Mathematical Modeling of In Vitro Rumen Fermentation Kinetics in Capiaçu Elephant Grass Silages with Inclusion of Dehydrated Cashew Pseudo-Fruit

This study aimed to evaluate and compare the performance of five mathematical models: Gompertz, Ørskov & McDonald, Brody, Richards, and the Dual Pool Logistic model, in describing the in vitro gas production kinetics of Capiaçu elephant grass (Pennisetum purpureum Schum 'BRS Capiaçu') silages. The effect of including dehydrated cashew pseudo-fruit on the in vitro degradation curves was also assessed. A completely randomized design was adopted, using Capiaçu silages containing 0%, 10%, 20%, or 30% dehydrated cashew pseudo-fruit. Rumen fermentation kinetics were measured through cumulative in vitro gas production. Model performance was evaluated using the Akaike Information Criterion (AIC), coefficient of determination (R²), concordance correlation coefficient (CCC), and mean square prediction error (MSPE). Accuracy (pMSPE) and precision (AIC) were also considered. The Richards model performed best with the lowest AIC (1119.07) and MSPE (0.246) and the highest R² (0.917) and CCC (0.966). It was over 350 times more likely to provide a correct fit (<i>p</i> < 0.05) compared to the other models. Significant differences (<i>p</i> < 0.05) were observed between degradation curves as a function of the pseudo-fruit inclusion level. Increasing pseudo-fruit inclusion improved silage composition, raising total digestible nutrients (from 54.6% to 67.1%) and reducing neutral detergent fiber (from 58.5% to 42.3%), which directly enhanced fermentation kinetics. These results indicate that the Richards model is the most suitable for describing the fermentation kinetics of Capiaçu elephant grass silages. Moreover, linking model performance to practice, the Richards model provides a reliable tool for determining optimal inclusion levels of dehydrated cashew pseudo-fruit (up to 30%), supporting better silage nutritional quality and more efficient feed utilization in ruminant production systems.