The transit of external markers throughout the ruminant digestive tract: 1. The fitting quality of models to marker profiles in feces using an information-theoretic approach

We used the information-theoretic (I–T) approach to evaluate the quality of fit of nonlinear mixed-effects models fitted to fecal profiles of the particulate markers Cr and La, and Co-EDTA as a fluid marker pulse dosed to cattle and sheep. Experiments with dry and lactating dairy cows, steers, and sheep fed tropical forages including corn silage ad libitum or at multiples of maintenance were the sources of the fecal marker profiles. We fit nonlinear compartmental models of one (GN), two (GNG1), or multiple compartments (MC) to those markers by animal species/category. The animal was the random effect introduced in the nonlinear mixed-effects model. Variance and correlation functions accounted for heterogeneity of variance. The model averaging technique was necessary to summarize inferences from the fit of the several compartmental models according to the I–T approach. Some models presented an overall excellent fit, with model probabilities ≥0.9. This probability threshold leaves a low level of uncertainty for choosing such models to represent reality, given the data, and for those fits, there was no need for model averaging. For many profiles, however, there was a need for model averaging to improve predictive accuracy. The Cr-fiber and Co-EDTA travelled at different transit times (τ) in steers; however, the confidence intervals for τ overlapped for dry, lactating cows, and sheep. Chromium-labeled forage particles remained within retention segments during overlapping residence times for steers, sheep and dry cows, whereas Cr-labelled forage fiber and La-labelled concentrate fiber segregate with respect to residence times for sheep. The liquid phase Co-EDTA marker for lactating cows had the shortest residence times if compared to other markers fed to dry cows, steers, and sheep. The total mean residence times of Cr-labelled particles were shorter for lactating cows, intermediate for dry cows and sheep, and were longer for steers. The I–T approach was useful for selecting models within the nonlinear mixed models' framework, by combining the ability of different models to fit marker excretion profiles, and by combining the predictive powers of the fitted models by averaging solutions whenever necessary.