Random regression models using B-splines functions provide more accurate genomic breeding values for milk yield and lactation persistence in Murrah buffaloes.

There is a great worldwide demand for cheese made with buffalo milk, due to its flavour and nutritional properties. In this context, there is a need for increasing the efficiency of buffalo milk production (including lactation persistence), which can be achieved through genomic selection. The most used methods for the genetic evaluation of longitudinal data, such as milk-related traits, are based on random regression models (RRM). The choice of the best covariance functions and polynomial order for modelling the random effects is an important step to properly fit RRM. To our best knowledge, there are no studies evaluating the impact of the order and covariance function (Legendre polynomials-LEG and B-splines-BSP) used to fit RRM for genomic prediction of breeding values in dairy buffaloes. Therefore, the main objectives of this study were to estimate variance components and evaluate the performance of LEG and BSP functions of different orders on the predictive ability of genomic breeding values for the first three lactations of milk yield (MY1, MY2, and MY3) and lactation persistence (LP1, LP2, and LP3) of Brazilian Murrah. Twenty-two models for each lactation were contrasted based on goodness of fit, genetic parameter estimates, and predictive ability. Overall, the models of higher orders of LEG or BSP had a better performance based on the deviance information criterion (DIC). The daily heritability estimates ranged from 0.01 to 0.30 for MY1, 0.08 to 0.42 for MY2, and from 0.05 to 0.47 for MY3. For lactation persistence (LP), the heritability estimates ranged from 0.09 to 0.32 for LP1, from 0.15 to 0.33 for LP2, and from 0.06 to 0.32 for LP3. In general, the curves plotted for variance components and heritability estimates based on BSP models presented lower oscillation along the lactation trajectory. Similar predictive ability was observed among the models. Considering a balance between the complexity of the model, goodness of fit, and credibility of the results, RRM using quadratic B-splines functions based on four or five segments to model the systematic, additive genetic, and permanent environment curves provide better fit with no significant differences between genetic variances estimates, heritabilities, and predictive ability for the genomic evaluation of dairy buffaloes.

Genomic prediction and genetic correlations estimated for milk production and fatty acid traits in Walloon Holstein cattle using random regression models.

The aims of this study were to: (1) estimate genetic correlation for milk production traits (milk, fat and protein yields and fat and protein contents) and fatty acids (FA: C16:0, C18:1 cis-9, LCFA, SFA, and UFA) over days in milk, (2) investigate the performance of genomic predictions using single-step GBLUP (ssGBLUP) based on random regression models (RRM), and (3) identify the optimal scaling and weighting factors to be used in the construction of the H matrix. A total of 302 684 test-day records of 63.875 first lactation Walloon Holstein cows were used. Positive genetic correlations were found between milk yield and fat and protein yield (rg from 0.46 to 0.85) and between fat yield and milk FA (rg from 0.17 to 0.47). On the other hand, negative correlations were estimated between fat and protein contents (rg from -0.22 to -0.59), between milk yield and milk FA (rg from -0.22 to -0.62), and between protein yield and milk FA (rg from -0.11 to -0.19). The selection for high fat content increases milk FA throughout lactation (rg from 0.61 to 0.98). The test-day ssGBLUP approach showed considerably higher prediction reliability than the parent average for all milk production and FA traits, even when no scaling and weighting factors were used in the H matrix. The highest validation reliabilities (r2 from 0.09 to 0.38) and less biased predictions (b1 from 0.76 to 0.92) were obtained using the optimal parameters (i.e., ω = 0.7 and α = 0.6) for the genomic evaluation of milk production traits. For milk FA, the optimal parameters were ω = 0.6 and α = 0.6. However, biased predictions were still observed (b1 from 0.32 to 0.81). The findings suggest that using ssGBLUP based on RRM is feasible for the genomic prediction of daily milk production and FA traits in Walloon Holstein dairy cattle.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics.

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

Autoregressive single-step test-day model for genomic evaluations of Portuguese Holstein cattle.

