Alternative strategies for genetic analyses of milk flow in dairy cattle

Measurements for average milk flow (AMF) in kilograms of milk per minute of milking time from 629,161 Holstein cows from calving years 1990 to 2008 were used to estimate genetic covariance components using a variety of statistical models. For bivariate linear-threshold model applications, Gaussian-distributed AMF (linear sire model) was categorized into 2 distinct classes (threshold sire model) by setting arbitrary thresholds for extremely slow or extremely fast milking cows. In different bivariate runs with the 2 traits, Gaussian AMF and binary AMF, within a Bayesian framework, thresholds for the binary trait were 1.2, 1.6, 2.6, and 2.8 kg/min. Posterior heritabilities for AMF from the linear and the threshold models in all runs were in a narrow range and close to 0.26, and the posterior genetic correlation between AMF, defined as either a Gaussian or binary trait, was 0.99. A data subset was used to infer genetic and phenotypic relationships between AMF with test-day traits milk yield, fat percentage, protein percentage, somatic cell score (SCS), fat-to-protein ratio, and energy-corrected milk using recursive linear sire models, standard multiple trait linear sire models, and multiple trait linear sire models accounting for the effect of a trait 1 on a trait 2, and of trait 2 on trait 3, via linear regressions. The time-lagged 3-trait system focused on the first test-day trait after calving (trait 1), on AMF (trait 2), and on the test-day trait (trait 3) after the AMF measurement. Posterior means for heritabilities for AMF from linear and recursive linear models used for the reduced data set ranged between 0.29 and 0.38, and were slightly higher than heritabilities from the threshold models applied to the full data set. Genetic correlations from the recursive linear model and the linear model were similar for identical trait combinations including AMF and test-day traits 1 and 3. The largest difference was found for the genetic correlation between AMF and fat percentage from the first test day (i.e., -0.31 from the recursive linear model vs. -0.26 from the linear model). Genetic correlations from the linear model, including an additional regression coefficient, partly differed, especially when comparing correlations between AMF and SCS and between AMF and fat-to-protein ratio recorded after the AMF measurement data. Structural equation coefficients from the recursive linear model and corresponding regression coefficients from the linear model with additional regression, both depicting associations on the phenotypic scale, were quite similar. From a physiological perspective, all models confirmed the antagonistic relationship between SCS with AMF on genetic and phenotypic scales. A pronounced recursive relationship was also noted between productivity (milk yield and energy-corrected milk) and AMF, suggesting further research using physiological parameters as indicators for cow stress response (e.g., level of hormones) should be conducted.