Evaluation of different mathematical models on fitting the in vitro gas production parameters in beef cattle

In vitro rumen gas production experiment was conducted with 57 kinds of feedstuff, which were categorized into energy feed, protein feed, and roughage, collected within China. Eight mathematical models were employed to describe the kinetics of in vitro rumen gas production. The results found that for energy feeds, protein feeds, and roughages, respectively, Michaelis-Menten (MM) or Logistic-Exponential with lag (LEL), MM, and Mitscherlich (MIT) exhibited the highest or shown no significant difference compared to the highest coefficient of determination (R²) (P < 0.05) for all categories of feed. Furthermore, regression estimation of intercept and slope for regression estimates of intercept and slope for Observed versus Predicted of aforementioned models shown no significant difference from 0 and 1, respectively (P < 0.05), except LEL for energy feed. Mean absolute error (MAE), root mean squared error of prediction (RMSEP), mean squared error of prediction (MSEP) of those models were relatively lower, with minimal systematic bias and regression bias. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) rankings were higher compared with other models. Given these results, in studies where feedstuff categories are not distinguished or multiple feedstuffs categories are included, the MM model proves to be a good choice. MM or LEL was considered to better fit energy feedstuffs. The MM model was the optimal choice for fitting protein feedstuffs. MIT provided the best accuracy and moderate precision when fitting roughages.