The multiple-lactation autoregressive test-day (AR) model is the adopted model for the national genetic evaluation of dairy cattle in Portugal. Under this model, animals' permanent environment effects are assumed to follow a first-order autoregressive process over the long (auto-correlations between parities) and short (auto-correlations between test-days within lactation) terms. Given the relevance of genomic prediction in dairy cattle, it is essential to include marker information in national genetic evaluations. In this context, we aimed to evaluate the feasibility of applying the single-step genomic (G)BLUP to analyze milk yield using the AR model in Portuguese Holstein cattle. In total, 11,434,294 test-day records from the first 3 lactations collected between 1994 and 2017 and 1,071 genotyped bulls were used in this study. Rank correlations and differences in reliability among bulls were used to compare the performance of the traditional (A-AR) and single-step (H-AR) models. These 2 modeling approaches were also applied to reduced data sets with records truncated after 2012 (deleting daughters of tested bulls) to evaluate the predictive ability of the H-AR. Validation scenarios were proposed, taking into account young and proven bulls. Average EBV reliabilities, empirical reliabilities, and genetic trends predicted from the complete and reduced data sets were used to validate the genomic evaluation. Average EBV reliabilities for H-AR (A-AR) using the complete data set were 0.52 (0.16) and 0.72 (0.62) for genotyped bulls with no daughters and bulls with 1 to 9 daughters, respectively. These results showed an increase in EBV reliabilities of 0.10 to 0.36 when genomic information was included, corresponding to a reduction of up to 43% in prediction error variance. Considering the 3 validation scenarios, the inclusion of genomic information improved the average EBV reliability in the reduced data set, which ranged, on average, from 0.16 to 0.26, indicating an increase in the predictive ability. Similarly, empirical reliability increased by up to 0.08 between validation tests. The H-AR outperformed A-AR in terms of genetic trends when unproven genotyped bulls were included. The results suggest that the single-step GBLUP AR model is feasible and may be applied to national Portuguese genetic evaluations for milk yield.

Milk losses associated with somatic cell counts by parity and stage of lactation.

The reduction of milk production caused by subclinical mastitis in dairy cows was evaluated through the regression of test-day milk yield on log-transformed somatic cell counts (LnSCC). Official test-day records (n = 1,688,054) of Holstein cows (n = 87,695) were obtained from 719 herds from January 2010 to December 2015. Editing was performed to ensure both reliability and consistency for the statistical analysis, and the final data set comprised 232,937 test-day records from 31,692 Holstein cows in 243 herds. A segmented regression was fitted to estimate the cutoff point in the LnSCC scale where milk yield started to be affected by mastitis. The statistical model used to explain daily milk yield included the effect of herd as a random effect and days in milk and LnSCC as fixed effects regressions, and analyses were performed by parity and stage of lactation. The cutoff point where milk yield starts to be affected by changes in LnSCC was estimated to be around 2.52 (the average of all estimates of approximately 12,400 cells/mL) for Holsteins cows from Brazilian herds. For first-lactation cows, milk losses per unit increase of LnSCC had estimates around 0.68 kg/d in the beginning of the lactation [5 to 19 d in milk (DIM)], 0.55 kg/d in mid-lactation (110 to 124 DIM), and 0.97 kg/d at the end of the lactation (289 to 304 DIM). For second-lactation cows, milk losses per unit increase of LnSCC had estimates around 1.47 kg/d in the beginning of the lactation (5 to 19 DIM), 1.09 kg/d in mid-lactation (110 to 124 DIM), and 2.45 kg/d at the end of the lactation (289 to 304 DIM). For third-lactation cows, milk losses per unit increase of LnSCC had estimates around 2.22 kg/d in the beginning of the lactation (5 to 19 DIM), 1.13 kg/d in mid-lactation (140 to 154 DIM), and 2.65 kg/d at the end of the lactation (289 to 304 DIM). Daily milk losses caused by increased LnSCC were dependent on parity and stage of lactation, and these factors should be considered when estimating losses associated with subclinical mastitis.

Reaction norm model to describe environmental sensitivity across first lactation in dairy cattle under tropical conditions.

