Background: Knowledge of genetic correlations and the economics of traits are essential to decide which traits should be used as selection criteria. Objective: To estimate heritabilities and genetic, environmental, and phenotypic correlations, and direct (DRS) and correlated (CRS) responses to selection by scrotal circumference (SC), frame score (FS), and yearling weight (YW) of Mexican Charolais (CH), and Charbray (CB) Young bulls. Methods: Actual SC, height and YW records (10,078 for CH, and 500 for CB) were adjusted to 365 d. The 0.0505 adjustment factor recommended by the Beef Improvement Federation was used to obtain the 365-d adjusted SC for both breeds. Height and age records were used to obtain FS. Data were analyzed using a three-trait animal model. The animal model for each trait included bull breed, contemporary group (groups of young bulls born in the same herd, year, and season of the year), and age of dam as a linear covariate as fixed effects, and direct additive genetic and residual as random effects. Results: Heritability estimates for SC, FS and YW were 0.21 ± 0.04, 0.25 ± 0.04, and 0.29 ± 0.04, respectively. The genetic correlation between YW with SC was 0.37 ± 0.16, and between YW with FS was 0.42 ± 0.16. The estimate of genetic correlation between SC and FS was low and positive (0.15 ± 0.14). The DRS was 0.38 cm, 0.18 units, and 8.30 kg for SC, FS and YW. The CRS was 0.16 cm, and 0.08 units for SC and FS from indirect selection on YW. Conclusions: Direct selection for YW is expected to be effective. Indirect selection for SC and FS based on YW would not be expected to be as effective as direct selection for improving SC and FS.
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