| Abstract: | Analysis of variance (ANOVA) and symmetric differences squared (SDS) methods were used to estimate additive genetic and environmental variances and covariances associated with weaning weight. The two methods were applied to 503 beef records collected over 19 yr from a relatively unselected university Angus herd. The SDS methodology was used with four models. The first model included direct (g) and maternal (gm) additive genetic effects, the genetic covariance between direct and maternal additive genetic effects (sigma ggm), permanent maternal environmental effects (m) and temporary environmental effects (e). The second model also allowed for a nonzero environmental covariance (sigma mem) between dam and offspring weaning weights. Models 3 and 4 were models 1 and 2, respectively, expanded to include a grandmaternal genetic effect (gn) and covariances sigma ggn and sigma gmgn. Two ANOVA solution sets for the parameters of model 4 were based on sire, dam, maternal grandsire, maternal grandam and phenotypic variances and offspring-dam (covOD), offspring-sire (covOS), offspring-grandam (covOGD) and offspring-maternal half-aunt or uncle (covOMH) covariances. Four ANOVA solution sets for the parameters of model 2 were based on sire, dam, within dam and maternal grandsire variances, covOD and either covOS or covOGD. Symmetric differences squared estimates of h2g and h2gm averaged .30 and .16, respectively. All SDS estimates of rho ggm (correlation between direct and maternal genetic effects) were less than -1. Estimates of sigma mem were positive. Both SDS estimates and one of the two ANOVA estimates of the grandmaternal variance were negative. The ANOVA model 4 estimates of h2g were .33. The estimates of h2gm were .44 and .39, while the estimates for rho ggm were -.88 and -.80. Both estimates of sigma mem were positive. The four ANOVA model 2 estimates of h2g and h2gm averaged .33 and .48, respectively. Three of the four estimates of rho ggm were less than -.97; the fourth was .35. Three of the four estimates of sigma mem were positive. Expectations show the extent to which SDS and ANOVA estimators were biased by nonzero grandmaternal components that were not accounted for. The extent to which dominance components bias the ANOVA estimators also is shown. Nonzero grandmaternal effects need to be taken into account in either SDS or ANOVA solution sets, or important biases occur with most of the estimators. More numerous, and generally more severe, biases occur with ANOVA estimators than with SDS estimators in solution sets that do not account for grandmaternal effects. |