Reaction norm models have been widely used to study genotype by environment interaction (G × E) in animal breeding. The objective of this study was to describe environmental sensitivity across first lactation in Brazilian Holstein cows using a reaction norm approach. A total of 50,168 individual monthly test day (TD) milk yields (10 test days) from 7476 complete first lactations of Holstein cattle were analyzed. The statistical models for all traits (10 TDs and for 305-day milk yield) included the fixed effects of contemporary group, age of cow (linear and quadratic effects), and days in milk (linear effect), except for 305-day milk yield. A hierarchical reaction norm model (HRNM) based on the unknown covariate was used. The present study showed the presence of G × E in milk yield across first lactation of Holstein cows. The variation in the heritability estimates implies differences in the response to selection depending on the environment where the animals of this population are evaluated. In the average environment, the heritabilities for all traits were rather similar, in range from 0.02 to 0.63. The scaling effect of G × E predominated throughout most of lactation. Particularly during the first 2 months of lactation, G × E caused reranking of breeding values. It is therefore important to include the environmental sensitivity of animals according to the phase of lactation in the genetic evaluations of Holstein cattle in tropical environments.

Estimation of genetic parameters for electrical conductivity of milk for Holstein breed using random regression / Estimativa de parâmetros genéticos para condutividade elétrica do leite para a raça holandesa utilizando regressão aleatória

The electrical conductivity of milk is an indirect method of mastitis diagnosis and can be used as selection criterion in breeding programs to obtain resistant animals to infection. For the present study data from 9,302 milk electrical conductivity measurements in the morning (ECM), from 1,129 Holstein cows in first lactation, calving between 2001 and 2011, belonging to eight herds in the Southeast of Brazil, obtained from automated milking equipment WESTFALIA® with system management "Dairyplan" was utilized. Classes of ECM were formed at weekly intervals, representing a total of 42 classes. The model included direct additive genetic, permanent environmental and residual effects as random and the fixed effects of contemporary group (herd - year and season of the control), age at calving as a covariate (linear and quadratic). Mean trends were modeled by an orthogonal Legendre polynomial with three coefficients of days in milk. The residual variance was considered homogeneous throughout lactation. Variance components were estimated by restricted maximum likelihood method (REML), using the statistical package Wombat (Meyer, 2006). The mean and standard deviation of the electrical conductivity of milk were 4.799 ± 0.543 ms/cm. The heritability for ECM were increased from the beginning to the middle of lactation (154 days), when it reached the maximum value (0.44), decreasing therea

O artigo não apresenta resumo em português.

Estimation of genetic parameters for electrical conductivity of milk for Holstein breed using random regression / Estimativa de parâmetros genéticos para condutividade elétrica do leite para a raça holandesa utilizando regressão aleatória

The electrical conductivity of milk is an indirect method of mastitis diagnosis and can be used as selection criterion in breeding programs to obtain resistant animals to infection. For the present study data from 9,302 milk electrical conductivity measurements in the morning (ECM), from 1,129 Holstein cows in first lactation, calving between 2001 and 2011, belonging to eight herds in the Southeast of Brazil, obtained from automated milking equipment WESTFALIA® with system management "Dairyplan" was utilized. Classes of ECM were formed at weekly intervals, representing a total of 42 classes. The model included direct additive genetic, permanent environmental and residual effects as random and the fixed effects of contemporary group (herd - year and season of the control), age at calving as a covariate (linear and quadratic). Mean trends were modeled by an orthogonal Legendre polynomial with three coefficients of days in milk. The residual variance was considered homogeneous throughout lactation. Variance components were estimated by restricted maximum likelihood method (REML), using the statistical package Wombat (Meyer, 2006). The mean and standard deviation of the electrical conductivity of milk were 4.799 ± 0.543 ms/cm. The heritability for ECM were increased from the beginning to the middle of lactation (154 days), when it reached the maximum value (0.44), decreasing therea

O artigo não apresenta resumo em português.

Genetic parameters for milk, fat and protein yields in Murrah buffaloes (Bubalus bubalis Artiodactyla, Bovidae).

The objective of the present study was to estimate genetic parameters for test-day milk, fat and protein yields and 305-day-yields in Murrah buffaloes. 4,757 complete lactations of Murrah buffaloes were analyzed. Co-variance components were estimated by the restricted maximum likelihood method. The models included additive direct genetic and permanent environmental effects as random effects, and the fixed effects of contemporary group, milking number and age of the cow at calving as linear and quadratic covariables. Contemporary groups were defined by herd-year-month of test for test-day yields and by herd-year-season of calving for 305-day yields. The heritability estimates obtained by two-trait analysis ranged from 0.15 to 0.24 for milk, 0.16 to 0.23 for protein and 0.13 to 0.22 for fat, yields. Genetic and phenotypic correlations were all positive. The observed population additive genetic variation indicated that selection might be an effective tool in changing population means in milk, fat and protein yields.

