Restricted Maximum Likelihood (REML) procedures for multiple trait animal models were used to estimate heritabilities, genetic correlations, and common environmental effects for average daily gain (ADG), backfat thickness (BF), and number of pigs born alive per litter (NBA). Data included 5561 litter records and 38622 ADG and BF individual performance records for on- farm-tested Large White, Landrace, and Duroc pigs fed ad libitum from three New Zealand nucleus herds recorded over the period 1980-93. A bivariate animal model for ADG and BF contained fixed effects for herd-year-season (HYS) of test, sex, and age as a linear covariable, as well as random litter and animal effects. The NBA model included fixed season of farrowing and parity effects, and random animal (sow) and permanent environmental effects. Repeated records for NBA were accommodated by fitting a permanent environmental effect, uncorrelated to additive genetic effects, for each sow. The estimates of heritability (h2) for ADG were 0.20, 0.18, and 0.16, and the estimates of the litter variance in proportion to the phenotypic variance (c2) were 0.11, 0.12, and 0.09 for Large White, Landrace, and Duroc breeds, respectively. The h2 estimates for BF were 0.44, 0.45, and 0.46 for Large White, Landrace, and Duroc breed, respectively, and proportionate c2 estimates were 0.06 for all breeds. The phenotypic, genetic, and litter correlations between ADG and BF ranged from 0.32 to 0.54. The h2 estimates for NBA were 0.13, 0.09, and 0.16, permanent environmental variance ratios (m2) were 0.06, 0.05, and 0.05, and repeatability estimates (t) were 0.19, 0.14, and 0.21 for Large White, Landrace, and Duroc breeds, respectively. Correlations found in this study between ADG and BF indicate that selection to improve one trait may be associated with unfavourable change in the other trait. Therefore, a multiple trait selection procedure such as a selection index is required to accommodate these antagonistic associations between traits.
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