Failed check for discrete-valued parameters in distribution dbin JAGS

I am trying to recreate an Integrated Population Model from Kery & Schaub's book "Bayesian Population Analysis using WinBUGS" in "Chapter 11 – Estimation of Demographic Rates, Population Size, and Projection Matrices from Multiple Data Types Using Integrated Population Models".

I am trying to use JAGS rather than WinBUGS, but I keep getting this error message:

"Failed check for discrete-valued parameters in distribution dbin"

Here is the data and the code - any idea what I am doing wrong? I suspect it is to do with Ntot not being a whole number but I am not sure. I am using R2jags in RStudio.

Many thanks

  `#Data
   #Population counts (from years 1 to 10)
   y <- c(45, 48, 44, 59, 62, 62, 55, 51, 46, 42)

  #Capture-recapture data (in m-array format, from years 1 to 10)
  m <- matrix(c(11, 0, 0, 0, 0, 0, 0, 0, 0, 70,

      0, 12, 0, 1, 0, 0, 0, 0, 0, 52,

      0, 0, 15, 5, 1, 0, 0, 0, 0, 42,

      0, 0, 0, 8, 3, 0, 0, 0, 0, 51,

      0, 0, 0, 0, 4, 3, 0, 0, 0, 61,

      0, 0, 0, 0, 0, 12, 2, 3, 0, 66,

      0, 0, 0, 0, 0, 0, 16, 5, 0, 44,

      0, 0, 0, 0, 0, 0, 0, 12, 0, 46,

      0, 0, 0, 0, 0, 0, 0, 0, 11, 71,

      10, 2, 0, 0, 0, 0, 0, 0, 0, 13,

      0, 7, 0, 1, 0, 0, 0, 0, 0, 27,

      0, 0, 13, 2, 1, 1, 0, 0, 0, 14,

      0, 0, 0, 12, 2, 0, 0, 0, 0, 20,

      0, 0, 0, 0, 10, 2, 0, 0, 0, 21,

      0, 0, 0, 0, 0, 11, 2, 1, 1, 14,

      0, 0, 0, 0, 0, 0, 12, 0, 0, 18,

      0, 0, 0, 0, 0, 0, 0, 11, 1, 21,

      0, 0, 0, 0, 0, 0, 0, 0, 10, 26), ncol = 10, byrow = TRUE)
   #Productivity data (from years 1 to 9)
   J <- c(64,132,86,154,156,134,116,106,110)# number

   R <- c(21, 28, 26, 38, 35, 33, 31, 30, 33)#surveyed broods

   #Specify model in JAGs
   sink("ipm.jags")
   cat("

   model {

  # Integrated population model

  # - Age structured model with 2 age classes:

  # 1-year old and adults (at least 2 years old)

  # - Age at first breeding = 1 year

  # - Prebreeding census, female-based

  # - All vital rates assumed to be constant

  # 1. Define the priors for the parameters

  # Observation error
  tauy <- pow(sigma.y, −2)
  sigma.y ~ dunif(0, 50)
  sigma2.y <- pow(sigma.y, 2)
  # Initial population sizes
  N1[1]~ dnorm(100, 0.0001)I(0,) # 1-year
  Nad[1]~ dnorm(100, 0.0001)I(0,) # Adults
  # Survival and recapture probabilities, as well as productivity
  for (t in 1:(nyears-1)){
  sjuv[t] <- mean.sjuv
  sad[t] <- mean.sad
  p[t] <- mean.p
  f[t] <- mean.fec
  }
  mean.sjuv ~ dunif(0, 1)
  mean.sad ~ dunif(0, 1)
  mean.p ~ dunif(0, 1)
  mean.fec ~ dunif(0, 20)
  # 2. Derived parameters
  # Population growth rate
  for (t in 1:(nyears−1)){
  lambda[t] <- Ntot[t+1] / Ntot[t]
  }
  # 3. The likelihoods of the single data sets

