Effect of including relationships in the estimation of genetic parameters of beef calves

Variances and covariances for birth weight, gain from birth to weaning (ADG), and 205-d weight were obtained from a sire-dam model and a sire-maternal grandsire model for a herd of Angus and a herd of Hereford cattle. Estimates of direct additive genetic variance (sigma 2A), maternal additive genetic variance (sigma 2M), covariance between direct and maternal additive genetic effects (sigma AM), permanent environmental variance (sigma 2PE), and residual variance (sigma 2e) were obtained both with and without the inverse of the numerator relationship matrix (A-1) included. Estimates of heritability for direct genetic effects (h2A), maternal genetic effects (h2M), and the correlation between direct and maternal effects (rAM) for birth weight were .37, .18, and -.01 in Angus and .53, .23, and -.19 in Herefords, respectively, for the analyses without A-1. For the analyses with A-1, estimates of h2A, h2M, and rAM were .42, .22, and -.12 for Angus and .58, .22, and -.13 for Herefords, respectively. Estimates of h2A, h2M, and rAM for ADG were .43, .15, and -.44 in Angus and .52, .38, and -.03 in Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .57, .15, and -.32 for Angus and .58, .39, and -.05 for Herefords, respectively. Estimates of h2A, h2M, and rAM for 205-d weight were .49, .15, and -.46 for Angus and .58, .43, and -.06 for Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .63, .16, and -.36 for Angus and .66, .43, and -.08 for Herefords, respectively. Estimates of h2A were higher with A-1 than without A-1, but estimates of h2M were similar. Using variances and covariances obtained from analyses including A-1 generally gave higher estimates of direct breeding values than using variances and covariances obtained from analyses not including A-1. Both Pearson product-moment and Spearman rank correlations were high (.99) between estimates of breeding values from the two analyses, although some changes in rank did occur.