Manure nitrogen (N) from cattle production facilities can lead to negative environmental effects, such as contribution to greenhouse gas emissions, leaching and runoff to aqueous ecosystems leading to eutrophication, and acid rain. To mitigate these effects and to improve the efficiency of N use, accurate prediction of N excretion and secretions are required. A genetic algorithm was implemented to select models to predict fecal, urinary, and total manure N excretions, and milk N secretions from 3 classes of animals: lactating dairy cows, heifers and dry cows, and steers. Two tiers of model classes were developed for each category of animals based on model input requirements. A total of 6 models for heifers and dry cows and steers and an additional 2 models for lactating dairy cattle were developed. Evaluation of the models using K-fold cross validation based on all data and using the most recent 6 yr of data showed better prediction for total manure N and fecal N compared with urinary N excretion, which was the most variable response in the database. Compared with extant models from the literature, the models developed in this study resulted in a significant improvement in prediction error for fecal and urinary N excretions from lactating cows. For total manure production by lactating cows, extant and new models were comparable in their prediction ability. Both proposed and extant models performed better than the prediction methods used by the US Environmental Protection Agency for the national inventory of greenhouse gases. Therefore, the proposed models are recommended for use in estimation of manure N from various classes of animals.

The objectives of the study were to develop a multivariate framework for analyzing energy balance data from lactating cows and investigate potential changes in maintenance requirements and partial efficiencies of energy utilization by lactating cows over the years. The proposed model accounted for the fact that metabolizable energy intake, milk energy output, and tissue energy balance are random variables that interact mutually. The model was specified through structural equations implemented in a Bayesian framework. The structural equations, along with a model traditionally used to estimate energetic parameters, were fitted to a large database of indirect calorimetry records from lactating cows. Maintenance requirements and partial efficiencies for both models were similar to values reported in the literature. In particular, the estimated parameters (with 95% credible interval in parentheses) for the proposed model were: net energy requirement for maintenance equal to 0.36 (0.34, 0.38) MJ/kg of metabolic body weight·day; the efficiency of utilizing dietary energy for milk production and tissue gain were 0.63 (0.61, 0.64) and 0.70 (0.68, 0.72), respectively; the efficiency of utilizing body stores for milk production was 0.89 (0.87, 0.91). Furthermore, additional analyses were conducted for which energetic parameters were allowed to depend on the decade in which studies were conducted. These models investigated potential changes in maintenance requirements and partial efficiencies over the years. Canonical correlation analysis was used to investigate the association between changes in energetic parameters with additional dietary and animal characteristics available in the database. For both models, net energy requirement for maintenance and the efficiency of utilizing dietary energy for milk production and tissue gain increased in the more recent decades, whereas the efficiency of utilizing body stores for milk production remained unchanged. The increase in maintenance requirements in modern milk production systems is consistent with the literature that describes increased fasting heat production in cows of higher genetic merit. The increase in utilization of dietary energy for milk production and tissue gain was partially attributed to the changes in dietary composition, in particular to the increase in dietary ether extract to levels closer to currently observed in modern milk production systems. Therefore, the estimated energetic parameters from this study can be used to update maintenance requirements and partial efficiencies of energy utilization in North American feeding systems for lactating cows.

Linear and non-linear models have been extensively utilised for the estimation of net and metabolisable energy requirements and for the estimation of the efficiencies of utilising dietary energy for maintenance and tissue gain. In growing animals, biological principles imply that energy retention rate is non-linearly related to the energy intake level because successive increments in energy intake above maintenance result in diminishing returns for tissue energy accretion. Heat production in growing cattle has been traditionally described by logarithmic regression and exponential models. The objective of the present study was to develop Bayesian models of energy retention and heat production in growing cattle using parametric and non-parametric techniques. Parametric models were used to represent models traditionally employed to describe energy use in growing steers and heifers whereas the non-parametric approach was introduced to describe energy utilisation while accounting for non-linearities without specifying a particular functional form. The Bayesian framework was used to incorporate prior knowledge of bioenergetics on tissue retention and heat production and to estimate net and metabolisable energy requirements (NEM and MEM, respectively), and the partial efficiencies of utilising dietary metabolisable energy for maintenance (km) and tissue energy gain (kg). The database used for the study consisted of 719 records of indirect calorimetry on steers and non-pregnant, non-lactating heifers. The NEM was substantially larger in energy retention models (ranged from 0.40 to 0.50 MJ/kg BW0.75.day) than were NEM estimates from heat-production models (ranged from 0.29 to 0.49 MJ/kg BW0.75.day). Similarly, km was also larger in energy retention models than in heat production models. These differences are explained by the nature of y-intercepts (NEM) in these two models. Energy retention models estimate fasting catabolism as the y-intercept, while heat production models estimate fasting heat production. Conversely, MEM was virtually identical in all models and approximately equal to 0.53 MJ/kg BW0.75.day in this database.

