src/Yoichiro-DM-Model.R

In Conte-Ecology/singlePassDetection: Compares detection corrected abundance estimates for single and multiple pass fish surveys

model{
  
  #### Survival
  for(t in 1:(nYears-1)){
    for(i in 1:nSites){  
      for(a in 1:nAges){
        omega[i,t,a] <- 1/(1 + exp(-lomega.lim[i,t,a]))
        lomega.lim[i,t,a] <- min(999, max(-999, lomega[i,t,a]))
        lomega[i,t,a] <- omega.mu[a] + omega.b[1,a]*fall.flow[t] + omega.b[2,a]*winter.flow[t] + 
          omega.b[3,a]*spring.flow[t] + omega.b[4,a]*spring.temp[t] + omega.b[5,a]*elev[i]   
      }
    }
  }
  
  #### Survival Priors
  for(a in 1:nAges){
    omega.mean[a] ~ dunif(0.1,0.9)
    omega.mu[a] <- log(omega.mean[a]/(1-omega.mean[a]))
    for(j in 1:5){
      omega.b[j,a] ~ dnorm(0,0.37)  # Jefferey's priors: vague on logit scale
    }
  }
  
  
  #### Per capita recruitment
  for(t in 1:(nYears-1)){
    for(i in 1:nSites){
      # Ricker stock-recruitment & environmental covariates (p. 174 Guy & Brown)
      log(gamma[i,t]) <- alpha - beta*N[i,t,2] +   # Ricker curve
        gamma.b[1]*fall.flow[t] + gamma.b[2]*winter.flow[t] +  # env covariates 
        gamma.b[3]*spring.flow[t] + gamma.b[4]*spring.temp[t] + gamma.b[5]*elev[i] 
    }
  }
  
  #### Recruitment Priors
  for(j in 1:5){
    gamma.b[j] ~ dnorm(0, 0.01)  
  }
  
  #### Ricker stock-recruitment priors
  alpha ~ dunif(0,5)
  beta ~ dnorm(0, 0.1)#T(0,)
  
  #### Initial abundance priors
  for(a in 1:nAges){
    lambda[a] ~ dunif(0,500)
  }
  
  
  ##### N section
  for(i in 1:nSites){
    for(a in 1:nAges){
      # Year 1 - initial abundance
      N[i,1,a] ~ dpois(lambda[a])             
    }
  }
  
  # Year 2+ 
  for(i in 1:nSites){
    for(t in 2:nYears) {
      #Estimate recruitment
      N[i,t,1] ~ dpois(gamma[i,t-1]*N[i,t-1,2])
      
      #Estimate survival
      S[i,t-1,1] ~ dbin(omega[i,t-1,1], N[i,t-1,1])
      S[i,t-1,2] ~ dbin(omega[i,t-1,2], N[i,t-1,2])
      N[i,t,2] <- S[i,t-1,1] + S[i,t-1,2]
    }
  }
  
  
  #### Detection
  for(i in 1:nSites) {
    for(t in 1:nYears){
      for(a in 1:nAges){
        y[i,t,a,1] ~ dbin(p[i,t,a], N[i,t,a])
        y[i,t,a,2] ~ dbin(p[i,t,a], (N[i,t,a]-y[i,t,a,1]))
        y[i,t,a,3] ~ dbin(p[i,t,a], (N[i,t,a]-y[i,t,a,1]-y[i,t,a,2]))  
        
        p[i,t,a] <- 1/(1 + exp(-lp.lim[i,t,a]))
        lp.lim[i,t,a] <- min(999, max(-999, lp[i,t,a]))
        lp[i,t,a] <- p.mu[a] + p.b[1]*Jdate[i,t] + p.b[2]*width[i,t]
      }
    }  
  }
  
  #### Detection priors
  for(a in 1:nAges){
    p.mean[a] ~ dunif(0.1,0.9)    # need to bound: otherwise stuck at values very close to 0
    p.mu[a] <- log(p.mean[a]/(1-p.mean[a]))
  }
  
  p.b[1] ~ dnorm(0,0.01)
  p.b[2] ~ dnorm(0,0.01)
  
  
  ## sum up the number of individuals in all sites to estimate annual total N
  for (t in 1:nYears){
    for(a in 1:2){ 
      Ntotal[t,a] <- sum(N[,t,a])
    } 
  }
  
}