Selection among nonlinear models for rate of passage studies in ruminants

Eight Toggenburg wether goats were fed either Coastal bermudagrass (Cynodon dactylon) or orchardgrass (Dactylis glomerata)-alfalfa (Medicago sativa) hay (57:43%) in a reversal design. Four markers were used to study the movement of different digesta fractions: erbium for large particles greater than 1,700 microns; ytterbium for medium particles less than 1,700 microns and greater than 500 microns; chromium for small particles less than 500 microns and greater than 32 microns; and cobalt to follow liquid passage. Fecal samples were collected every 4 h for 6 d. The excretion curves obtained for every marker in each animal were used for model selection. One-compartment gamma age-dependent models (gamma 2, 3 and 4 age-dependent), two-compartment (gamma 2 and gamma 3 age-dependent, age-independent) models and a biexponential model were fitted to the data. Residual sums of squares and the Davidson and MacKinnon test were used to select the most appropriate models. These procedures indicated that the models best describing the movement of different digesta fractions through the gastrointestinal tract of goats, in this experiment, were the biexponential model for liquids, gamma 2 two-compartment model for small and medium particles and gamma 3 two-compartment model for large particles. To accurately describe the behavior of different components of digesta in the digestive tract, different mathematical models are required. In general, models that describe the movement of large particles have higher orders of age-dependency than models that describe the passage of liquids or small particles.