The role of dynamic modelling in understanding the microbial contribution to rumen function

Mechanistic models of microbial metabolism in the rumen aim at an improved understanding and integration for research purposes or at an improved prediction for practical purposes. The standard way of representing such models is the rate: state formalism. The system is defined by a number of state variables and a set of differential equations describe the change of the state variables with time. Three different types of solution to these dynamic models are distinguished, and examples of these solutions are described to illustrate the applications and contributions of dynamic modelling in the study of the rumen microbial ecosystem. Type I solutions are obtained when the system is in steady state and the differential equations are solved by setting the differentials to zero. An application of the type I solution is the indirect approach to quantifying the fibrolytic anaerobic fungi in the rumen. The solutions of the model describing the alternate life cycle of rumen fungi, with its free-swimming dispersal and particle-attached stages, appear to be consistent with ruminal and faecal observations. Type II solutions are obtained when the system is not in steady state but the differential equations can be integrated analytically. An application of this type of solution is the quantification of the growth and growth yield in batch cultures. Such models help to quantify the degradation of substrates in the rumen and to elucidate the interactions between groups of rumen micro-organisms. Type III solutions are obtained when the system is not in steady state and when the differential equations have to be solved numerically. Applications of the type III solutions are the rumen simulation models that describe substrate degradation, endproduct formation and microbial metabolism in an integrated manner. To illustrate this type III solution, a model of lactic acid metabolism in the rumen is defined, and its contribution to understanding of the paths and rates of lactic acid disappearance described. It is essential that the models are based on sound mathematical and biological principles. However, the various applications described in the paper show that models need not necessarily be complex and very detailed to contribute to better understanding