Economic values and selection index in different Angus-Nellore cross-bred production systems.

Bioeconomic models were developed to calculate economic values (EV) for economically important traits in beef cattle, to evaluate the impact of these traits on production profitability, to assess possible market changes with a payment system and to develop economic selection indexes for Angus cattle for two production systems. Two beef cattle production systems were simulated as follows: a cow-calf cycle (CC) and a complete cycle (CoC). Following selection, positive changes in the EV were observed. In the CC, each 1.0% increment in weaning weight (WW), weaning rate (WR) and pregnancy rate (PR) resulted in increases in US$ 1.30, US$ 3.68 and US$ 3.55 per cow/year in profit, respectively. In the CoC, EV of US$ 1.01, US$ 1.79, US$ 1.19, US$ 1.34, US$ 6.84 and US$ 7.86 per cow/year were obtained for WW, year weight, yearling weight, final weight, WR and PR, respectively. The payment system for carcass quality showed that the scenario considering that 100% of the animals displayed uniform carcasses exhibited the highest EV and was considered optimal. Considering the sensitivity analysis, the price paid per animal was the factor that most affected the EV in both systems. The selection indexes obtained may be used in similar production systems, and the use of EV and selection indexes are important tools for any production system with positive change in profit after selection.

Estimates of genetic parameters for stayability and their associations with traits of economic interest in Gir dairy cows.

The objective of the present study was to estimate genetic parameters for stayability at 60 months of age (STAY60) and its association with first lactation cumulative milk yield (P305), age at first calving (AFC), and first calving interval (FCI), in order to adopt these traits as selection criteria for longevity in Gir dairy cattle. Records for 2770 cows born between 1982 and 2008 from six herds in the Brazilian states of Minas Gerais, São Paulo, and Paraíba were analyzed. The (co)variance components were estimated by a Bayesian approach using bivariate animal models. The heritability estimates were 0.37 ± 0.09, 0.23 ± 0.04, 0.26 ± 0.06, and 0.07 ± 0.03 for STAY60, P305, AFC, and FCI, respectively. The genetic correlations of STAY60 with P305, AFC, and FCI were moderate to high, with values of 0.61 (0.17), -0.44 (0.23), and 0.88 (0.13), respectively. STAY60, P305, and AFC exhibited additive genetic variability, and these traits should be considered in selection indices. The indirect selection for longevity through the correlated responses of early-expression traits, such as milk production at first lactation, could be used to improve the ability of animals to remain in the herd.

Detrimental effect of selection for milk yield on genetic tolerance to heat stress in purebred Zebu cattle: Genetic parameters and trends.

In an attempt to determine the possible detrimental effects of continuous selection for milk yield on the genetic tolerance of Zebu cattle to heat stress, genetic parameters and trends of the response to heat stress for 86,950 test-day (TD) milk yield records from 14,670 first lactations of purebred dairy Gir cows were estimated. A random regression model with regression on days in milk (DIM) and temperature-humidity index (THI) values was applied to the data. The most detrimental effect of THI on milk yield was observed in the stage of lactation with higher milk production, DIM 61 to 120 (-0.099kg/d per THI). Although modest variations were observed for the THI scale, a reduction in additive genetic variance as well as in permanent environmental and residual variance was observed with increasing THI values. The heritability estimates showed a slight increase with increasing THI values for any DIM. The correlations between additive genetic effects across the THI scale showed that, for most of the THI values, genotype by environment interactions due to heat stress were less important for the ranking of bulls. However, for extreme THI values, this type of genotype by environment interaction may lead to an important error in selection. As a result of the selection for milk yield practiced in the dairy Gir population for 3 decades, the genetic trend of cumulative milk yield was significantly positive for production in both high (51.81kg/yr) and low THI values (78.48kg/yr). However, the difference between the breeding values of animals at high and low THI may be considered alarming (355kg in 2011). The genetic trends observed for the regression coefficients related to general production level (intercept of the reaction norm) and specific ability to respond to heat stress (slope of the reaction norm) indicate that the dairy Gir population is heading toward a higher production level at the expense of lower tolerance to heat stress. These trends reflect the genetic antagonism between production and tolerance to heat stress demonstrated by the negative genetic correlation between these components (-0.23). Monitoring trends of the genetic component of heat stress would be a reasonable measure to avoid deterioration in one of the main traits of Zebu cattle (i.e., high tolerance to heat stress). On the basis of current genetic trends, the need for future genetic evaluation of dairy Zebu animals for tolerance to heat stress cannot be ruled out.