  # 3.1. Likelihood for population population count data (state-space model)

  # 3.1.1 System process
  for (t in 2:nyears){
  mean1[t] <- f[t−1] / 2 * sjuv[t−1] * Ntot[t−1]
  N1[t] ~ dpois(mean1[t])
  Nad[t] ~ dbin(sad[t-1],Ntot[t-1])# problem here I think
  }
  for (t in 1:nyears){
  Ntot[t] <- Nad[t] + N1[t]
  }
  # 3.1.2 Observation process
  for (t in 1:nyears){
  y[t] ~ dnorm(Ntot[t], tauy)
   }
  # 3.2 Likelihood for capture-recapture data: CJS model (2 age classes)
 # Multinomial likelihood
 for (t in 1:2*(nyears−1)){
 m[t,1:nyears] ~ dmulti(pr[t,], r[t])
 }
 # Calculate the number of released individuals
 for (t in 1:2*(nyears−1)){
 r[t] <- sum(m[t,])
 }
 # m-array cell probabilities for juveniles
for (t in 1:(nyears−1)){
# Main diagonal
q[t] <- 1−p[t]
pr[t,t] <- sjuv[t] * p[t]
# Above main diagonal
for (j in (t+1):(nyears−1)){
pr[t,j] <- sjuv[t]*prod(sad[(t+1):j])*prod(q[t:(j−1)])*p[j]
} #j
# Below main diagonal
for (j in 1:(t−1)){
pr[t,j] <- 0
} #j
# Last column: probability of non-recapture
pr[t,nyears] <- 1-sum(pr[t,1:(nyears-1)])
} #t
# m-array cell probabilities for adults
for (t in 1:(nyears-1)){
# Main diagonal
pr[t+nyears−1,t] <- sad[t] * p[t]
# Above main diagonal
for (j in (t+1):(nyears−1)){
 pr[t+nyears−1,j] <- prod(sad[t:j])*prod(q[t:(j-1)])*p[j]
} #j
# Below main diagonal
for (j in 1:(t−1)){
pr[t+nyears−1,j] <- 0
} #j
# Last column
pr[t+nyears−1,nyears] <- 1 − sum(pr[t+nyears−1,1:(nyears−1)])
} #t
# 3.3. Likelihood for productivity data: Poisson regression
for (t in 1:(nyears−1)){
J[t] ~ dpois(rho[t])
rho[t] <- R[t]*f[t]
}
}
",fill = TRUE)
sink()
#Bundle data
jags.data <- list(m = m, y = y, J = J, R = R, nyears = dim(m)[2])
#Initial values
inits <- function(){list(mean.sjuv = runif(1, 0, 1), mean.sad = runif(1, 0, 
          1), mean.p = runif(1, 0, 1), mean.fec = runif(1, 0, 10), N1 = 
          rpois(dim(m)[2], 30), Nad = rpois(dim(m)[2], 30), sigma.y = 
          runif(1, 0, 10))}

 #Parameters monitored
 parameters <- c("mean.sjuv", "mean.sad", "mean.p", "mean.fec", "N1", "Nad", 
 "Ntot", "lambda", "sigma2.y")
 #MCMC settings
 ni <- 20000
 nt <- 6
 nb <- 5000
 nc <- 3
 ipm <- jags(data=jags.data, inits=inits, parameters.to.save=parameters, 
 n.chains = nc, n.thin = nt, n.iter = ni, n.burnin =nb, model.file = 
 "ipm.jags")

Solution

Ntot must be an integer but it is currently the mixture of two normal distributions at t=1. This is likely the source of your error.

Here are your priors for t=1

N1[1]~ dnorm(100, 0.0001)I(0,) # 1-year
Nad[1]~ dnorm(100, 0.0001)I(0,) # Adults

Here is the system process:

for (t in 2:nyears){
mean1[t] <- f[t−1] / 2 * sjuv[t−1] * Ntot[t−1]
N1[t] ~ dpois(mean1[t])
Nad[t] ~ dbin(sad[t-1],Ntot[t-1])# problem here I think
}
for (t in 1:nyears){
Ntot[t] <- Nad[t] + N1[t]
}

What you could be missing is that N1[1] and Nad[1] should be Poisson random variables (or perhaps those two truncated normal distributions are supposed to represent lambdas for a Poission random variable. Possibly something like:

N1_lambda~ dnorm(100, 0.0001)I(0,) # 1-year
N1[1] ~ dpois(N1_lambda)
Nad_lambda~ dnorm(100, 0.0001)I(0,) # Adults
Nad[1] ~ dpois(Nad_lambda)