Genetic parameters for milk, fat and protein yields in Murrah buffaloes (Bubalus bubalis Artiodactyla, Bovidae)

The objective of the present study was to estimate genetic parameters for test-day milk, fat and protein yields and 305-day-yields in Murrah buffaloes. 4,757 complete lactations of Murrah buffaloes were analyzed. Co-variance components were estimated by the restricted maximum likelihood method. The models included additive direct genetic and permanent environmental effects as random effects, and the fixed effects of contemporary group, milking number and age of the cow at calving as linear and quadratic covariables. Contemporary groups were defined by herd-year-month of test for test-day yields and by herd-year-season of calving for 305-day yields. The heritability estimates obtained by two-trait analysis ranged from 0.15 to 0.24 for milk, 0.16 to 0.23 for protein and 0.13 to 0.22 for fat, yields. Genetic and phenotypic correlations were all positive. The observed population additive genetic variation indicated that selection might be an effective tool in changing population means in milk, fat and protein yields.

Persistência na lactação para vacas da raça Holandesa criadas no Estado do Rio Grande do Sul via modelos de regressão aleatória / Lactation persistency for Holstein cows raised in the State of Rio Grande do Sul using a random regression model

Foram utilizados 21.702 registros de produção de leite no dia do controle de 2.429 vacas primíparas da raça Holandesa, filhas de 233 touros, coletados em 33 rebanhos do Estado do Rio Grande do Sul, entre 1992 e 2003, para estimar parâmetros genéticos, para três medidas de persistência (PS1, PS2 e PS3) e para a produção de leite até 305 dias (P305) de lactação. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 300o dia de lactação incluíram o efeito de rebanho-ano-mês do controle, a idade da vaca ao parto e os parâmetros do polinômio de Legendre de ordem quatro, para modelar a curva média da produção de leite da população e os parâmetros do mesmo polinômio, para modelar os efeitos aleatórios genético-aditivo direto e de ambiente permanente. As estimativas de herdabilidade obtidas foram 0,05, 0,08 e 0,19, respectivamente, para PS1, PS2 e PS3 e 0,25, para P305 sugerindo a possibilidade de ganho genético por meio da seleção para PS3 e para P305. As correlações genéticas entre as três medidas de persistência e P305, variaram de -0,05 a 0,07, indicando serem persistência e produção, características determinadas por grupos de genes diferentes. Assim, consequentemente, a seleção para P305, geralmente praticada, não promove progresso genético para a persistência.

There were used 21,702 test day milk yields from 2,429 first parity Holstein breed cows, daughters of 2,031 dams and 233 sires, distributed over 33 herds in the state of Rio Grande do Sul, from 1992 to 2003. Genetic parameters for three measures of lactation persistency (PS1, PS2 e PS3) and for milk production to 305 days (P305) were evaluated. A random regression model adjusted by fourth order Legendre polynomial was used. The random regression model adjusted to test day between the sixth and the 305th lactation day included the herd-year-season of the test day, the age of the cow at the parturition effects and the order fourth Legendre polinomial parameters, for modeling the milk production average curve of the population, and parameters of the same polinomial for modeling the random additive genetic and permanent environmental effects. The estimated heritabilities were 0.05, 0.08 and 0.19, respectively to PS1, PS2 and PS3, and 0.25 to P305, suggesting the possibility of a genetic gain by selection for PS3 and P305. The genetic correlations between persistency measurements and P305 ranged from -0.05 to 0.07, suggesting being, persistency and milk yield, characteristics determined by different gene groups, and that the selection for P305, usually done, do not promote genetic progress for persistency.

