Assignment: unrooted trees

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

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

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

rooted: (2n-3)!/(2^(n-2))(n-2)!

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 <- function(n = 3){
  
  #eqn: (2n-5)!/[2n-3*(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

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

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