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

# change the code below to work for an un-rooted tree
tree_count <- function(n = 3){
  
  numerator <- factorial(2*n-5)
  
  denominator <- 2^(n-3)*factorial(n-3)
  trees  <- numerator / denominator 
  print(trees)
}

Assignment part 2

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

numberTrees <- function(n = 3, type = "rooted"){
  
  if(type == "rooted"){
  numerator <- factorial(2*n-3)
  denominator <- 2^(n-2)*factorial(n-2)
  trees  <- numerator / denominator 
  }
  
  if(type == "unrooted"){
  numerator <- factorial(2*n-5)
  denominator <- 2^(n-3)*factorial(n-3)
  trees  <- numerator / denominator 
  }
  
  print(trees)
}
numberTrees(11, "rooted")
## [1] 654729075
numberTrees(11, "unrooted")
## [1] 34459425

For this assignment, render to RRubps, submit the link, and submit a screen grab that contains