model {

   p[1:num.prey] ~ ddirch(alpha[]);  # these are weights for means
   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) {
      resid.sigma[iso] ~ dunif(0,100);
      resid2[iso] <- (resid.sigma[iso]*resid.sigma[iso]);
         mix.mu[iso] <- inprod(u[,iso],p[]);
         mix.var[iso] <- inprod(sigma2[,iso],p2[]);
         mix.totalVar[iso] <- mix.var[iso] + resid2[iso];
         mix.prcsn[iso] <- 1/(mix.totalVar[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]);
      }
   }

}