Fitting of some Nonlinear Models for Predicting Ruminal Fermentation Kinetics in Different Forages

 The in vitro gas production test is used as a laboratory method for studying the ruminal fermentation of feed-stuffs. This method is an ideal technique, because it allows to record gas production at different hours an incubation time. In this technique, the parameters of fermentation kinetic are predicted using nonlinear models. The Exponential Model (EXP) is the easiest nonlinear model which is applied for this regard. However, it has been reported that some nonlinear models predict the parameters of gas production kinetic more accurately than the EXP model. In this study, different forages were used as feed samples and the accuracy of some nonlinear models for predicting the parameters of gas production kinetic has been studied and compared.

For this experiment, alfalfa forage (first, second and third cutting), sainfoin hay, wheat straw, barley straw and corn silage were used as feed samples. Feed samples were analyzed for Dry matter, ash, crude protein, neutral detergent fiber and acid detergent fiber according to standard methods. Rumen fluid was collected from three ruminally fistulated mature Mehraban rams before the morning feeding. Obtained rumen fluids were pooled and strained through four layers of cheesecloth into a pre-warmed (38 to 39 ˚C) insulated flask and immediately transported to the laboratory. In laboratory, ruminal fluid was filtered through four layers of cheese cloth and then mixed continuously with CO2 and maintained near 39o C before usage. To evaluate the ruminal fermentation kinetic of feeds, the in vitro gas production test was carried out during 144 h incubation time for 3 run. For this purpose, 200 mg of dried and milled feeds with 30 ml of buffered rumen fluid were poured into glass vials (in 3 replicates). Two glass vials containing 30 ml of buffered rumen fluid without substrate were considered as blanks. After capping (plus tow glass vials as blanks), all glass vials were incubated at 39 ° C. The volume of gas produced was recorded at 2, 4, 6, 8, 10, 12, 16, 20, 24, 36, 48, 72, 96, 120, 144 h after incubation.The obtained results (volume of gas produced at each incubation time) were fitted to four nonlinear models included the exponential (EXP), Gompertz (GOM), Richard (RCH) and France (FRC) models. The mean square error (MSE), coefficient of determination (R2), residual mean absolute deviation (RMAD) and mean percentage error (MPE) statistics were used as goodness of fit parameters. The run test, accuracy factor (AF), Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to compare the accuracy of the models for predicting the gas production kinetic.

The results showed that the asymptotic gas volume (A) predicted by the FRC model (104.68 ml per 200 mg dry matter) was significantly different from the EXP (100.18 ml per 200 mg dry matter) model (p <0.05). But the value of A predicted by the EXP, GOM and RCH models did not show a significantly difference. The rate of gas production (c) predicted by the studied models were significantly different and the lowest value was observed in the FRC model (p<0.05). The highest and lowest values for MSE (15.11) and R2 (0.984) were observed in the EXP model, respectively. Which indicated the EXP model goodness of fit was weak compared to the other models. The RMAD statistic in the studied models had significantly difference (p<0.05) and the highest (2.88) and lowest (0.85) values were observed in the EXP and FRC models, respectively. So, the FRC and EXP models had the highest and lowest goodness of fit, respectively. The MPE statistic in the FRC and RCH models were closer to zero (0.32 and 0.48, respectively) compared to the other models (EXP and GOM models), which indicated better goodness of fit in these models. The run test was significant in the EXP and GOM models (p<0.05). So, these models were less accurate for predicting the gas production kinetic. The value of AF, AIC and BIC statistics (2.85, 15.87 and 10.04, respectively) showed that the FRC model had the highest accuracy for predicting the gas production kinetic among the studied models.

The results showed that the EXP model had the lowest accuracy for predicting ruminal fermentation kinetic of feeds, among the studied models. However, the FRC model had the highest accuracy.