Assumindo que a seleção em rebanhos fechados pode promover a redução da variância genética aditiva, foi estudada a possibilidade do uso de um modelo de regressão múltipla para estimar os componentes de (co)variância genética aditiva, ao longo dos anos em que a seleção foi praticada. Foram utilizados dados simulados de peso aos 550 dias em dez rebanhos de bovinos de corte submetidos à seleção por 20 anos. Assumindo que a cada cinco anos o peso aos 550 dias era uma nova característica, por meio de análises multicaráter envolvendo quatro características, em um modelo animal, foram estimados componentes de (co)variância. Foram ajustadas três equações de regressão múltipla, RMI, RMM, RMF, estimando componentes de (co)variância genética aditiva para 20 anos de seleção e para oito anos anteriores à seleção. Na RMI, foram utilizados os anos iniciais de cada geração de seleção, para a RMM os anos intermediários e na RMF os anos finais como covariável. As equações apresentaram altos coeficientes de determinação, no entanto, não houve diferença de ajuste entre os três modelos. Observou-se que os modelos de regressão múltipla podem ser usados na estimação dos componentes de (co)variância genética quando se admite heterocedasticidade ao longo do tempo, causada pela seleção.

Assuming that selection in closed herds can promote reduction in additive genetic variance, multiple regression models were used to estimate this change in additive genetic (co)variance component, over the years when the selection was done. Weights at 550 days (W550) were studied using simulated data of herds submitted to 20 years of selection. (Co)variance components were estimated assuming that the weight at 550 days was a new trait every five years, by multiple-trait analyses involving four traits in the animal model. Three multiple regression equations were fitted-RMI, RMM, RMF-estimating thus the additive genetic (co)variance components for the 20 years of selection and eight years prior to the selection process. The initial years of each generation of selection were used as a covariate in the RMI. In the RMM, intermediate years were used, and the final years were considered in the RMF. The equations showed high coefficients of determination. However, there was no difference in the adjustment between the models. It was observed that the multiple regression models can be used in the estimation of genetic (co)variance components, when heteroscedasticity is assumed over time due to the selection process.

Genetic and phenotypic parameters considering the genetic effect on hygienic behavior of queen and workers from 40 Africanized honeybees colonies were estimated separately. Maternal origin of queens was controlled whereas the paternal was unknown, and different groups of workers were considered in three seasons, October 2006, April 2007 and August 2007, but with the same queen. Colonies were 21 honey producers and 19 royal jelly producers. After the method of freezing capped brood, hygienic behavior was determined by the ratio between the number of dead capped brood removed at 24, 48 and 72 hours and the total number of capped brood at zero hour. Data was submitted to single and three traits analyses using Bayesian inference. Estimates of direct heritability at 24, 48 and 72 hours (0.10, 0.11 and 0.11) were identical to the motherly ones. Estimates by three trait analysis of direct heritability were 0.28, 0.15, 0.24, and of maternal heritability were 0.23, 0.29, 0.27, at 24, 48 and 72 hours, respectively. Correlations between maternal and genetic effects were 0.12, 0.09 and - 0.08 at, 24, 48 and 72 hours, respectively. Correlation between 24 and 48 hours was 0.49; between 24 and 72 hours, 0.40; and between 48 and 72 hours, 0.47. Moderate genetic correlations with the number of capped brood removed until 48 and 72 hours indicate that after the selection of a few generations, these traits can become an efficient criterion for selection in 24 hours.