Mathematical models to adjust the parameters of in vitro cumulative gas production of diets containing preserved Gliricidia

Abstract

This study examined the use of the Gompertz, Groot, monomolecular, Richards and two-compartment-logistic mathematical models to investigate the kinetics of in vitro gas production of diets composed of combinations of Gliricidia hay or silage. In addition, the effects of Gliricidia hay or silage inclusion on the in vitro cumulative gas production of these diets were evaluated. Rumen fermentation kinetics were analyzed by the in vitro cumulative gas production methodology. The model parameters were estimated using the Gauss Newton method, with the exception of the Richards model, which was used by Marquardt’s algorithm. Model fit was assessed using the determination coefficient, F test for parameters identity, concordance correlation coefficient, root mean square error of prediction, and decomposition of mean square error of prediction into mean error, systematic bias and random error. The models were compared for accuracy (pairwise mean square error of prediction) and precision (delta Akaike’s information criterion). All model evaluation and comparison statistics were calculated using Model Evaluation System software version 3.2.2. The Groot and Richards models did not differ from each other (P>0.05) and were the most precise and accurate (P<0.05). Therefore, the Groot model was selected due to its better accuracy and precision and easier access to the parameters. The inclusion of Gliricidia silage in the diet resulted in an increase in the time to obtain the maximum rate of degradation and in the time after incubation when half of the asymptotic level was reached. The Groot model is recommended to estimate the average curve. Dietary inclusion of Gliricidia silage alters the gas production curve due to the longer time required for the diet to reach the maximum rate of degradation, this can increase the time the diet remains in rumen and promote a reduction in the consumption.

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

“…The MM model exhibited the highest R 2 across all four groups which surpassed all other models signi cantly in the protein feeds and the uncategorized group. This nding aligned with the conclusions drawn by most previous studies 1,20,23,31 . After deriving the formulas, France et al 12 noted that the MM model's assumption regarding gas production rate was the most exible.…”

“…Cone et al 30 classi ed gas production into three stages: the initial stage involves the neutral detergent soluble fraction (NDS), the subsequent stage entails NDF fermentation, and the nal stage relates to microbial population limitation. Some researchers believe that compared to single-pool analysis, this nonlinear multi-pool analysis increased the number of parameters in the model, potentially compromising its robustness and posing numerous challenges to tting 1,19,31 . Therefore, this study only selected single-pool models for analysis and comparison.…”

Kinetics of In Vitro Gas Production and Fitting Mathematical Models of Corn Silage

“…However, despite the good fit, the Richards model showed convergence problems in the iterative process, requiring the use of the Marquardt algorithm and an increase in the number of iterations, possibly because this model needs to estimate an additional parameter. According to Gurgel et al [14], some researchers have also reported convergence difficulties using the Richards model. In addition, a model with three parameters-as is the case with the Groot model-will exhibit more degrees of freedom in the estimates, which can be important when a curve displays a smaller amount of information or data [14].…”

“…According to Gurgel et al [14], some researchers have also reported convergence difficulties using the Richards model. In addition, a model with three parameters-as is the case with the Groot model-will exhibit more degrees of freedom in the estimates, which can be important when a curve displays a smaller amount of information or data [14]. It is also important that all parameters have biological significance.…”

“…However, the Dual-pool Logistic model [8] has been widely used to fit the in vitro gas production of feedstuffs and diets for ruminants [9][10][11][12][13]. Nevertheless, it should be noted that a single model should not be used for all types of feed; rather, it is essential that different models be adjusted for each nutritional situation [14].…”