Assignment: unrooted trees

We often don’t root phylogenetic trees. This reduces the number of possible trees and is described by the equation:

Text: (2n-5)!/[2n-3*(n-3)!]

Rendered:

\(\frac{(2*n-5)!}{2^{n-3} * (n-3)!}\)

Assignment part 1

Modify the function used in the “number of phylogenetic trees” tutorial to work for unrooted trees.

Compare your results to http://carrot.mcb.uconn.edu/mcb396_41/tree_number.html

You can use the simplest form of the function which doesn’t have any additional argument, eg

The function is here; make the necessary changeas

# change the code below to work for an un-rooted tree
tree_count_unrooted <- function(n = 3){
  
  # change the denominator if need
  numerator   <- factorial(2*n-5)
  
  # change the denominator if needed
  denominator <- 2^(n-3)*factorial(n-3)
  trees  <- numerator / denominator 
  print(trees)
  if(n<3) {warning("This function is only valid for n>2")}
  
}

Assignment part 2

Create a function that will work for rooted OR unrooted trees. Do this by adding an additional argument like

type = “rooted”

and conditional additional statements like

if(type == "rooted){ #do this }

if(type == "unrooted){ #do something else }

Again, you can use the simplest form of the argument.

tree_count_varying <- function(n = 3, style = "rooted, unrooted"){
  
  if(style %in% "unrooted") {numerator   <- factorial(2*n-5)
  
  denominator <- 2^(n-3)*factorial(n-3) }
  
  if(style %in% "rooted") {numerator <- factorial(2*n-3)
  denominator <- 2^(n-2)*factorial(n-2)}
  trees  <- numerator / denominator 
  print(trees)
  if(n<3) {warning("This function is only valid for unrooted trees: n > 2 and for rooted trees: n > 1")}}