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
#unrooted: Nu=(2n-5)*(2n-7)*...*3*1=(2n-5)!/[2n-3*(n-3)!]
tree_count <- function(n = 3) # n - number of taxa
  {
    # changed numerator
    numerator <- factorial(2*n-5)
    #changed denominator
    denominator <- 2^(n-3)*factorial(n-3)
      
    trees <- numerator/denominator
    print(trees)
  
}
 tree_count()
## [1] 1

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.

phylo_tree <- function(n, type)
{
  if(type == "rooted")
  {
    numerator   <- factorial(2*n-3)
    denominator <- 2^(n-2)*factorial(n-2)
    
    trees  <- numerator / denominator 
    print(trees)
  }
  if(type == "unrooted")
  {
   
    numerator <- factorial(2*n-5)
    denominator <- 2^(n-3)*factorial(n-3)
    trees <- numerator/denominator
    print(trees)
  }
}

phylo_tree(11 ,type = "rooted")
## [1] 654729075
phylo_tree(11 ,type = "unrooted")
## [1] 34459425

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