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.

On identifiability of (co)variance components in animal models with competition effects.

There is an increased interest in estimating the (co)variance components of additive animal models with direct and competition effects (AMC). However, some attempts to estimate the dispersion parameters in different animal species faced problems of convergence or inaccurate estimates when pen effects entered the model. We argue that the problem relates to lack of identifiability of the (co)variance components in some AMC. The check for identifiability of the dispersion parameters in mixed models with linear (co)variance structure requires that all the eigenvalues of the restricted maximum likelyhood information matrix (I(theta)) be positive. We show, by way of simple numerical examples, that the singularity of I(theta) is due to confounding between fixed pen effects and the additive competition effects (SBVs). It is also observed that setting pen effects as random does not always remedy the collinearity with SBVs. An alternative AMC is presented in which the incidence matrix of the SBVs can be written as a function of the 'intensity of competition' (IC) among animals in the same pen. Examples are presented in which the ICs are related to time. The distribution of families of full and half sibs across pens also plays a role in the identifiability and asymptotic variances of the (co)variance components.