model{

#noninformative priors
alphaS~dunif(0,20)
betaS1~dunif(-10,10)
beta1~dunif(-20,20)
beta2~dunif(-20,20)
beta3~dunif(-20,20)
beta4~dunif(-20,20) #year effect
alpha~dunif(-20,20)
r~dunif(0,5)
rout<-log(r)

for (j in 1:nsites){

  log(sigma[j])<-alphaS+betaS1*chap[j]  

      for(k in 1:nG){
        log(p[k,j])<- -xg[k]*xg[k]/(2*sigma[j]*sigma[j])  #						
        f[k,j]<- p[k,j]*pi[k]                         
        fc[k,j]<- f[k,j]/pcap[j]       
        fct[k,j]<-fc[k,j]/sum(fc[1:nG,j])                 
      }

  pcap[j]<-sum(f[1:nG,j])  # overall detection probability

      for ( t in 1:T){
        log(lambda[j,t])<- alpha +beta1*chap[j] +beta2*chap2[j]+ beta3*elev[j] + beta4*yr[t]
        y[j,t]~ dbin(pcap[j],N[j,t])
        N[j,t]~dnegbin(prob[j,t], r)
        prob[j,t]<-r/(r+lambda[j,t])
	}
}


      for(i in 1:nind){
      dclass[i] ~ dcat(fct[1:nG,site[i]]) 
      }


}