Animal temperament is a trait of economic relevance and its use as a selection criterion requires the identification of environmental factors that influence this trait, as well as the estimation of its genetic variability and interrelationship with other traits. The objectives of this study were to evaluate the effect of the covariates dam age at calving (ADC), long yearling age (YA) and long yearling weight (YW) on temperament score (T) and to estimate genetic parameters for T, scrotal circumference (SC) at long YA and age at first calving (AFC) in Nellore cattle participating in a selection program. The traits were analyzed by the restricted maximum likelihood method under a multiple-trait animal model. For all traits, contemporary group was included as a fixed effect and additive genetic and residual as random effects. In addition to these effects, YA, YW and ADC were considered for analyzing T. In the case of SC and AFC, the effect of long YW was included as a covariate. Genetic parameters were estimated for and between traits. The three covariates significantly influenced T. The heritability estimates for T, SC and AFC were 0.18 6 0.02, 0.53 6 0.04 and 0.23 6 0.08, respectively. The genetic correlations between T and SC, and T and AFC were 20.07 6 0.17 and 20.06 6 0.19, respectively. The genetic correlation estimated between SC and AFC was 20.57 6 0.16. In conclusion, a response to selection for T, SC and AFC is expected and selection for T does not imply correlated responses with the other traits.

Stayability is a trait that has a large impact on the costs of rural properties because it is directly related to the cow's ability to produce a certain number of calves over a given period of time. Thus, the objective of this study was to estimate the genetic variance of stayability (STAY) and its genetic associations with age at first calving (AFC), body weight of males and females at 420 days of age (BW420), and scrotal circumference at 420 days of age (SC420), in order to provide support for a genetic evaluation program on Canchim beef cattle. Genetic parameters were estimated by Bayesian inference using the THRGIBBS2F90 program, considering two-trait analysis between STAY and the other traits. A threshold model was established for STAY and a linear model was established for all other traits. The animal model included the contemporary group as the fixed effect and the genetic additive and residual effects as random effects. The heritability estimates and their respective standard deviations (in parentheses) obtained for STAY, AFC, BW420 and SC420 were 0.03 (0.01), 0.04 (0.01), 0.24 (0.04) and 0.24 (0.06), respectively. STAY presented genetic associations with AFC, BW420 and SC420 of − 0.63 (0.20), − 0.09 (0.11) and 0.45 (0.21), respectively. It had environmental correlations with AFC and BW420 of 0.02 (0.01) and − 0.06 (0.04). For SC420, the environmental covariance was set at zero. Selection for BW420 would not contribute towards improving STAY because the genes that acted on one trait did not act on the other. However, selection to increase SC420 should result in changes in this trait and also favor STAY. Despite the favorable genetic correlation estimates between AFC and STAY, the selection response for both traits would be low. Changes in management and environmental conditions could improve both traits.