model{

##noninformative priors
alphaS~dunif(0,20)
betaS1~dunif(-10,10)
beta1~dunif(-20,20)
beta2~dunif(-20,20)
beta3~dunif(-20,20)
alpha~dunif(-20,20)
gamma~dunif(0,5)

r~dunif(0,5)
rout<-log(r)

for (j in 1:nsites){

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

      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


### Abundance model for Yr1, as in Sillett et al 2012
   log(lambda[j,1])<- alpha +beta1*chap[j] + beta2*chap2[j] +beta3*elev[j]
   y[j,1]~ dbin(pcap[j],N[j,1])
   N[j,1]~ dnegbin(prob[j,1], r)
   prob[j,1]<- r/(r+lambda[j,1])


	for (t in 2:T){
	  N[j,t]~ dpois(N[j, t-1]*gamma)
      	  y[j,t]~ dbin(pcap[j],N[j,t]) 
	}

}

     ### all years' worth of data in one long vector  
      for(i in 1:nind){
      dclass[i] ~ dcat(fct[1:nG,site[i]]) 
      }


}