Statistical and optimization modeling of energy utilization by cattle

The objective of this dissertation was to study energy utilization by cattle using quantitative approaches. In the first chapter, several optimization models were presented and described mathematically. The potential use of these models in diet formulation and in the minimization of environmental impacts of livestock production was discussed. Further, a linear programming model to examine methane emission regulatory policies in a hypothetical dairy herd was decribed in detail. In chapter two, a weighted goal programming optimization model was developed to simultaneously minimize diet costs and methane emissions. A strategy based on the systematic variation of the objective function weights was proposed for the construction of the set of feasible solutions. The mitigation costs, representing the change in dietary costs associated with a unit reduction in methane emissions, were determined using feed prices and dairies from the Central Valley in California. In the third chapter, linear hierarchical models were developed to predict methane emissions from several cattle categories. A large database of indirect calorimetry was used to select, fit and evaluate models of different complexity levels. Bayesian techniques were implemented for robust model selection and fitting resulting in substantial reductions of prediction errors from the extant models in the literature. The last two chapters examined utilization of metabolizable energy by growing and lactating cattle. In chapter four, parametric and nonparametric Bayesian hierarchical models were developed to model energy retention and heat production as a function of metabolizable energy intake. The nonparametric model estimates maintenance requirements and energetic efficiencies without specifying a particular functional form for the relationship between dependent and independent variables. The biological and mathematical assumptions behind the estimation of energetic parameters for each model were comprehensively described. In the last chapter univariate and multivariate hierarchical models were used to estimate maintenance requirements and the partial efficiencies of utilizing dietary energy for milk production and tissue gain. The multivariate model was formulated with structural equations respecting the biological principles governing mutually interactive energy traits. The models were used to demonstrate that maintenance requirements and the efficiencies of utilizing dietary energy increased in contemporary Northern American milk production systems. Canonical correlation analysis suggested that changes in dietary composition and genetic selection for milk production may have altered these energetic parameters over the past five decades.