Persistência na lactação para vacas da raça Holandesa criadas no Estado do Rio Grande do Sul via modelos de regressão aleatória

There were used 21,702 test day milk yields from 2,429 first parity Holstein breed cows, daughters of 2,031 dams and 233 sires, distributed over 33 herds in the state of Rio Grande do Sul, from 1992 to 2003. Genetic parameters for three measures of lactation persistency (PS1, PS2 e PS3) and for milk production to 305 days (P305) were evaluated. A random regression model adjusted by fourth order Legendre polynomial was used. The random regression model adjusted to test day between the sixth and the 305th lactation day included the herd-year-season of the test day, the age of the cow at the parturition effects and the order fourth Legendre polinomial parameters, for modeling the milk production average curve of the population, and parameters of the same polinomial for modeling the random additive genetic and permanent environmental effects. The estimated heritabilities were 0.05, 0.08 and 0.19, respectively to PS1, PS2 and PS3, and 0.25 to P305, suggesting the possibility of a genetic gain by selection for PS3 and P305. The genetic correlations between persistency measurements and P305 ranged from -0.05 to 0.07, suggesting being, persistency and milk yield, characteristics determined by different gene groups, and that the selection for P305, usually done, do not promote genetic progress for persistency.

Foram utilizados 21.702 registros de produção de leite no dia do controle de 2.429 vacas primíparas da raça Holandesa, filhas de 233 touros, coletados em 33 rebanhos do Estado do Rio Grande do Sul, entre 1992 e 2003, para estimar parâmetros genéticos, para três medidas de persistência (PS1, PS2 e PS3) e para a produção de leite até 305 dias (P305) de lactação. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 300o dia de lactação incluíram o efeito de rebanho-ano-mês do controle, a idade da vaca ao parto e os parâmetros do polinômio de Legendre de ordem quatro, para modelar a curva média da produção de leite da população e os parâmetros do mesmo polinômio, para modelar os efeitos aleatórios genético-aditivo direto e de ambiente permanente. As estimativas de herdabilidade obtidas foram 0,05, 0,08 e 0,19, respectivamente, para PS1, PS2 e PS3 e 0,25, para P305 sugerindo a possibilidade de ganho genético por meio da seleção para PS3 e para P305. As correlações genéticas entre as três medidas de persistência e P305, variaram de -0,05 a 0,07, indicando serem persistência e produção, características determinadas por grupos de genes diferentes. Assim, consequentemente, a seleção para P305, geralmente praticada, não promove progresso genético para a persistência.

Persistência na lactação para vacas da raça Holandesa criadas no Estado do Rio Grande do Sul via modelos de regressão aleatória

There were used 21,702 test day milk yields from 2,429 first parity Holstein breed cows, daughters of 2,031 dams and 233 sires, distributed over 33 herds in the state of Rio Grande do Sul, from 1992 to 2003. Genetic parameters for three measures of lactation persistency (PS1, PS2 e PS3) and for milk production to 305 days (P305) were evaluated. A random regression model adjusted by fourth order Legendre polynomial was used. The random regression model adjusted to test day between the sixth and the 305th lactation day included the herd-year-season of the test day, the age of the cow at the parturition effects and the order fourth Legendre polinomial parameters, for modeling the milk production average curve of the population, and parameters of the same polinomial for modeling the random additive genetic and permanent environmental effects. The estimated heritabilities were 0.05, 0.08 and 0.19, respectively to PS1, PS2 and PS3, and 0.25 to P305, suggesting the possibility of a genetic gain by selection for PS3 and P305. The genetic correlations between persistency measurements and P305 ranged from -0.05 to 0.07, suggesting being, persistency and milk yield, characteristics determined by different gene groups, and that the selection for P305, usually done, do not promote genetic progress for persistency.

Foram utilizados 21.702 registros de produção de leite no dia do controle de 2.429 vacas primíparas da raça Holandesa, filhas de 233 touros, coletados em 33 rebanhos do Estado do Rio Grande do Sul, entre 1992 e 2003, para estimar parâmetros genéticos, para três medidas de persistência (PS1, PS2 e PS3) e para a produção de leite até 305 dias (P305) de lactação. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 300o dia de lactação incluíram o efeito de rebanho-ano-mês do controle, a idade da vaca ao parto e os parâmetros do polinômio de Legendre de ordem quatro, para modelar a curva média da produção de leite da população e os parâmetros do mesmo polinômio, para modelar os efeitos aleatórios genético-aditivo direto e de ambiente permanente. As estimativas de herdabilidade obtidas foram 0,05, 0,08 e 0,19, respectivamente, para PS1, PS2 e PS3 e 0,25, para P305 sugerindo a possibilidade de ganho genético por meio da seleção para PS3 e para P305. As correlações genéticas entre as três medidas de persistência e P305, variaram de -0,05 a 0,07, indicando serem persistência e produção, características determinadas por grupos de genes diferentes. Assim, consequentemente, a seleção para P305, geralmente praticada, não promove progresso genético para a persistência.

