How to remove loop from the following model function? - r

Question

I'm rewriting some code, and I am currently creating a small population model. I have re-created the current model function below from a book, it's a simple population model based on a few parameters. I've left them at default and returned the data frame. Everything works well. However, I was wondering whether I could somehow exclude the loop from the function.
I know R is great because of vectorized calculation, but I'm not sure in this case whether it would be possible. I thought of using something like lead/lag to do it, but would this work? Perhaps not as things need to be calculated sequentially?
# Nt numbers at start of time t
# Ct = removed at the end of time t
# Nt0 = numbers at time 0
# r = intrinsic rate of population growth
# K = carrying capacity
mod_fun = function (r = 0.5, K = 1000, N0 = 50, Ct = 0, Yrs = 10, p = 1)
{
# sets years to year value plus 1
yr1 <- Yrs + 1
# creates sequence of length years from year 1 to Yrs value +!
years <- seq(1, yr1, 1)
# uses years length to create a vector of length Yrs + 1
pop <- numeric(yr1)
# sets population at time 0
pop[1] <- N0
# creates a loop that calculates model for each year after first year
for (i in 2:yr1) {
# sets starting value of population for step to one calculated previous step
# thus Nt is always the previous step pop size
Nt <- pop[i - 1]
pop[i] <- max((Nt + (r * Nt/p) * (1 - (Nt/K)^p) -
Ct), 0)
}
# sets pop2 to original pop length
pop2 <- pop[2:yr1]
# binds together years (sequence from 1 to length Yrs),
# pop which is created in loop and is the population at the start of step t
# pop2 which is the population at the end of step t
out <- cbind(year = years, nt = pop, nt1 = c(pop2, NA))
# sets row names to
rownames(out) <- years
out <- out[-yr1, ]
#returns data.frame
return(out)
}
result = mod_fun()
This is what the output looks like. Basically rowwise starting from row 1 given the starting population of 50 the loop calculates nt1 then sets next nt row to lag(nt1) and then things continue in a similar fashion.
result
#> year nt nt1
#> 1 1 50.0000 73.7500
#> 2 2 73.7500 107.9055
#> 3 3 107.9055 156.0364
#> 4 4 156.0364 221.8809
#> 5 5 221.8809 308.2058
#> 6 6 308.2058 414.8133
#> 7 7 414.8133 536.1849
#> 8 8 536.1849 660.5303
#> 9 9 660.5303 772.6453
#> 10 10 772.6453 860.4776
Created on 2022-04-24 by the reprex package (v2.0.1)

Answer 1

mod_fun = function (r = 0.5, K = 1000, N0 = 50, Ct = 0, Yrs = 10, p = 1)
{
years <- seq_len(Yrs)
pop <- Reduce(function(Nt, y)max((Nt + (r * Nt/p) * (1 - (Nt/K)^p) - Ct), 0),
years, init = N0, accumulate = TRUE)
data.frame(year = years, nt = head(pop,-1), nt1 = pop[-1])
}
year nt nt1
1 1 50.0000 73.7500
2 2 73.7500 107.9055
3 3 107.9055 156.0364
4 4 156.0364 221.8809
5 5 221.8809 308.2058
6 6 308.2058 414.8133
7 7 414.8133 536.1849
8 8 536.1849 660.5303
9 9 660.5303 772.6453
10 10 772.6453 860.4776