Genetic parameters of test-day milk yield in Guzerá cattle under tropical conditions.

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.

Growth curves of carcass traits obtained by ultrasonography in three lines of Nellore cattle selected for body weight.

The effect of selection for postweaning weight was evaluated within the growth curve parameters for both growth and carcass traits. Records of 2404 Nellore animals from three selection lines were analyzed: two selection lines for high postweaning weight, selection (NeS) and traditional (NeT); and a control line (NeC) in which animals were selected for postweaning weight close to the average. Body weight (BW), hip height (HH), rib eye area (REA), back fat thickness (BFT), and rump fat thickness (RFT) were measured and records collected from animals 8 to 20 (males) and 11 to 26 (females) months of age. The parameters A (asymptotic value) and k (growth rate) were estimated using the nonlinear model procedure of the Statistical Analysis System program, which included fixed effect of line (NeS, NeT, and NeC) in the model, with the objective to evaluate differences in the estimated parameters between lines. Selected animals (NeS and NeT) showed higher growth rates than control line animals (NeC) for all traits. Line effect on curves parameters was significant (P < 0.001) for BW, HH, and REA in males, and for BFT and RFT in females. Selection for postweaning weight was effective in altering growth curves, resulting in animals with higher growth potential.

Random regression analysis of test-day milk yields in the first and second lactations of Brazilian Gyr cows.

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.

Association between ACTA1 candidate gene and performance, organs and carcass traits in broilers.

This study investigates the genetic association of the SNP present in the ACTA1 gene with performance traits, organs and carcass of broilers to help marker-assisted selection of a paternal broiler line (TT) from EMBRAPA Swine and Poultry, Brazil. Genetic and phenotypic data of 1,400 broilers for 68 traits related to body performance, organ weights, weight of carcass parts, and yields as a percentage of organs and carcass parts were used. The maximum likelihood method, considering 4 analytical models, was used to analyze the genetic association between the SNP and these important economic traits. The association analysis was performed using a mixed animal model including the random effect of the animal (polygenic), and the fixed effects of sex (2 levels), hatch (5 levels) and SNP (3 levels), besides the random error. The traits significantly associated (P<0.05) with the SNP were analyzed, along with body weight at 42 days of age (BW42), by the restricted maximum likelihood method using the multi-trait animal model to estimate genetic parameters. The analysis included the residual and additive genetic random effects and the sex-hatch fixed effect. The additive effects of the SNP were associated with breast meat (BMY), liver yield (LIVY), body weight at 35 days of age (BW35); drumstick skin (DSW), drumstick (DW) and breast (BW) weights. The heritability estimates for these traits, in addition to BW42, ranged from 0.24±0.06 to 0.45±0.08 for LIVY and BW35, respectively. The genetic correlation ranged from 0.02±0.18 for LIVY and BMY to 0.97±0.01 for BW35 and BW42. Based on the results of this study, it can be concluded that ACTA1 gene is associated with performance traits BW35, LIV and BMY, DW, BW and DW adjusted for body weight at 42 days of age. Therefore, the ACTA1 gene is an important molecular marker that could be used together with others already described to increase the economically important traits in broilers.

Estimates of genetic parameters for total milk yield over multiple ages in Brazilian Murrah buffaloes using different models.

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.

Random regression models using different functions to model milk flow in dairy cows.

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.

Genetic and phenotypic parameters of carcass and organ traits of broiler chickens.

The objective of this study was to estimate the genetic and environmental parameters for carcass, carcass part, and organ weights in a paternal strain of broiler chickens that was selected mainly for body weight at 42 days of age (BW42) to provide support for poultry genetic improvement programs. A total of 1448 chickens were used that resulted from the expansion of a pure paternal strain named TT, which was developed by Embrapa Suínos e Aves. The following weights were evaluated: BW42, chilled carcass, wing, drumstick meat, thigh meat, breast meat, breast fillet, back, liver, heart (HRT), and gizzard (GIZ). The variance component was estimated by the restricted maximum likelihood method using a multi-trait animal model. The general model included the additive genetic and residual random effects and the fixed effect of the sex-hatch group (10 levels). The heritability estimates ranged from 0.27 ± 0.06 for HRT to 0.44 ± 0.08 for GIZ. These results indicated that all the traits have enough additive genetic variability to respond to selection. The genetic correlation estimates between BW42 and the carcass and carcass part weights were high and positive. However, the genetic correlation estimates between BW42 and organ weights were low. In this population, the carcass traits might respond indirectly to selection applied to BW42. It can be concluded that selection to increase BW42 is not effective in improving broiler organ weight. Therefore, to obtain suitable genetic improvement for these traits, the selection indexes for broilers should include organ weight-based criteria.

