### flock[i] is flock size of group i and is only observed for a subset of flocks (Nspec) ### We want an estimate of total abundance, including those flocks we did not observe ### In the full model, Nspec is estimated based on data, but I set it here as a random number ### that's larger than the number of observed flocks (which is 282) ### Also in the full model, Nmax is chosen arbitrarily, but large enough so it does not truncate Nspec. ### Flock sizes comes from a 0-truncated negative binomial distribution ### anything above Nspec is not part of the population and thus has a fixed size of 0 ### this is an attempt to get around using the random 'Nspec' as upper limit for the 'flock' loop ### Essentially, this is a negative binomial hurdle model (I believe) ### Following an example in the BUGS manual, we model the negative binomial explicitly as a Poisson-gamma mixture ### because using the negative binomial directly gave counterintuitive estimates of mu and r ### if you remove the truncation of the Poisson, or if Nspec is fixed rather than random, the model works model{ #priors r~dunif(0,100) mu~dunif(0,100) Nspec~dunif(283, Nmax) for (i in 1:Nmax){ Pin[i]<-step( (Nspec+0.1) - i) flock[i]~dpois(mustar[i,Pin[i]+1]) T(Pin[i],) mustar[i,1]<-0 mustar[i,2]<-mu * rho[i] rho[i]~dgamma(r,r) } Atot<-sum(flock) }