Test-day milk yield records of 11,023 first-parity Holstein cows were used to estimate genetic parameters for milk yield during different lactation periods. (Co)variance components were estimated using two random regression models, RRM1 and RRM2, and the restricted maximum likelihood method, compared by the likelihood ratio test. Additive genetic variances determined by RRM1 and additive genetic and permanent environmental variances estimated by RRM2 were described, using the Wilmink function. Residual variance was constant throughout lactation for the two models. The heritability estimates obtained by RRM1 (0.34 to 0.56) were higher than those obtained by RRM2 (0.15 to 0.31). Due to the high heritability estimates for milk yield throughout lactation and the negative genetic correlation between test-day yields during different lactation periods, the RRM1 model did not fit the data. Overall, genetic correlations between individual test days tended to decrease at the extremes of the lactation trajectory, showing values close to unity for adjacent test days. The inclusion of random regression coefficients to describe permanent environmental effects led to a more precise estimation of genetic and non-genetic effects that influence milk yield.

Genetic relationships between Brazilian and US Holstein cattle populations were studied using first-lactation records of 305-d mature equivalent (ME) yields of milk and fat of daughters of 705 sires in Brazil and 701 sires in the United States, 358 of which had progeny in both countries. Components of(co)variance and genetic parameters were estimated from all data and from within herd-year standard deviation for milk (HYSD) data files using bivariate and multivariate sire models and DFREML procedures distinguishing the two countries. Sire (residual) variances from all data for milk yield were 51 to 59% (58 to 101%) as large in Brazil as those obtained from half-sisters in the average US herd. Corresponding proportions of the US variance in fat yield that were found in Brazil were 30 to 41% for the sire component of variance and 48 to 80% for the residual. Heritabilities for milk and fat yields from multivariate analysis of all the data were 0.25 and 0.22 in Brazil, and 0.34 and 0.35 in the United States. Genetic correlations between milk and fat were 0.79 in Brazil and 0.62 in the United States. Genetic correlations between countries were 0.85 for milk, 0.88 for fat, 0.55 for milk in Brazil and fat in the US, and 0.67 for fat in Brazil and milk in the United States. Correlated responses in Brazil from sire selection based on the US information increased with average HYSD in Brazil. Largest daughter yield response was predicted from information from half-sisters in low HYSD US herds (0.75 kg/kg for milk; 0.63 kg/kg for fat), which was 14% to 17% greater than estimates from all US herds because the scaling effects were less severe from heterogeneous variances. Unequal daughter response from unequal genetic (co)variances under restrictive Brazilian conditions is evidence for the interaction of genotype and environment. The smaller and variable yield expectations of daughters of US sires in Brazilian environments suggest the need for specific genetic improvement strategies in Brazilian Holstein herds. A US data file restricting daughter information to low HYSD US environments would be a wise choice for across-country evaluation. Procedures to incorporate such foreign evaluations should be explored to improve the accuracy of genetic evaluations for the Brazilian Holstein population.

-Data comprising 263,390 test-day (TD) records of 32,448 first parity cows calving in 467 herds between 1991 and 2001 from the Brazilian Holstein Association were used to estimate genetic and permanent environmental variance components in a random regression animal model using Legendre polynomials (LP) of order three to five by REML. Residual variance was assumed to be constant in all or in some classes of lactation periods for each LP. Estimates of genetic and permanent environmental variances did not show any trend due to the increase in the LP order. Residual variance decreased as the order of LP increased when it was assumed constant, and it was highest at the beginning of lactation and relatively constant in mid lactation when assumed to vary between classes. The range for the estimates of heritability (0.27 -0.42) was similar for all models and was higher in mid lactation. There were only slight differences between the models in both genetic and permanent environmental correlations. Genetic correlations decreased for near unity between adjacent days to values as low as 0.24 between early and late lactation. A five parameter LP to model both genetic and permanent environmental effects and assuming a homogeneous residual variance would be a parsimonious option to fit TD yields of Holstein cows in Brazil. foi assumida como constante em todo ou em algumas classes do período de lactação para cada PL. As estimativas dos efeitos genético e permanente de ambiente não apresentaram qualquer tendência atribuída ao aumento da ordem do PL. A variância residual diminuiu com o aumento da ordem do PL quando assumida como constante e foi maior no início da lactação e relativamente constante na fase intermediária quando assumida como heterogênea entre classes do período de lactação. As estimativas de herdabilidade variaram de 0,27 a 0,42 em todos os modelos e foram maiores na fase intermediária da lactação.As diferenças entre modelos para as correlações genéticas e de ambiente permanente foram pequenas. As correlações genéticas decresceram de valores próximos à unidade entre as produções de leite de controles próximos para 0,24 entre as produções de leite dos controles do início e do final da lactação. O polinômio de Legendre de cinco parâmetros para a modelagem dos efeitos genético e de ambiente permanente com homogeneidade de variância residual é uma opção parcimoniosa para o ajuste das PC de vacas da raça Holandesa no Brasil.Palavras-chave: avaliação genética, bovinos de leite, componentes de co-variância, herdabilidade, seleção

-Data from 26,558 Holstein cows in 802 herds were used to estimate genetic, residual and phenotypic parameters for 22 type traits. The model included the fixed effects of herd-year, period of classification, classifier, stage of lactation and age of cows at calving (covariate) and random genetic and residual effects. Heritability for type traits ranged from 0.10 to 0.39. The genetic variability in these traits suggested the possibility for moderate genetic gains through selection. The phenotypic correlations were moderated, mainly in the section conformation. Genetic correlations between type traits ranged from -0.44 to 0.85. High genetic correlations indicated that breeding programs could be successful without including all type traits. The selection for the final score at the expense of other traits must be performed with restraint, because in the long term, this may promote undesirable changes in some type traits.