Longitudinal genetic dynamics of weaning index and implications for cow-calf production efficiency.

In beef cattle, the selection for higher weights at young ages has been questioned with the argument that this criterion may increase the adult weight of cows, resulting in higher costs. Therefore, selection criteria should be employed to increase weights at young ages with minimal impact on the adult weight of cows. Additionally, the relationship between measures of cow production efficiency and other well-established selection criteria in breeding programs remains poorly understood. The objective of this study was to longitudinally evaluate the relationship between the weaning index (WIndex) as a measure of efficiency and growth traits of the cows. Possible changes over time in WIndex due to selection applied for yearling weight (YW) were also investigated. The WIndex was proposed to maximize genetic response in the weaning weight of the calf while maintaining genetic gain in BW of the cow at zero. A random regression model was adopted to estimate correlations between WIndex, BW, hip height (HH), and body condition score (BCS) using records of Nelore cows from three lines. Genetic trends were calculated for the control line (NeC) and lines selected for greater YW (NeS and NeT). The age of 3 years was the most critical for the weaning efficiency of the cows. At this stage, young cows are still growing and wean lighter calves than their adult counterparts. The genetic correlation estimates between WIndex and BW (-0.58 to 0.04), HH (-0.05 to -0.34), and BCS (-0.51 to -0.17) were close to zero or negative. BW and HH were strongly correlated genetically across all ages (0.73-0.76). In general, HH exhibited a weak and negative genetic relationship with BCS. The genetic correlation between BW and BCS was stronger for advanced ages (0.45-0.68). In lines selected for YW, important increases in WIndex were observed. However, NeS has been selected since the 1980s until the present for YW, and thus, it showed a more pronounced trend of increasing BW and, consequently, a more modest trend of increasing WIndex compared to NeT. In contrast, WIndex exhibited a trend close to zero for NeC. In this context, monitoring HH and BCS can be useful to avoid losses in the weaning efficiency of cows. Furthermore, we suggest that one way to mitigate efficiency losses in calf production could involve stabilizing the BW of cows and increasing the weaning weight of calves using the WIndex.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records.

Estimates of genetic parameters and eigenvector indices for milk production of Holstein cows.

The objectives of the present study were to estimate genetic parameters of monthly test-day milk yield (TDMY) of the first lactation of Brazilian Holstein cows using random regression (RR), and to compare the genetic gains for milk production and persistency, derived from RR models, using eigenvector indices and selection indices that did not consider eigenvectors. The data set contained monthly TDMY of 3,543 first lactations of Brazilian Holstein cows calving between 1994 and 2011. The RR model included the fixed effect of the contemporary group (herd-month-year of test days), the covariate calving age (linear and quadratic effects), and a fourth-order regression on Legendre orthogonal polynomials of days in milk (DIM) to model the population-based mean curve. Additive genetic and nongenetic animal effects were fit as RR with 4 classes of residual variance random effect. Eigenvector indices based on the additive genetic RR covariance matrix were used to evaluate the genetic gains of milk yield and persistency compared with the traditional selection index (selection index based on breeding values of milk yield until 305 DIM). The heritability estimates for monthly TDMY ranged from 0.12 ± 0.04 to 0.31 ± 0.04. The estimates of additive genetic and nongenetic animal effects correlation were close to 1 at adjacent monthly TDMY, with a tendency to diminish as the time between DIM classes increased. The first eigenvector was related to the increase of the genetic response of the milk yield and the second eigenvector was related to the increase of the genetic gains of the persistency but it contributed to decrease the genetic gains for total milk yield. Therefore, using this eigenvector to improve persistency will not contribute to change the shape of genetic curve pattern. If the breeding goal is to improve milk production and persistency, complete sequential eigenvector indices (selection indices composite with all eigenvectors) could be used with higher economic values for persistency. However, if the breeding goal is to improve only milk yield, the traditional selection index is indicated.

Comparison of factor-analytic and reduced rank models for test-day milk yield in Gyr dairy cattle (Bos indicus).

