| The main objectives of this dissertation research were (1) to investigate the nature of the association between milk production and reproductive performance of dairy cows taking into consideration the within-herd (cow-level) and between-herd (herd -level) components of this association, and (2) to evaluate management factors and herd attributes as potential sources of heterogeneity in the association. A formal assessment of these objectives required the development of novel statistical methods, thereby setting an interdisciplinary foundation to this dissertation research.;First, this dissertation develops and validates hierarchical Bayesian extensions to classical bivariate linear mixed modeling of residual (cow-level) and random (herd-level) (co)variances for the joint analysis of two Gaussian outcomes. This approach involves modeling heterogeneous associations between outcomes using dispersion parameters generated from a square-root-free Cholesky reparameterization of (co)variances. These reparameterizations are unconstrained and hence can themselves be readily modeled as functions of fixed and random effects. This approach is extended further to bivariate generalized linear models, whereby modeling of heterogeneous associations between Gaussian and non-Gaussian outcomes, such as health and reproductive fitness, is facilitated using data augmentation techniques. The proposed hierarchical Bayesian models constitute an important advancement in statistical methodology as they introduce a new dimension of heterogeneity in the study of complex biological systems, namely that of heterogeneous covariances (or correlations) between outcomes of interest.;The nature of the cow-level and herd-level associations between milk production and reproduction in dairy cows was explored by applying the aforementioned hierarchical Bayesian models to large datasets from commercial dairy farms in Michigan. Means, variances, and covariances between indicators of milk production and reproductive performance were jointly modeled as separate functions of management practices and herd attributes, with statistically important factors selected based on the Deviance Information Criterion. Evidence for heterogeneity in the association between milk production and reproduction was overwhelming. Most notably, inferred relationships were generally quite different and, in some cases, opposite in sign between the cow-level and the herd-level components. Secondly, management practices and herd attributes were identified as contributors to heterogeneity in the nature, as well as the magnitude, of the link between milk yield and reproductive performance. In particular, intensive management conditions appeared to contribute to a more favorable association in some cases (e.g., estimated herd calving interval decreased by 1.4+/-0.1 d per 100 kg increase in cumulative milk yield for herds using bovine somatotropin treatment) or to a partial alleviation of an overall antagonism in others (i.e. 21% greater pregnancy rates among herds implementing more frequent milking schemes). Understanding the multidimensional levels of heterogeneity in the associations between milk production and reproductive performance should have direct implications for tailoring dairy management programs that optimize overall dairy cow performance in current production systems. |
