#' # Population Models
#' 
#' This file contains JAGS code for fitting each of the different populations models.  The models and priors
#' are specified exactly as in the PVAClone package.  The PVAClone package, however, does not allow one to specify the number
#' of clones =1, as done here (i.e., PVAClone does not allow one to fit models under a Bayesian framework). 
#' 
#'  
#---------------------------------------------------------------------------------------

#' ## Density Independent Models
#' 
#' 
#' ### Density-Independent Model Without Observation Error

di.noerror<-function(){ 
  N[1] <- exp(x[1]) 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
   } 
   a ~ dnorm(1, 0.01) 
   sigma <- exp(lnsigma) 
   lnsigma ~ dnorm(0, 1) 
   prcx <- 1/sigma^2 
} 

#' ### Density-Independent Model with Poisson Observation Error
#' 

di.Poisson<-function() { 
  N[1] <- O[1] 
  x[1] <- log(O[1]) 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
     O[j] ~ dpois(N[j]) 
  } 
  a ~ dnorm(1, 0.01) 
  sigma <- exp(lnsigma) 
  lnsigma ~ dnorm(0, 1) 
  prcx <- 1/sigma^2 
} 

#' ### Density-Independent Model with Log-Normal Observation Error
#' 
di.LogN<-function(){ 
  N[1] <- exp(y[1]) 
  x[1] <- y[1] 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
     y[j] ~ dnorm(x[j], prcy) 
  } 
  sigma <- exp(lnsigma) 
  tau <- exp(lntau) 
  lnsigma ~ dnorm(0, 1) 
  lntau ~ dnorm(0, 1) 
  a ~ dnorm(0, 0.01) 
  prcx <- 1/sigma^2 
  prcy <- 1/tau^2 
} 


#---------------------------------------------------------------------------------------

#' ## Ricker models
#' 
#' ### Ricker model without observation error
#' 
Ricker.noerror<-function() { 
  N[1] <- exp(x[1]) 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + b * N[j-1] + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
  } 
  a ~ dnorm(1, 0.01) 
  b ~ dnorm(0, 10) 
  sigma <- exp(lnsigma) 
  lnsigma ~ dnorm(0, 1) 
  prcx <- 1/sigma^2 
} 


#' ### Ricker model with Poisson observation error
#' 

Ricker.Poisson<-function() { 
  N[1] <- O[1] 
  x[1] <- log(O[1]) 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + b * N[j-1] + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
     O[j] ~ dpois(N[j]) 
  } 
  a ~ dnorm(1, 0.01) 
  b ~ dnorm(0, 10) 
  sigma <- exp(lnsigma) 
  lnsigma ~ dnorm(0, 1) 
  prcx <- 1/sigma^2 
} 


#' ### Ricker model with Log-Normal observation error
#' 
Ricker.LogN<-function(){ 
  N[1] <- exp(y[1]) 
  x[1] <- y[1] 
  for (j in 2:T) { 
     x[j] ~ dnorm(mu[j], prcx) 
     mu[j] <- a + b * N[j-1] + x[j-1] 
     N[j] <- min(exp(x[j]), 10000) 
     y[j] ~ dnorm(x[j], prcy) 
  } 
  sigma <- exp(lnsigma) 
  tau <- exp(lntau) 
  lnsigma ~ dnorm(0, 1) 
  lntau ~ dnorm(0, 1) 
  a ~ dnorm(0, 0.01) 
  b ~ dnorm(0, 10) 
  prcx <- 1/sigma^2 
  prcy <- 1/tau^2 
}