如何使用 R 创建简单的分支流程？

Question

I'm trying to use R to make a simple branching process to calculate the population of foxes over 10 generations using

I'm using lambda = 1.5, and I'm aware that the number of foxes in the initial generation can be calculated using rpois(1, 1.5) .

However, I'm stuck on how to create a function that calculates the population of the next generations, and adds up the total population together. If anyone could give some starting pointers that would be great.

Answer 1

I believe you are looking for a function like the following:

pois_bprocess <- function(generations, lambda, trace = TRUE){
  z_i <- rpois(1, lambda)
  i <- 1
  
  if(trace) print(paste(i, ':', z_i))
  
  while(i < generations){
    # draw z_i samples from a poisson distribution with lambda and sum them
    z_i <- sum(rpois(z_i, lambda)) 
    i <- i + 1
    if(trace) print(paste(i, ':', z_i))
  }
  
  return(z_i)
}


# Example usage : pois_bprocess(10, 1.5)
# Example usage : pois_bprocess(10, 1.5, trace = F)

Note that as the assumed lambda for the Poisson distribution at 1.5 results in a fairly high the chance to draw a zero early on and get stuck.

HTH