R deSolve: how are arguments en thus parameters interpreted? - r

Question

I'm building predator-prey models based on Lotka-Volterra derivatives in R using package deSolve. I define parameters, initial state and timesteps and the model function. Then I solve everyting using ode() or dede() when using a time lag.
I noticed there's a big difference in output depending on how you define the parameters WITHIN the model function and I really don't understand why. You can extract the parameters either by calling them via the argument: parms['r'], or via the previously defined object I passed to the argument: parameters['r']. Same result in both cases.
This is different voor the initial state though: calling the argument: y[1] or y['N'], gives a totally different result than calling it via the object passed to the argument: init[1] or init['N'].
Also in the DDE: there's a difference in time - tau vs times - tau and ylag <- y vs ylag <- init.
Why is there a different result for argument vs object for the initial state and time and not for the parameters? I need to comprehend this well in order to use the FME package in a later stage, so I hope someone can explain this behaviour.
My code:
library(deSolve)
## Parameters
parameters <- c(r = 0.25, K = 200, a = 0.01, c = 0.01, m = 1, tau = 7)
init <- c(N = 20, P = 2)
time <- seq(0, 100, by = 0.01)
## Ordinary DE
PreyPred <- function(times, y, parms){ #chose same argument names as ode()
N <- y['N'] #y[1] works as well
P <- y['P']
#N <- init['N'] #(or init[1]) gives a totally different result!
#P <- init['P']
r <- parms['r'] #growth rate prey parameters['r'] gives same result
K <- parms['K'] #carrying capacity prey
a <- parms['a'] #attack rate predator
c <- parms['c'] #assimilation rate (?) predator
m <- parms['m'] #mortality predator
dN <- r * N * (1-N/K) - a * N * P
dP <- c * N * P - m * P
return(list(c(dN, dP)))
}
oderesult <- ode(func = PreyPred, parms = parameters, y = init, times = time)
plot(oderesult, lwd = 2, mfrow = c(1,2))
## Delayed DE
PreyPredLag <- function(times, y, parms){
N <- y['N']
P <- y['P']
#N <- init['N']
#P <- init['P']
r <- parms['r'] #growth rate prey
K <- parms['K'] #carrying capacity prey
a <- parms['a'] #attack rate predator
c <- parms['c'] #assimilation rate (?) predator
m <- parms['m'] #mortality predator
tau <- parms['tau'] #time lag
tlag <- times - tau
#tlag <- time - tau #different result
if (tlag < 0)
ylag <- y
#ylag <- init
else
ylag <- lagvalue(tlag)
# dede
dN <- r * N * (1-N/K) - a * N * P
dP <- c * ylag[1] * ylag[2] - m * P
return(list(c(dN, dP), lag = ylag))
}
dederesult <- dede(func = PreyPredLag, parms = parameters, y = init, times = time)
plot(dederesult, lwd = 2, mfrow = c(2,2))

Answer 1

The observed behavior is correct. A short explanation:
'parms' is the local variable in the model function, while 'parameters' the global variable in the workspace. This is nothing special for deSolve, it is the general way how R works. The in most cases preferred way is to use the local variable.
For the states, this is indeed different. here the outer value 'init' is the initial value at the beginning, while the local 'y' is the current value for the time step.
The dede parameters are analogous. init is the start, y the instantaneous value, times is the global vector of all time steps and time the actual time step.