A mathematical model is described that stimulates the digestion, absorption and outflow of nutrients in the rumen. The model consists of 17 state variables, representing nitrogen, carbohydrate, lipid, microbial and volatile fatty acid pools. The flux equations are described by Michaelis-Menten or mass action forms with parameters calculated from the literature. Several specific areas of improvement in representation of rumen processes were reconsidered during model development. These included microbial substrate preference, differential outflow and chemical composition of rumen microbes, recycling of microbial matter within the rumen, uncoupling of fermentation with respect to nitrogen availability, reduced microbial activity at reduced rumen pH and pH-dependent absorption of volatile fatty acids and ammonia. The model was used to examine the effects of the diet on the profile of nutrients available for absorption and was shown to respond appropriately to different intake and nitrogen levels. The validity of the improvements and the predictions of nutrient supply on a variety of dietary inputs are tested in a companion paper.

A simple model of the mammary gland is described. In this model secretory cells are produced by cell division from undifferentiated cells, and the rate of division is determined by the level of a postulated hormone. The total activity of the milk secreting cells depends on the number of cells, substrate supply (assumed constant), and the amount of milk currently present in the animal. The secretory cells have a finite life, although their death may be expedited by milk remaining in the animal over a longer period of time. The model gives a good description of an experimental lactation curve; it is able to simulate the removal of milk by a suckling calf and machine milking with a variable number of milking periods a day.

S U M M A R YA previously described model of digestion in cattle fed sugarcane diets was applied to predict nutrient supply to the host animal from dietary intake, to indicate pre-experimentally the suitability of various supplements to enhance the milk production of dairy cattle in the tropics fed sugarcane-based diets. Potential milk production was calculated according to simulated energy and lipogenic, glucogenic and aminogenic nutrient availability. The addition of small amounts of urea (10 g/kg sugarcane fresh weight) improved microbial efficiency and degradation of substrates in the rumen, but further increases could only be achieved by supplements containing rumen degradable protein. The simulated level of absorbed amino acids was low in comparison with the level of absorbed energy and glucogenic substrates. This low amino acid availability was the factor most limiting milk production on sugarcane diets and supplements which increase the amino acid availability in the gastrointestinal tract are recommended. At increasing supplementation or intake levels, and once amino acid requirements were met, an increased absorption of energy and long chain fatty acids could enhance milk production. These suggestions should be evaluated experimentally in order to improve the model and ultimately, to result in an improved system to evaluate feeds, based on the supply and utilization of individual substrates.

A dynamic model of digestion and absorption of nutrients in cattle fed sugarcane-based diets is described. There are 11 rumen state variables, and four zero pools representing absorbed nutrients. The rumen state variables represent nitrogen, carbohydrate, long chain fatty acid, microbial and volatile fatty acid pools. The zero pools relate to absorbed amino acids, glucose, long chain fatty acids, and volatile fatty acids. The flux equations are described by mass-action and Michaelis-Menten forms. Wherever possible, data derived from trials with cattle fed sugarcane-based diets were used to parameterize the model. Sensitivity analyses revealed that stability and behaviour of the model was generally satisfactory. The model was most sensitive to changes in fractional passage and substrate hydrolysis rates and to the microbial maintenance requirement. Within the limited information available for comparison, the simulations agreed with observations of fibre flows and ammonia and volatile fatty acid concentrations in rumen fluid. Duodenal non-ammonia nitrogen flow was consistently underpredicted and reasons for this underprediction are suggested.

A mathematical model of the rumen fermentation processes constructed to predict nutrient supply to the host animal was evaluated. Sensitivity analysis on high fiber, starch and protein diets indicated that the model responds appropriately to these types of diets and to changes in parameter values, and revealed that the model is sensitive to the availability of hexose for non-growth microbial processes and to the maximum storage rate of polysaccharides in amylolytic microbes, although sensitivity varied with diet composition. Of the parameters whose values were dependent on diet, the fraction of protozoa in the amylolytic microbial pool and the fluid and solid passage rates needed the most careful estimation. When model predictions of nutrient supply were compared with the experimental observations, those for duodenal flows of neutral detergent fiber, total non-ammonia nitrogen (NAN) and total volatile fatty acid rumen concentration were satisfactory for several feeding strategies. The partition of NAN flow into microbial and non-microbial NAN flow and the molar proportions of volatile fatty acid production and concentration were not predicted well. The representation of the complex interactions between rumen microbial populations and of their effects on the production of specific volatile fatty acids merits further study for an improvement in the prediction of nutrient supply.

This study reports the psychometric development of a measure to assess individual differences in exercise motivations using a functionalist strategy (Snyder & Cantor, 1997). Factor analyses revealed two subscales for the newly developed Function of Exercise Scale (FES): Weight and Appearance (WA), and Health and Enjoyment (HE). FES-HE scores correlated with better psychological well-being and predicted prospectively monitored as well as concurrently and longitudinally assessed exercise behavior. FES-HE scores also correlated with lower pulse, systolic blood pressure, and salivary cortisol readings, indicating its association with better physical health. In contrast, FES-WA scores correlated with greater depressive and eating disorder symptoms, as well as lower self-esteem, and predicted the later emergence of eating disorder, but not depressive, symptoms. FES-WA scores failed to show a relationship with measures of physical well-being, including exercise engagement and vital sign data. Overall, the FES appears to hold promise as a succinct and psychometrically sound heuristic for meaningfully relating exercise motivations to important indices of both physical and psychological well-being.

Rations for dairy cows are often formulated using predictions of voluntary feed intake calculated from regression equations. The accuracy of the predictions of drymatter intake by seven equations is investigated. Comparisons are made when live weight is taken to be the observed weekly mean (MLW), the observed live weight after calving (CLVV) or an estimated breed weight accompanied by a notional pattern of liveweight change (BIAV). Data recorded on a British Friesian dairy herd at the Grassland Research Institute fed mostly silage ad libitum and various supplements are used. The mean square prediction error (MSPE) is calculated for each week and summarized over the whole experimental period.The least MSPE's are 2-1, 2-8 and 2-4 (kg D.M.) 2 for comparisons using MLW, CLW and BLW respectively. The Ministry of Agriculture, Fisheries and Food (1975) equation involving only live weight and milk yield performs well and would be useful when only the limited measurements of live weight and milk yield are available, but the more complex equations of Vadiveloo & Holmes (1979) and of Lewis (1981) give consistently the best predictions. The importance of using the original definitions of the variables when applying a predictive equation is illustrated. Even so, the large errors found in the predictions of intake points to the need for further research.

A model of ensiling is described which incorporates the interactions of lactic acid bacteria and clostridia with water soluble carbohydrates. The processes modelled include bacterial growth, the production of lactic and butyric acids from water soluble carbohydrates, and the conversion of lactic acid to butyric acid. The calculation of pH, and the regulation of bacterial activity by pH are important components ofthe model. The model predicts time courses for pH and the five state variables, which are the concentrations of water soluble carbohydrates, lactic acid, butyric acid, lactic acid bacteria and clostridia. There is good qualitative agreement between the predictions of the model and experimental data on ensiling.