Symmetric Differences Squared and Analysis of Variance Procedures for Estimating Genetic and Environmental Variances and Covariances for Beef Cattle Weaning Weight: I. Comparison via Simulation

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 (σgg^m), permanent maternal environmental effects (m) and temporary environmental effects (e). The second model also allowed for a nonzero environmental covariance (σ_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 σ_ggn and σ_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 ρ_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 ρ_ggm were very large. It is important to allow for a nonzero σ_mem (at least when it is negative) when using SDS methods; otherwise estimators of σ²_gm and σ_ggm are biased upward and downward, respectively. Copyright © 1986. American Society of Animal Science . Copyright 1986 by American Society of Animal Science.