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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: I. Comparison via Simulation¹

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 for estimating genetic and environmental variances and covariances associated with beef cattle weaning weight were compared via simulation. Simulation was based on the pedigree and record structure of 503 beef weaning weights collected over 19 yr from a university herd. The SDS methodology was used with four models. The simplest model included direct (g) and maternal (g^m) additive genetic effects, genetic covariance between direct and maternal additive genetic effects (gg^m), permanent maternal environmental effects (m) and temporary environmental 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 obtained using 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 obtained using sire, dam, within dam and maternal grandsire variances, covOD and either covOS or covOGD. Two sets of 1,000 replicates of the data were simulated. These data were used to compare precision and accuracy of SDS and ANOVA estimators, to estimate correlations among SDS and ANOVA estimators, and to study the importance of taking inbreeding into account with SDS methodology. All ANOVA estimators for _ggm were biased downward. The SDS procedure had a clear advantage over ANOVA. Averages of SDS estimates were closer to parameter values used to simulate the data and their Standard deviations were generally smaller. The Standard deviations of both SDS and ANOVA estimates of _ggm were very large. It is important to allow for a nonzero _mem (at least when it is negative) when using SDS methods; otherwise estimators of ²_gm and _ggm are biased upward and downward, respectively.

¹ Published with the approval of the Director of the North Dakota Agr. Exp. Sta. as Journal Article No. 1481.

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

⁴ Anim. and Range Sci. Dept.