Bayesian analysis of birth weight and litter size in Baluchi sheep using Gibbs sampling

Variance and covariance components for birth weight (BWT), as a lamb trait, and litter size measured on ewes in the first, second, and third parities (LS1 through LS3) were estimated using a Bayesian application of the Gibbs sampler. Data came from Baluchi sheep born between 1966 and 1989 at the Abbasabad sheep breeding station, located northeast of Mashhad, Iran. There were 10,406 records of BWT recorded for all ewe lambs and for ram lambs that later became sires or maternal grandsires. All lambs that later became dams had records of LS1 through LS3. Separate bivariate analyses were done for each combination of BWT and one of the three variables LS1 through LS3. The Gibbs sampler with data augmentation was used to draw samples from the marginal posterior distribution for sire, maternal grandsire, and residual variances and the covariance between the sire and maternal grandsire for BWT, variances for the sire and residual variances for the litter size traits, and the covariances between sire effects for different trait combinations, sire and maternal grandsire effects for different combinations of BWT and LS1 through LS3, and the residual covariations between traits. Although most of the densities of estimates were slightly skewed, they seemed to fit the normal distribution well, because the mean, mode, and median were similar. Direct and maternal heritabilities for BWT were relatively high with marginal posterior modes of .14 and .13, respectively. The average of the three direct-maternal genetic correlation estimates for BWT was low, .10, but had a high standard deviation. Heritability increased from LS1 to LS3 and was relatively high, .29 to .37. Direct genetic correlations between BWT and LS1 and between BWT and LS3 were negative, -.32 and -.43, respectively. Otherwise, the same correlation between BWT and LS2 was positive and low, .06. Genetic correlations between maternal effects for BWT and direct effects for LS1 through LS3 were all highly negative and consistent for all parities, circa -.75. Environmental correlations between BWT and LS1 through LS3 were relatively low and ranged from .18 to .29 and had high standard errors.