Milk and fat production of crossbred Holstein-Gir cows (Bos taurus taurus-Bos taurus indicus) in the agreste region of the Brazilian state of Pernambuco

The productive performance of four Holstein-Gir genetic groups (1/2H, 1/4H, 5/8H, 5/8Hinter se) and the effects of non-genetic factors on production traits was evaluated using a data set of 7,951 test-day samples collected between January 1980 and December 1999 from the Arcoverde Experimental Station in the Brazilian state of Pernambuco (Empresa Pernambucana de Pesquisa Agropecuária). The statistical model included the fixed effects of calving year (1980 to 1999) and month (January to December), genetic group of the cow, age at months of calving (33 to 190) and days in milk at each test-day. Random effects were sire, cow and residual with test-days treated as repeated records within each cow within each lactation. For the four genetic groups the milk yield (MY) means were 1/2H = 8.61 kg ± 1.16 kg, 1/4H = 5.34 kg ± 0.46 kg, 5/8H = 7.42 kg ± 0.39 kg and 5/8Hinter se = 5.76 kg ± 0.46 kg; the fat yield (FY) means were 1/2H = 0.375 kg ± 0.052 kg, 1/4H = 0.231 kg ± 0.026 kg, 5/8H = 0.299 kg ± 0.025 kg and 5/8Hinter se = 0.231 kg ± 0.026 kg; and the fat percentage (FP) means were 1/2H = 4.45 kg ± 0.29 percent, 1/4H = 4.08 kg ± 0.12 percent, 5/8H = 3.87 kg ± 0.10 percent and 5/8Hinter se = 3.89 kg ± 0.12 percent. Phenotypic correlations between tests were MY = 0.97, FY = 0.94 and FP = 0.98. The best productive performance was for the 1/2H group, followed by the 5/8H group. The performance of the synthetic group was substantially below the performance of the 5/8H group.

Utilização dos polinômios de Legendre e da função de Wilmink em avaliações genéticas para persistência na lactação de animais da raça Holandesa / Use of Legendre polynomials and Wilmink function in genetic evaluations for persistency of lactation in Holstein cows

Os registros de produção de leite de 11.023 primeiras lactações de vacas da raça Holandesa pertencentes a 251 rebanhos distribuídos no estado de Minas Gerais foram usados para comparar os polinômios de Legendre e a função Wilmink em modelos de regressão aleatória (MRA) quanto aos seus efeitos na estimação de parâmetros genéticos e predição de valores genéticos para nove medidas de persistência na lactação e produção de leite até 305 dias. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 3050 dia de lactação incluíram o efeito de rebanho-ano-mês do controle, os parâmetros dos polinômios de Legendre de ordens 3 a 5 ou da função de Wilmink, para modelar as curvas fixas da regressão dentro das subclasses de idade-estação de parto da vaca e os parâmetros dos polinômios de Legendre de ordens 3 a 5, para modelar os efeitos aleatórios genético-aditivo e permanente de ambiente. Os testes do critério de informação de Akaike e Bayesiano indicaram o modelo com maior número de parâmetros como o que melhor se ajustou aos dados de produção de leite. Observaram-se grandes variações nas estimativas de herdabilidade para a maioria das medidas de persistência na lactação, com uso dos modelos que envolveram ajustes dos polinômios de Legendre. As estimativas de herdabilidade variaram de 0,11 a 0,33 para produção de leite ao longo da lactação, de 0,33 a 0,36 para a produção de leite até 305 dias e de 0,00 a 0,32 para persistência na lactação. As correlações genéticas entre persistência e produção de leite até 305 dias diferiram com o modelo e a medida de persistência. A utilização da função de Wilmink, comparada aos polinômios de Legendre, proporcionou mudanças expressivas na ordem dos animais quando classificados para persistência na lactação.(AU)

