##OpenBUGS implementation of the combined known-fate open N-mixture model for the 
##applied wolf survival and recruitment example

model  {

#Priors
  #Survival
  beta.int~dunif(-5,5)   
  beta1.int~dunif(-5,5) 

  for(i in 2:9){
    beta[i]<-beta.int                                    
    beta1[i]<-beta1.int
    }
  #Recruitment
  for(i in 1:5){
    mean.count[i]~dunif(-3,3)
    recruit3[i]~dunif(-3,3)
    }
  #Detection
  p.int[1]~dunif(0,1)
  p.int[2]<-0.99999   

  #Between-year survival (April-May)
  btw.yr.surv1<-1/(1+exp(-beta.int))
  btw.yr.surv2<-1/(1+exp(-beta1.int))

  #May-Aug survival, period 1
  beta[1]<-logit(pow(1/(1+exp(-beta.int)),3))
  beta1[1]<-logit(pow(1/(1+exp(-beta1.int)),3))
                       
#Model for collared animals
for(i in  1:144){                                      
    mu[i,1]<-collar.prev.yr[i]*(btw.yr.surv1)+collar.not.prev[i] #if previously collared, estimate between-year survival
    y.collar[i,1]~dbern(mu[i,1])
  for(j in (first[i]+1):last[i]){                      #Basically a nest survival model here
    logit(phi[i,j-1])<-beta[j-1]                       #Collared animal survival
    mu[i,j]<-phi[i,j-1]*y.collar[i,j-1]                              
    y.collar[i,j]~dbern(mu[i,j])
    }
    }

#Model for counts of rest of pack members
#Getting initial counts in May (beginning of year)
  for(i in 1:16){                                       #Study initiated, 16 packs marked
    n[i,1]~dpois(mean.count1[i,1])                      #Initial number in group   
    log(mean.count1[i,1])<-mean.count[year.count[i]]    #Year-specific initial group size                   
    n1[i,1]<-n[i,1]                                     #May only 
       }
  for(i in 17:25){                                      #9 newly marked packs, some collars added
    n[i,1]~dpois(mean.count1[i,1])                      #Initial number in group   
    log(mean.count1[i,1])<-mean.count[year.count[i]]    #Year-specific initial group size                   
    n1[i,1]<-n[i,1]-new.col[i,1]                        #Accounting for removals to the collared sample
       }
     
  for(i in 26:88){                                      #packs marked in previous years
    n[i,1]~dbin(btw.yr.surv2,n1[prev.count.pos[i],10])  #Between year survival (i.e. Apr-May)
    n1[i,1]<-n[i,1]+(recruit[i])-new.col[i,1]           #Survived, recruits, remove new collars 
      }
#Recruitment submodel (recruits only added in May (period 1))     
for(i in 1:88){ 
  recruit[i]~dpois(recruit2[i])
  lrecruit2[i]<-recruit3[year.count[i]]
  recruit2[i]<-exp(lrecruit2[i])
  for(j in 1:10){                                      #10 revisit periods, 9 intervals (May-Aug = inteval 1)
    pp[i,j]<-p.int[test[i,j]]                          #Test indicates whether counts were perfect
    y.count[i,j]~dbin(pp[i,j],n1[i,j])
    } 
#Survival of uncollared animals  
  for(j in 2:10){
    lphi.1[i,j-1]<-beta1[j-1]                         
    phi.1[i,j-1]<-1/(1+exp(-lphi.1[i,j-1]))
    n1[i,j]<-n[i,j]-new.col[i,j]                      #Remove newly collared individuals from the count
    n[i,j]~dbin(phi.1[i,j-1],n1[i,j-1]) 
    }
    }
}