Covariance functions and random regression models for cow weight in beef cattle.

Data from the first four cycles of the Germplasm Evaluation program at the U.S. Meat Animal Research Center were used to evaluate weights of Angus, Hereford, and F1 cows produced by crosses of 22 sire and 2 dam (Angus and Hereford) breeds. Four weights per year were available for cows from 2 through 8 yr of age (AY) with age in months (AM). Weights (n = 61,798) were analyzed with REML using covariance function-random regression models (CF-RRM), with regression on orthogonal (Legendre) polynomials of AM. Models included fixed regression on AM and effects of cow line, age in years, season of measurement, and their interactions; year of birth; and pregnancy-lactation codes. Random parts of the models fitted RRM coefficients for additive (a) and permanent environmental (c) effects. Estimates of CF were used to estimate covariances among all ages. Temporary environmental effects were modeled to account for heterogeneity of variance by AY. Quadratic fixed regression was sufficient to model population trajectory and was fitted in all analyses. Other models varied order of fit and rank of coefficients for a and c. A parsimonious model included linear and quartic regression coefficients for a and c, respectively. A reduced cubic order sufficed for c. Estimates of all variances increased with age. Estimates for older ages disagreed with estimates using traditional bivariate models. Plots of covariances for c were smooth for intermediate, but erratic for extreme ages. Heritability estimates ranged from 0.38 (36 mo) to 0.78 (94 mo), with fluctuations especially for extreme ages. Estimates of genetic correlations were high for most pairs of ages, with the lowest estimate (0.70) between extreme ages (19 and 103 mo). Results suggest that although cow weights do not fit a repeatability model with constant variances as well as CF-RRM, a repeatability model might be an acceptable approximation for prediction of additive genetic effects.