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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 (σgg m), permanent maternal environmental effects (m) and temporary enviornmental effects (e). The second model also allowed for a nonzero environmental covariance (σmem ) 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 σgg n and σg mg n. 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 h2 g and h2 g n averaged .30 and .16, respectively. All SDS estimates of ρgg m (correlation between direct and maternal genetic effects) were less than -1. Estimates of σmem were positive. Both SDS estimates and one of the two ANOVA estimates of the grandmaternal variance were negative. The ANOVA model 4 estimates of h2 g were .33. The estimates of h2 g m were .44 and .39, while the estimates for ρgg m were −.88 and −.80. Both estimates of σmem were positive. The four ANOVA model 2 estimates of h2 g and h2 g m averaged .33 and .48, respectively. Three of the four estimates of ρgg m were less than −.97; the fourth was .35. Three of the four estimates of ρgg m 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. Copyright © 1986. American Society of Animal Science . Copyright 1986 by American Society of Animal Science.