Bayesian analysis of selection for greater weaning weight while maintaining birth weight in beef cattle.

An experimental Hereford herd established in 1960 was used from 1986 to 2006 to select for increased weaning weight (W) without increasing birth weight (B). Data were B and W collected over the 47 yr from 2,124 calves. Including ancestors, the pedigree file had 2,369 animals. Selection was practiced only in males. In the first stage (1986 to 1993), mass-selected bulls were chosen with the index I = B + 9374.76 RDG (relative daily gain). From 1994 to 2006, the selection criterion for bull i was I(i) = BLUP(i)(WD) - 2.33 BLUP(i)(BD), where the BLUP were for the direct BV of B (BD) and W (WD), respectively. Predictions were obtained from a 2-trait animal model with B having only BD, and W with WD and WM (maternal additive effects). Selection response was estimated using a Bayesian approach by means of the Gibbs sampler for a 2-trait animal model including BD, BM (maternal BV for B), WD, and WM. Estimated heritabilities for BD, BM, WD, and WM were 0.40, 0.23, 0.05, and 0.23, respectively. The correlation between BD and BM was close to zero (0.01), and between WD and WM was positive (0.37). The correlation between BD and WD was 0.07, and between BM and WM was 0.58. The 2 methods used to estimate selection response gave similar results. In both periods BD decreased, whereas BM increased. The reduction of BD due to selection was slightly larger in the second period than in the first one. The regression of BV for W increased due to selection in both stages, but selection response was 21.6% larger from 1986 to 1992 than from 1993 to 2006. The maternal effect, WM increased more than 3 times compared with WD in the first period, but ended up being almost the same value as WD in period 2. The Bulmer effect was manifested by the decrease in magnitude of all (co)variance components during selection. It is concluded that selection to increase BW at weaning in beef cattle, although not increasing BW at birth, was moderately effective.

Semiparametric animal models via penalized splines as alternatives to models with contemporary groups.

Contemporary groups (CG) are used in genetic evaluation to account for systematic environmental effects of management, nutritional level, or any other differentially expressed group effect; however, because the functional form of the distribution of those effects is unknown, CG serve as an approximation to a time-varying mean. Conversely, in semiparametric models, there is no need to assume any functional form for the time-varying effects. In this research, we present a semiparametric animal model (AMS) using the covariate day of birth (DOB) by means of penalized splines (P-splines), as an alternative to fitting CG. In the AMS, the functionality of the data on DOB is expressed by means of a Basic segmented polynomial line (B-spline) basis, and proper covariance matrices are used to reflect the serial correlation among the points of support (or knots) at different times. Three different covariance matrices that reflect either short- or long-range dependences among knots are discussed. Different models were fitted to birth weight data from Polled Hereford calves. Models compared were an animal model with CG, an animal model with CG and the covariate DOB nested within CG (CG + DOB), and P-splines with the first difference penalty matrix and three different AMS with 20, 40, 60, 80, or 120 knots. Models were compared using a modified Akaike information criterion (AICC), which was calculated as a byproduct of the estimation of variance components by REML using the expectation maximization algorithm. All three AMS had smaller (better) values of AICC than the regular model with CG, while producing almost the same ranking of predicted breeding values and similar average predicted error variance. In all AMS, the inference and all measures of comparison were similar when the number of knots was equal > or = 40. The model CG + DOB had analogous performance to the AMS, but at the expense of using more parameters. It is concluded that the use of penalized regression splines using a B-spline basis with proper covariance matrices is a competitive method to the fitting of CG into animal models for genetic evaluation, without having to assume any functional form for the covariate DOB.

Comparison of restricted maximum likelihood and method R for estimating heritability and predicting breeding value under selection.

Method R and Restricted Maximum Likelihood (REML) were compared for estimating heritability (h2) and subsequent prediction of breeding values (a) with data subject to selection. A single-trait animal model was used to generate the data and to predict breeding values. The data originated from 10 sires and 100 dams and simulation progressed for 10 overlapping generations. In simulating the data, genetic evaluation used the underlying parameter values and sires and dams were chosen by truncation selection for greatest predicted breeding values. Four alternative pedigree structures were evaluated: complete pedigree information, 50% of phenotypes with sire identities missing, 50% of phenotypes with dam identities missing, and 50% of phenotypes with sire and dams identities missing. Under selection and with complete pedigree data, Method R was a slightly less consistent estimator of h2 than REML. Estimates of h2 by both methods were biased downward when there was selection and loss of pedigree information and were unbiased when no selection was practiced. The empirical mean square error (EMSE) of Method R was several times larger than the EMSE of REML. In a subsequent analysis, different combinations of generations selected and generations sampled were simulated in an effort to disentangle the effects of both factors on Method R estimates of h2. It was observed that Method R overestimated h2 when both the sampling that is intrinsic in the method and the selection occurred in generations 6 to 10. In a final experiment, BLUP(a) were predicted with h2 estimated by either Method R or REML. Subsequently, five more generations of selection were practiced, and the mean square error of prediction (MSEP) of BLUP(a) was calculated with estimated h2 by either method, or the true value of the parameter. The MSEP of empirical BLUP(a) using Method R was greater than the MSEP of empirical BLUP(a) using REML. The latter statistic was closer to prediction error variance of BLUP(a) than the MSEP of empirical BLUP(a) using Method R, indicating that empirical BLUP(a) calculated using REML produced accurate predictions of breeding values under selection. In conclusion, the variability of h2 estimates calculated with Method R was greater than the variability of h2 estimates calculated with REML, with or without selection. Also, the MSEP of EBLUP(a) calculated using estimates of h2 by Method R was larger than MSEP of EBLUP(a) calculated with REML estimates of h2.