Evaluation of models to describe ruminal degradation kinetics from in situ ruminal incubation of whole soybeans

Different mathematical models were evaluated as candidates to describe ruminal dry matter (DM) and crude protein (CP) degradation kinetics of raw and roasted whole soybeans from data obtained using the in situ polyester bag technique. Three models were used: segmented with up to 3 straight lines (model I), negative exponential (model II), and rational function or inverse polynomial (linear over linear; model III). A fourth, a generalized sigmoidal model, was also considered but the data did not exhibit sigmoidicity, so it was dropped from the analysis. Lagged and nonlagged versions of each model were fitted to the DM and CP disappearance curves of 6 different feeds (2 cultivars of raw or differently heat-processed whole soybean). The comparison between lagged and nonlagged versions of each model, based on statistical and behavior characteristics, showed for all models that the discrete lag parameter did not significantly improve the fit to ruminal DM and CP disappearance curves. The comparison between models (using nonlagged equations) showed that models I and II gave better goodness-of-fit than model III. Based on biological characteristics, models II and III underestimated the undegradable DM and CP fractions, but there was no significant difference between models for extent of degradation.