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The objective of the present study was to estimate the genetic parameters for test-day milk yields (TDMY) in the first and second lactations using random regression models (RRM) in order to contribute to the application of these models in genetic evaluation of milk yield in Gyr cattle. A total of 53,328 TDMY records from 7118 lactations of 5853 Gyr cows were analyzed. The model included the direct additive, permanent environmental, and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cows at calving were included as fixed effects. A random regression model fitting fourth-order Legendre polynomials for additive genetic and permanent environmental effects, with five classes of residual variance, was applied. In the first lactation, the heritabilities increased from early lactation (0.26) until TDMY3 (0.38), followed by a decrease until the end of lactation. In the second lactation, the estimates increased from the first (0.29) to the fifth test day (0.36), with a slight decrease thereafter, and again increased on the last two test days (0.34 and 0.41). There were positive and high genetic correlations estimated between first-lactation TDMY and the remaining TDMY of the two lactations. The moderate heritability estimates, as well as the high genetic correlations between half the first-lactation TDMY and all TDMY of the two lactations, suggest that the selection based only on first lactation TDMY is the best selection strategy to increase milk production across first and second lactations of Gyr cows.

The objective of this study was to estimate genetic parameters for 305-day cumulative milk yield (MY305) and its association with test-day milk yield (TDMY) in Saanen and Alpine goats in order to provide information that allows the use of TDMY as selection criteria. This was done using standard multi-trait and reduced rank models. Data from 1157 lactations, including the first three kiddings, and 5435 test-day records from 683 Saanen and 449 Alpine goats were used. MY305 was analyzed together with TDMY by multi-trait analysis, from the first to tenth test-day, using records of the first three lactations as repeated measures. Three multi-trait models were used: a standard (SM) and two reduced rank models that fitted the first two (PC2) and three (PC3) genetic principal components. Akaike and Schwarz Bayesian information criteria were used to compare models. Heritability for TDMY estimated with the SM ranged from 0.20 to 0.66, whereas the range calculated from the PC2 model was 0.16 to 0.63. Genetic correlations between TDMY and MY305 were positive and moderate to high, ranging from 0.56 to 0.98 when estimated with the SM, and 0.91 to 1.00 when estimated with the PC2. The standard multi-trait model produced estimates that were more accurate than the reduced rank models. Although the SM provided the worst fit according to the two model selection criteria, it was the best in this dataset.

The objective of this study was to estimate genetic parameters for test-day milk yield (TDMY) in Guzerá cows using random regression models. Additive and permanent environmental random effects were modeled by random regression on fourth- and fifth-order orthogonal Legendre polynomials, respectively. The residual variances were heterogeneous, with seven classes. Heritability estimates for TDMY ranged from 0.24 to 0.52, with higher heritabilities for yields during early lactation. Genetic correlations between TDMYs ranged from -0.03 to 0.95. The phenotypic and permanent environmental correlations were all positive, and the highest estimates were between adjacent TDMYs. The results suggest that TDMYs obtained with random regression models may be used as selection criteria for Guzerá cattle.

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.

The objective of this study was to estimate variance components and genetic parameters for accumulated 305-day milk yield (MY305) over multiple ages, from 24 to 120 months of age, applying random regression (RRM), repeatability (REP) and multi-trait (MT) models. A total of 4472 lactation records from 1882 buffaloes of the Murrah breed were utilized. The contemporary group (herd-year-calving season) and number of milkings (two levels) were considered as fixed effects in all models. For REP and RRM, additive genetic, permanent environmental and residual effects were included as random effects. MT considered the same random effects as did REP and RRM with the exception of permanent environmental effect. Residual variances were modeled by a step function with 1, 4, and 6 classes. The heritabilities estimated with RRM increased with age, ranging from 0.19 to 0.34, and were slightly higher than that obtained with the REP model. For the MT model, heritability estimates ranged from 0.20 (37 months of age) to 0.32 (94 months of age). The genetic correlation estimates for MY305 obtained by RRM (L23.res4) and MT models were very similar, and varied from 0.77 to 0.99 and from 0.77 to 0.99, respectively. The rank correlation between breeding values for MY305 at different ages predicted by REP, MT, and RRM were high. It seems that a linear and quadratic Legendre polynomial to model the additive genetic and animal permanent environmental effects, respectively, may be sufficient to explain more parsimoniously the changes in MY305 genetic variation with age.

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.

We investigated the effect of stage of pregnancy on estimates of breeding values for milk yield and milk persistency in Gyr and Holstein dairy cattle in Brazil. Test-day milk yield records were analyzed using random regression models with or without the effect of pregnancy. Models were compared using residual variances, heritabilities, rank correlations of estimated breeding values of bulls and cows, and number of nonpregnant cows in the top 200 for milk yield and milk persistency. The estimates of residual variance and heritabilities obtained with the models with or without the effect of pregnancy were similar for the two breeds. Inclusion of the effect of pregnancy in genetic evaluation models for these populations did not affect the ranking of cows and sires based on their predicted breeding values for 305-day cumulative milk yield. In contrast, when we examined persistency of milk yield, lack of adjustment for the effect of pregnancy overestimated breeding values of nonpregnant cows and cows with a long days open period and underestimated breeding values of cows with a short days open period. We recommend that models include the effect of days of pregnancy for estimation of adjustment factors for the effect of pregnancy in genetic evaluations of Dairy Gyr and Holstein cattle.