Models based on variable fractional digestion rates to describe ruminal in situ digestion

Using a first-order model to describe ruminal in situ digestion implies that the rate of digestion is affected only by the quantity of potentially digestible substrate remaining. Other factors, like the microbial efficacy for digesting substrate, are assumed to be constant. However, microbes are not only the cause but also the result of digestion, being one of the digestion end-products. Two sigmoidal models (a logistic and a Gompertz-like model) were derived from a general digestion function in which the rate of digestion equals the product of the quantity of potentially digestible substrate remaining and a non-constant fractional rate of digestion (microbial efficacy function). The models were compared with a first-order model with a discrete lag time. The logistic model specifically accounted for the conversion of substrate mass to microbial mass, but did not describe microbial migration between the substrate and the ruminal fluid. In contrast, the Gompertz-like model assumed that the change in microbial efficacy was only time-dependent. There was little difference between models in estimates of scale parameters, but the asymptotic microbial efficacy was consistently higher for the logistic model than for the other models. Estimates of discrete lag time in the first-order model were biased towards obtaining values identical to the independent variable. Scale estimators appeared to be more robust than kinetic estimators. Lack-of-fit was present for most model-data set combinations. The similar patterns of residuals between models suggested that a four-parameter model may be insufficient to describe the data. It was concluded that if a four-parameter model is to be used, the model with a discrete lag time would be the least biologically appropriate.