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Symmetric Differences Squared and Analysis of Variance Procedures for Estimating Genetic and Environmental Variances and Covariances for Beef Cattle Weaning Weight: II. Estimates from a Data Set¹

North Dakota State University^,4 Fargo 58105

³ To whom reprint requests are to be directed.

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 (g^m) additive genetic effects, the genetic covariance between direct and maternal additive genetic effects (_ggm), permanent maternal environmental effects (m) and temporary enviornmental effects (e). The second model also allowed for a nonzero environmental covariance (_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 _ggn and _gm_gn. 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_gn averaged .30 and .16, respectively. All SDS estimates of _ggm (correlation between direct and maternal genetic effects) were less than -1. Estimates of _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 h²_g were .33. The estimates of h²_gm were .44 and .39, while the estimates for _ggm were –.88 and –.80. Both estimates of _mem were positive. The four ANOVA model 2 estimates of h²_g and h²_gm averaged .33 and .48, respectively. Three of the four estimates of _ggm were less than –.97; the fourth was .35. Three of the four estimates of _ggm 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.

¹ Published with the approval of the Director of the North Dakota Agr. Exp. Sta. as Journal Article No. 1482.

² Current address: Coastal Plain Exp. Sta., Tifton, GA 31793.

⁴ Anim. and Range Sci. Dept.