We analyzed 46,161 monthly test-day records of milk production from 7453 first lactations of crossbred dairy Gyr (Bos indicus) x Holstein cows. The following seven models were compared: standard multivariate model (M10), three reduced rank models fitting the first 2, 3, or 4 genetic principal components, and three models considering a 2-, 3-, or 4-factor structure for the genetic covariance matrix. Full rank residual covariance matrices were considered for all models. The model fitting the first two principal components (PC2) was the best according to the model selection criteria. Similar phenotypic, genetic, and residual variances were obtained with models M10 and PC2. The heritability estimates ranged from 0.14 to 0.21 and from 0.13 to 0.21 for models M10 and PC2, respectively. The genetic correlations obtained with model PC2 were slightly higher than those estimated with model M10. PC2 markedly reduced the number of parameters estimated and the time spent to reach convergence. We concluded that two principal components are sufficient to model the structure of genetic covariances between test-day milk yields.

Genetic parameters and principal component analysis for egg production from White Leghorn hens.

The objectives of this study were to estimate genetic parameters for accumulated egg production over 3-wk periods and for total egg production over 54 wk of egg-laying, and using principal component analysis (PCA), to explore the relationships among the breeding values of these traits to identify the possible genetic relationships present among them and hence to observe which of them could be used as selection criteria for improving egg production. Egg production was measured among 1,512 females of a line of White Leghorn laying hens. The traits analyzed were the number of eggs produced over partial periods of 3 wk, thus totaling 18 partial periods (P1 to P18), and the total number of eggs produced over the period between the 17 and 70 wk of age (PTOT), thus totaling 54 wk of egg production. Estimates of genetic parameters were obtained by means of the restricted maximum likelihood method, using 2-trait animal models. The PCA was done using the breeding values of partial and total egg production. The heritability estimates ranged from 0.05 ± 0.03 (P1 and P8) to 0.27 ± 0.06 (P4) in the 2-trait analysis. The genetic correlations between PTOT and partial periods ranged from 0.19 ± 0.31 (P1) to 1.00 ± 0.05 (P10, P11, and P12). Despite the high genetic correlation, selection of birds based on P10, P11, and P12 did not result in an increase in PTOT because of the low heritability estimates for these periods (0.06 ± 0.03, 0.12 ± 0.04, and 0.10 ± 0.04, respectively). The PCA showed that egg production can be divided genetically into 4 periods, and that P1 and P2 are independent and have little genetic association with the other periods.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle.

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Estimation of genetic parameters for partial egg production periods by means of random regression models.

We estimated genetic parameters for egg production in different periods by means of random regression models, aiming at selection based on partial egg production from a generation of layers. The production was evaluated for each individual by recording the number of eggs produced from 20 to 70 weeks of age, with partial records taken every three weeks for a total of 17 periods. The covariance functions were estimated with a random regression model by the restricted maximum likelihood method. A model composed of third-order polynomials for the additive effect, ninth-order polynomials for the permanent environment, and a residual variance structure with five distinct classes, was found to be most suitable for adjusting the egg production data for laying hens. The heritability estimates varied from 0.04 to 0.14. The genetic correlations were all positive, varying from 0.10 to 0.99. Selection applied in partial egg production periods will result in greater genetic profit for the adjacent periods. However, as the distance in time between periods increases, selection becomes less efficient. Selection based on the second period (23 to 25 weeks of age), where greater heritability was estimated, would note benefit the final egg-laying cycle periods.

Egg production curve fitting using nonlinear models for selected and nonselected lines of White Leghorn hens.

Egg production curves describe the laying patterns of hen populations over time. The objectives of this study were to fit the weekly egg production rate of selected and nonselected lines of a White Leghorn hen population, using nonlinear and segmented polynomial models, and to study how the selection process changed the egg-laying patterns between these 2 lines. Weekly egg production rates over 54 wk of egg production (from 17 to 70 wk of age) were measured from 1,693 and 282 laying hens from one selected and one nonselected (control) genetic line, respectively. Six nonlinear and one segmented polynomial models were gathered from the literature to investigate whether they could be used to fit curves for the weekly egg production rate. The goodness of fit of the models was measured using Akaike's information criterion, mean square error, coefficient of determination, graphical analysis of the fitted curves, and the deviations of the fitted curves. The Logistic, Yang, Segmented Polynomial, and Grossman models presented the best goodness of fit. In this population, there were significant differences between the parameter estimates of the curves fitted for the selected and nonselected lines, thus indicating that the effect of selection changed the shape of the egg production curves. The selection for egg production was efficient in modifying the birds' egg production curve in this population, thus resulting in genetic gain from the 5th to the 54th week of egg laying and improved the peak egg production and the persistence of egg laying.

Effect of pregnancy on the genetic evaluation of dairy cattle.

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.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows.

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.