I've written some code that has a logistic growth component (i.e. as N approaches the 'carrying capacity' it grows at a slower rate, until when it reaches the 'carrying capacity' it stops growing). However, when I run it in R it doesn't seem to be working. Some populations end up being larger than the carrying capacity. I've looked at the maths and its all OK. So I think that the problem is that dN/dt is only being calculated once for each population. Does anyone know how to fix this problem?
Any help would be greatly appreciated!
Example code below:
library('optimbase')
library('deSolve')
library('tidyverse')
K = 150000 #carrying capacity
deaths = 0.2567534 #death rate
treesize = 0.23523 #resource size
K_mat = K*ones(10, 1) #matrix of Ks
death_mat = deaths*ones(10, 1) #matrix of deathrates
tree_mat = treesize*ones(11, 1) #matrix of resources
for_mat <- matrix(rbinom(11 * 10, 1, 0.2), ncol = 11, nrow = 10) #connection
#matrix of foraging
parameters <- c(for_mat, tree_mat, death_mat, K_mat) #outline parameters
N <- runif(10,0,K)
state <- N #starting state
nestchange <- function(t, state, parameters){
with(as.list(c(state, parameters)),{
r = for_mat %*% tree_mat - death_mat
dNdt = r*N - r*N*(N/K_mat)
list(c(dNdt))
})
}
times <- seq(0,100)
out <- ode (y = state,
times = times,
func = nestchange,
parms = parameters)
results <- as.data.frame(out)
results <- gather(results, 'nest', 'N', 2:11)
ggplot(data=results,
aes(x=time, y=N, colour=nest)) +
geom_line() +
theme_bw()
Should your function actually be,
nestchange <- function(t, state, parameters){
with(as.list(c(state, parameters)),{
r <- for_mat %*% tree_mat - death_mat
dNdt <- r*state - r*state*(state/K_mat)
list(c(dNdt))
})
}
as the ODE solver is passing state to the function at each time step, yet the function is using the variable N for the calculations instead which isn't updated by the ODE solver.