THE POISSON-PROCESS AS A MODEL FOR COMPARTMENT DIGESTA FLOW IN RUMINANTS

The Poisson process, the simplest stochastic flow process, was used to develop a multicompartment model of ruminant digesta flow with Gamma distributed retention times. Although mathematically the model is a ge neralization of many previously published models, the physiological mo del differs substantially in asserting that the distributed delay time and the exponential rate (scale) parameters, including the scale para meter of the Gamma distribution, are determined by total digesta flow, and thus invariant with respect to the fraction marked. The shape fac tor of the Gamma distribution is shown to be sufficient to explain the difference between markers in rate of marker excretion. Consequently, the parameters of multiple markers can be simultaneously estimated wi th the constraint that the exponential scale parameters and the delay time are invariant with respect to marker. This constraint leads to a measure of pure error to strengthen statistical tests for model reject ion. Steady-state digesta retention time is estimated from the transie nt marker retention parameters, eliminating the necessity of speculati ng on what fraction of digesta the marked fraction represents. Tests o f various models, using simulations and animal experiments indicate th at, even if a model is correct, it is not possible to obtain reliable parameter estimates by fitting to a single marker. Even with multiple markers some caution must be used in interpreting parameter estimates derived from least squares fitting.