Organic compounds in dairy manure undergo a series of reactions producing pollutants such as ammonia and methane. Because various organic compounds have different reaction rates, the emissions could be accurately determined if amounts and concentrations of individual nutrients in manure are known. A set of empirical models were developed for predicting faecal and urinary water, carbon (C), nitrogen (N), acid detergent fibre and neutral detergent fibre output (kg/day) from lactating Holstein cows. Dietary nutrient contents, milk yield and composition, bodyweight, age and days in milk were used with or without dry matter intake (DMI) as potential predictor variables. Multi-collinearity, goodness of fit, model complexity, and random study and animal effects were taken into account during model development, which used 742 measured faecal or urinary nutrient output observations (kg/day). The models were evaluated with an independent dataset (n ≤ 364). When DMI was used as a predictor variable, the models predicted faecal and urinary nutrient outputs successfully with root mean square prediction error as a percentage of average observed values (RMSPE%) ranging from 9.1% to 20.7%. All the predictions except urine output had RMSPE% ranging from 18.3% to 24.6% when DMI was not used. The nutrient output predictions were in reasonable agreement with observed values throughout the data range (systematic bias <14% of total bias). Fresh manure C:N ratio predictions were acceptable (RMSPE% ≤ 14.3-15.2%) although the systematic bias were notable (17.1-20.7% of total bias). The models could be integrated successfully with process-based manure or soil models to assess nutrient transformation in dairy production systems.

Enteric methane emission is a major greenhouse gas from livestock production systems worldwide. Dietary manipulation may be an effective emission-reduction tool; however, the associated costs may preclude its use as a mitigation strategy. Several studies have identified dietary manipulation strategies for the mitigation of emissions, but studies examining the costs of reducing methane by manipulating diets are scarce. Furthermore, the trade-off between increase in dietary costs and reduction in methane emissions has only been determined for a limited number of production scenarios. The objective of this study was to develop an optimization framework for the joint minimization of dietary costs and methane emissions based on the identification of a set of feasible solutions for various levels of trade-off between emissions and costs. Such a set of solutions was created by the specification of a systematic grid of goal programming weights, enabling the decision maker to choose the solution that achieves the desired trade-off level. Moreover, the model enables the calculation of emission-mitigation costs imputing a trading value for methane emissions. Emission imputed costs can be used in emission-unit trading schemes, such as cap-and-trade policy designs. An application of the model using data from lactating cows from dairies in the California Central Valley is presented to illustrate the use of model-generated results in the identification of optimal diets when reducing emissions. The optimization framework is flexible and can be adapted to jointly minimize diet costs and other potential environmental impacts (e.g., nitrogen excretion). It is also flexible so that dietary costs, feed nutrient composition, and animal nutrient requirements can be altered to accommodate various production systems.

Quantification of dairy cattle nitrogen (N) excretion and secretion is necessary to improve the efficiency with which feed N is converted to milk N (ENU). Faecal and urinary N excretion and milk N secretion are correlated with each other and thus are more accurately described by a multivariate model that can accommodate the covariance between the three observations than by three separate univariate models. Further, by simultaneously predicting the three routes of excretion and taking advantage of the mass balance relationships between them, covariate effects on N partitioning from feed to faeces and absorbed N and from absorbed N to milk and urine N and animal ENU can be estimated. A database containing 1094 lactating dairy cow observations collated from indirect calorimetry experiments was used for model development. Dietary metabolisable energy content (ME, MJ/kg DM) increased ENU at a decreasing rate, increased the efficiency with which feed N was converted to absorbed N and decreased the efficiency with which absorbed N was converted to milk N. However, the parameter estimate of the effect of ME on post-absorption efficiency was not different from zero when the model was fitted to a data subset in which net energy and metabolisable protein were at or above requirement. This suggests the effect of ME on post-absorption N use is dependent on the energy status of the animal.