model {

   # region-specific means
   p[1:num.prey] ~ ddirch(alpha[]);  
   for(i in 1:num.prey) {
      p2[i] <- p[i]*p[i]; # these are weights for variances
   }

   # for each isotope and population, calculate the predicted mixtures
   for(iso in 1:num.iso) {
      mix.mu[iso] <- inprod(u[1:num.prey,iso],p[1:num.prey]);
      mix.var[iso] <- inprod(sigma2[1:num.prey,iso],p2[1:num.prey]);
      mix.prcsn[iso] <- 1/(mix.var[iso]);
   }
   # This section does the likelihood / posterior, N data points
   for(i in 1:N) {
      for(iso in 1:num.iso) {
         X[i,iso] ~ dnorm(mix.mu[iso], mix.prcsn[iso]);
      }
   }

}