Comparison of mathematical models to describe disappearance curves obtained using the polyester bag technique for incubating feeds in the rumen.

Different nonlinear models were evaluated as candidates to describe ruminal degradation kinetics of forages from data obtained by the incubation of the feeds in the rumen using polyester bags. Nine models were used: segmented model with three straight lines (Mod0); simple Mitscherlich or exponential (Mod1); inverse polynomial (Mod2); compartmental model with two exponential terms (Mod3); generalized Mitscherlich (Mod4); generalized Michaelis-Menten (Mod5); logistic (Mod6); Gompertz (Mod7); and generalized Von Bertalanffy (Mod8). All these models can be represented in the general form D = W + S0 x phi(t), where D is in situ disappearance at incubation time t, W and S0 are positive scalars, and phi is a positive monotonically increasing function unique to each of the models studied. Based on first principles, a general formula for calculating the extent of degradation of feeds in the rumen has been derived that is applicable to all the models. The disappearance curves of different feed components (DM, N, and NDF) of 87 Mediterranean forages (i.e., a total of 261 curves) were fitted to all the models. A comparative study was carried out based on the mathematical, statistical, and biological characteristics of the models. Flexible models that can accommodate both diminishing returns and sigmoidal behavior were more appropriate in describing the curves. A discrete-lag parameter was introduced into Mod0, Mod1, and Mod2 to describe the initial stage of the disappearance curve, and this parameter considerably improved the fit of experimental data. Based on statistical criteria, models Mod1, Mod4, Mod5, and Mod8 were better than the others for most statistical tests and disappearance curves, but differences among these four models were not consistent. The estimates of degradation parameters to quantify the rate (half-life, fractional degradation rate), and extent (undegradable fraction, effective degradability) of ruminal degradation of feeds were also used as a means to discriminate between models, although in most cases all of the models gave similar values of the degradation parameters. In particular, when the extent of degradation was calculated for each forage and feed component, differences between the estimates obtained with the different models were of little nutritional significance for the animal.