Some generalized stochastic compartment models for digesta flow

Abstract

Digesta flow models have been based on linear compartment theory that assumes exponential retention times, and on a generalized theory that incorporates nonexponential (Erlang) retention times (Matis, 1987, Journal of Theoretical Biology 124, 371-376). This paper develops a new family of passage models for heterogeneous digesta by mixing the previous models with assumed parametric, usually gamma, mixing distributions. The utility of the resulting models is demonstrated with experimental data on two treatments, namely a chopped and a ground straw, given to each of four cows. Treatment differences are apparent in the preferred model form and in the means of the estimated mean residence times. The models are relatively easy to fit to data using standard estimation procedures, and they should have broad application to other compartment modeling problems with "heterogeneous particles."