1,2), as.integer)

    ## Update the tree with the new node and the new edge.length
    tree$edge <- tree_edge
    if(!is.null(tree$edge.length)) {
        tree$edge.length <- new_edge_lengths
    }
    tree$Nnode <- tree$Nnode+1

    return(tree)
}

You can then add a node to your tree using the following pipeline:

## Generate a similar tree as in the example
set.seed(20)
tree <- rtree(4)
plot(tree)
axisPhylo(); nodelabels(); tiplabels(); edgelabels()

## Adding a node between elements 7 (node) and 4 (tip)
test <- add.internal.node(tree, element.IDs = c(7, 4), edge.length = 0.1)
plot(test)
axisPhylo(); nodelabels(); tiplabels(); edgelabels()