Bayesian estimation in maternally ancestral animal models for weaning weight of beef cattle1

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The Bayesian approach was implemented for fitting several maternally ancestral models for weaning weight data of Angus calves. The goal was to evaluate to what extent genetic evaluation models with additive grand maternal effects (G), or with an ancestrally structured covariance matrix for maternal environmental effects (E), or with a sire × year interaction (ISY), or combinations thereof (GE, GSY, ESY, GESY), redistribute the additive variability and reduce the negative magnitude of the additive correlation between direct and maternal effects (r(AoAm)), when compared with the regular maternal animal model (I). All animals with records had known dams and maternal granddams. The sampling scheme induced low autocorrelations among all variables and tended to converge quickly. The signs of the estimates of r(AoAm) were consistently negative for all models fitted. The magnitudes of the estimates of r(AoAm) from models E, G, GE, ESY, and GESY were almost one-third of those from models I and ISY. Inclusion of the sire × year interaction had some effect in reducing the negative magnitude of r(AoAm), but also reduced the size of the estimates of direct (h(0)(2)) and maternal (h(m)(2)) heritabilities. In comparison, models E or G reduced the negative magnitude of r(AoAm) by 0.50 units and produced more favorable estimates of H(0)(2) and h(m)(2) than models I and ISY. The estimate of h(0)(2) from G was similar to the one from I; however, the estimated h(m)(2) was 0.04 units greater, whereas the estimate of r(AoAm) was much less negative (-0.21 vs. -0.71) than the respective estimates from I. The environmental correlation between the weaning weights of dams and their daughters (λ) was estimated to be -0.28 ± 0.03 in E and ESY, and -0.21 ± 0.03 in GE and GESY. Inclusion of the sire × year interaction effect by itself did not have much of an impact in the reduction of the estimated magnitude of r(AoAm). Rank correlations among EBV for direct effects were larger than 0.94 and did not show any appreciable difference among models, whereas the rank correlation among maternal breeding values displayed differences in the ranking between I and the other models. Models E and ESY recovered the largest amount of total additive variability with maternal effects.