Branching Processes R Code Tree Diagram

Question

Code:

1) Write an R code for a function that simulates a branching process of a Poisson progeny distribution with mean 𝜆 and for number of generations n.

2) Then run the simulations for several values of 𝜆 like .5, 1, and 2 for a reasonable number of generations like 3, 4 or 5.

3) Make a plot of the resulting tree. (Think about placing the generations on concentric circles and make line plots between coordinates of the parents and their children).

Answer 1

install.packages("data.tree")

install.packages("DiagrammeR")

library(data.tree)

library(DiagrammeR)

#creates amount of leaves specified by poisson distribution

add.children <- function(node){

name <- node$name

children <- rpois(1,lambda) #pulled from poisson distribution

if (children == 0){

node$AddChild("X")

}

else{

for (i in c(1:children)){

name.new <- paste(name,".", i, sep = "")

node$AddChild(name.new)

}

}

}

#searches siblings for available leaf, if not moves up a level

next.leaf <- function(node){

sib <- node$siblings

print(node$parent$name)

temp <- node$parent

if(length(sib)>0){

for (i in c(1:length(sib))){

node.sib <- sib[[i]]

if(node.sib$isLeaf){

temp <- node.sib

}

}

}

return(temp)

}

depth <- 3

lambda <- 4

parent <- Node$new("1")

add.children(parent)

node <- parent$children[[1]]

if(node$name == "X"){

node <- parent

}

while (node$name != parent$name){

print("i")

if (node$level>depth||node$name == "X"){

print("j")

node <- node$parent

while(!(node$isLeaf) & node$name != parent$name){

node <- next.leaf(node)

}

}

if (node$level<=depth & node$isLeaf & node$name != parent$name){

add.children(node)

if (node$leafCount > 0){

node <- node$children[[1]]

}

}

}

parent

plot(parent)