Looping through parameters to get equilibrium with deSolve - r

Question

I struggle with loops intuitively. I have a simple consumer-resource model, and I want to loop through values of resource growth rate g to get final state values to then plot equilibrium as a function of the parameter values. This is what I have so far:
param.values = seq(from = 1, to = 10, by = 1)
variable = rep(0,length(param.values))
for (i in 1:length(param.values)){
state <- c(r = 1, n = 1)
parameters = c(g = variable[i],# resource growth rate
d = 0.5, # n mortality rate
k = 5, # r carrying capacity
c = 1, # consumption rate of n on r
e = 1, # conversion efficiency for n on r
h = 1 # handling time n on r
)
function1 <- function(times, state, parameters) {
with(as.list(c(state, parameters)),{
# rate of change
dr = variable[i]*r*(1 - (r/k)) - (c*n*r/(1+(h*c*r)))
dn = (e*c*n*r/(1+(h*c*r)))- n*d
# return the rate of change
list(c(dr, dn))
})
}
times <- seq(0, 100, by = 1)
out <- ode(y = state, times = times, func = function1, parms = parameters)
sol <- out[101, 2:3] # trying to get last equilibrium value to plot against param values...
print(sol[i])
}
plot(sol[,1] ~ param.values)
plot(sol[,2] ~ param.values)
I think I have thinks right up until the ode function - where should I be indexing i after this? I hope this makes sense.

Answer 1

Your approach had several issues, so I tried to re-organize it so that it runs through. But, as your model shows a stable cycle, it does not reach an equilibrium.
Here a few hints
The loop should only contain things that change during the simulation. Fixed code segments should come before the loop. This is easier to maintain and faster.
First, run the model without the loop, to see whether it works.
Then define a data structure (matrix or data frame) to store the results.
Here one approach how it can be implemented:
library("deSolve")
## define as much as possible outside the loop
function1 <- function(times, state, parameters) {
with(as.list(c(state, parameters)),{
# rate of change
dr = g*r*(1 - (r/k)) - (c*n*r/(1+(h*c*r)))
dn = (e*c*n*r/(1+(h*c*r)))- n*d
# return the rate of change
list(c(dr, dn))
})
}
state <- c(r = 1, n = 1)
parameters = c(g = 1, # resource growth rate
d = 0.5, # n mortality rate
k = 5, # r carrying capacity
c = 1, # consumption rate of n on r
e = 1, # conversion efficiency for n on r
h = 1 # handling time n on r
)
times <- seq(0, 100, by = 1)
## first test single run of model
out <- ode(y = state, times = times, func = function1, parms = parameters)
plot(out)
## It runs and we see a cycling model. I suspect it has no equilibrium!
param.values = seq(from = 1, to = 10, by = 1)
## define a matrix where results can be stored
sol <- matrix(0, nrow=length(param.values), ncol=2)
for (i in 1:length(param.values)){
## replace single parameter g with new value
parameters["g"] <- param.values[i]
out <- ode(y = state, times = times, func = function1, parms = parameters)
## store result of last value in row of matrix.
## Note that it may not be an equilibrium
sol[i, ] <- out[101, 2:3] # trying to get last equilibrium value to plot against param values...
print(sol[i, ])
}
plot(sol[,1] ~ param.values, type="l")
plot(sol[,2] ~ param.values, type="l")
## We see that the model has no equilibrium.
There are several other ways and, as said, the model has no equilibrium. Here another model example, a so-called chemostat with equilibrium.