Records of 11,023 first-parity Holstein cows belonging to 251 herds in the State of Minas Gerais were used to compare the Legendre polynomials and Wilmink function in random regression models (RRM) as for their effects in the estimate of genetic parameters and prediction of breeding values for nine types of persistency measurements and 305-day milk yield. The random regression test day models included the effect of herd-year-month test day, parameters of the function of Wilmink or 3th to 5th order Legendre polynomials to model fixed curves of the subclasses and 3th to 5th order Legendre polynomials to model genetic and permanent environmental effects. The Akaikes Information Criterion (AIC) and Bayesian Information Criterion (BIC) indicated the model with larger number of parameters as the one that best fitted the data of milk yield. Using the Legrendre polynomial model large variation was observed in the estimates heritabilities for most of the persistency measures. The estimates herdabilities varied from 0.11 to 0.33 to milk yield throughout the lactation, from 0.33 to 0.36 for the 305-day milk yield and, from 0.00 to 0.32 for persistency. Genetic correlations between persistency and 305-day milk yield differed according to the model and persistency measure. Compared the Legendre polynomials to the Wilmink function provided expressive changes in rank of animals for persistency of lactation.(AU)

Genetic and environmental effects of test day milk yield on Holstein cattle / Fatores que influem na produção de leite no dia do controle em vacas da raça holandesa de primeira lactação

Data from 17.968 test day milk yield (PLDC) of first lactations of Holstein cows were studied. Some environmental effects were analysed such as: class of age at calving, interval from calving to first test day and herd-year-season on PLDC. The results showed that the influence of these effects was not constant throughout the lactation.The Restricted Maximum Likelihood estimates of (co)variances components were obtained from a sire model. The heritabilities for PLDC ranged from 0.04 to 0.28. The largest value was obtained in the second third of the lactation (C5 to C7). The results suggest that test day yields can be used in the genetic evaluation and could reduce the generation interval.

Dados de 17.968 registros de produção de leite no dia do controle (PLDC) em vacas da raça Holandesa de primeira lactação foram estudados para analisar o efeito de alguns fatores de meio tais como: idade da vaca em classes, intervalo parto-primeiro controle e rebanho-ano-estação do parto sobre estas produções. Os resultados mostraram que o efeito desses fatores não foi constante no decorrer da lactação. O método da máxima verossimilhança restrita foi utilizado para estimar os componentes de variância, sob modelo de touro. As herdabilidades para as PLDC variaram de 0,04 a 0,28 sendo os maiores valores obtidos no segundo terço da lactação (C5 e C7). Os resultados sugerem que as PLDC nesta fase podem ser utilizadas nas avaliações genéticas, o que levaria uma diminuição no intervalo de gerações.

Genetic and environmental effects of test day milk yield on Holstein cattle / Fatores que influem na produção de leite no dia do controle em vacas da raça holandesa de primeira lactação

Data from 17.968 test day milk yield (PLDC) of first lactations of Holstein cows were studied. Some environmental effects were analysed such as: class of age at calving, interval from calving to first test day and herd-year-season on PLDC. The results showed that the influence of these effects was not constant throughout the lactation.The Restricted Maximum Likelihood estimates of (co)variances components were obtained from a sire model. The heritabilities for PLDC ranged from 0.04 to 0.28. The largest value was obtained in the second third of the lactation (C5 to C7). The results suggest that test day yields can be used in the genetic evaluation and could reduce the generation interval.

Dados de 17.968 registros de produção de leite no dia do controle (PLDC) em vacas da raça Holandesa de primeira lactação foram estudados para analisar o efeito de alguns fatores de meio tais como: idade da vaca em classes, intervalo parto-primeiro controle e rebanho-ano-estação do parto sobre estas produções. Os resultados mostraram que o efeito desses fatores não foi constante no decorrer da lactação. O método da máxima verossimilhança restrita foi utilizado para estimar os componentes de variância, sob modelo de touro. As herdabilidades para as PLDC variaram de 0,04 a 0,28 sendo os maiores valores obtidos no segundo terço da lactação (C5 e C7). Os resultados sugerem que as PLDC nesta fase podem ser utilizadas nas avaliações genéticas, o que levaria uma diminuição no intervalo de gerações.