Residual Random Effects Research Articles

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.

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.

Variance Components and Genetic Parameters for Milk Production and Lactation Pattern in an Ethiopian Multibreed Dairy Cattle Population

The objective of this study was to estimate variance components and genetic parameters for lactation milk yield (LY), lactation length (LL), average milk yield per day (YD), initial milk yield (IY), peak milk yield (PY), days to peak (DP) and parameters (ln(a) and c) of the modified incomplete gamma function (MIG) in an Ethiopian multibreed dairy cattle population. The dataset was composed of 5,507 lactation records collected from 1,639 cows in three locations (Bako, Debre Zeit and Holetta) in Ethiopia from 1977 to 2010. Parameters for MIG were obtained from regression analysis of monthly test-day milk data on days in milk. The cows were purebred (Bos indicus) Boran (B) and Horro (H) and their crosses with different fractions of Friesian (F), Jersey (J) and Simmental (S). There were 23 breed groups (B, H, and their crossbreds with F, J, and S) in the population. Fixed and mixed models were used to analyse the data. The fixed model considered herd-year-season, parity and breed group as fixed effects, and residual as random. The single and two-traits mixed animal repeatability models, considered the fixed effects of herd-year-season and parity subclasses, breed as a function of cow H, F, J, and S breed fractions and general heterosis as a function of heterozygosity, and the random additive animal, permanent environment, and residual effects. For the analysis of LY, LL was added as a fixed covariate to all models. Variance components and genetic parameters were estimated using average information restricted maximum likelihood procedures. The results indicated that all traits were affected (p<0.001) by the considered fixed effects. High grade B×F cows (3/16B 13/16F) had the highest least squares means (LSM) for LY (2,490±178.9 kg), IY (10.5±0.8 kg), PY (12.7±0.9 kg), YD (7.6±0.55 kg) and LL (361.4±31.2 d), while B cows had the lowest LSM values for these traits. The LSM of LY, IY, YD, and PY tended to increase from the first to the fifth parity. Single-trait analyses yielded low heritability (0.03±0.03 and 0.08±0.02) and repeatability (0.14±0.01 to 0.24±0.02) estimates for LL, DP and parameter c. Medium heritability (0.21±0.03 to 0.33±0.04) and repeatability (0.27±0.02 to 0.53±0.01) estimates were obtained for LY, IY, PY, YD and ln(a). Genetic correlations between LY, IY, PY, YD, ln(a), and LL ranged from 0.59 to 0.99. Spearman’s rank correlations between sire estimated breeding values for LY, LL, IY, PY, YD, ln(a) and c were positive (0.67 to 0.99, p<0.001). These results suggested that selection for IY, PY, YD, or LY would genetically improve lactation milk yield in this Ethiopian dairy cattle population.

Bayesian analysis of generalized partially linear single-index models

We extend generalized partially linear single-index models by incorporating a random residual effect into the nonlinear predictor so that the new models can accommodate data with overdispersion. Based on the free-knot spline techniques, we develop a fully Bayesian method to analyze the proposed models. To make the models spatially adaptive, we further treat the number and positions of spline knots as random variables. As random residual effects are introduced, many of the completely conditional posteriors become standard distributions, which greatly facilitates sampling. We illustrate the proposed models and estimation method with a simulation study and an analysis of a recreational trip data set.

Genetic variability for temperament indicators of Nellore cattle1

The aim of this study was to estimate genetic parameters of 4 temperament indicator traits for Nellore cattle and evaluate the possibility of using such traits as selection criteria in breeding programs. Temperament was assessed for 23,420 male and female animals at 550 d of age, which were born between 2002 and 2009. A temperament score (TS) was used, which is based on a scale from 1 to 5 and considers the reaction of animals after exiting the crush. Moreover, 9,150 individuals born in 2008 and 2009 were measured for these characteristics: movement score (MOV), where animals were scored from 1 to 5 according to their movement inside the crush; crush score (CS), which assigns scores from 1 to 4 for the general reactivity inside the crush; and flight speed (FS), which is a recording of the speed (m/s) at which animals exit the crush after being weighed. The weaning weight (WW) was included in the multitrait analysis to reduce the effect of the selection performed at weaning. Bayesian inference using Gibbs sampling was applied to estimate (co)variance components and breeding values of the animals. The model included random direct additive genetic and residual effects, fixed effects of contemporary groups, age of the dam (classes), and age of the animal as covariate (linear and quadratic effects for WW and TS, and only linear effects for the other traits). A linear model was applied to WW and FS, whereas a threshold model was used for TS, CS, and MOV. Heritability estimates for FS, TS, CS, and MOV were 0.35, 0.15, 0.19, and 0.18, respectively. The genetic correlation estimates of FS with TS (0.85), CS (0.85), and MOV (0.76) were high, although the phenotypic correlations were low (between 0.18 and 0.25). For CS and MOV, the genetic and phenotypic correlation estimates were high (0.99 and 0.71, respectively). We concluded that all of the temperament indicator traits addressed in this study presented enough genetic variability to respond to selection; however, the use of FS would result in a faster genetic gain. With regard to the practical applicability in breeding programs, the use of FS is also favorable because it produces data on a continuous scale, allows for recording of the data electronically, and requires low investment.

Principal components and factor analytic models for birth to mature weights in Nellore cattle

A total of 61,528 weight records from 22,246 Nellore animals born between 1984 and 2002 were used to compare different multiple-trait analysis methods for birth to mature weights. The following models were used: standard multivarite model (MV), five reduced-rank models fitting the first 1, 2, 3, 4 and 5 genetic principal components, and five models using factor analysis with 1, 2, 3, 4 and 5 factors. Direct additive genetic random effects and residual effects were included in all models. In addition, maternal genetic and maternal permanent environmental effects were included as random effects for birth and weaning weight. The models included contemporary group as fixed effect and age of animal at recording (except for birth weight) and age of dam at calving as linear and quadratic effects (for birth weight and weaning weight). The maternal genetic, maternal permanent environmental and residual (co)variance matrices were assumed to be full rank. According to model selection criteria, the model fitting the three first principal components (PC3) provided the best fit, without the need for factor analysis models. Similar estimates of phenotypic, direct additive and maternal genetic, maternal permanent environmental and residual (co)variances were obtained with models MV and PC3. Direct heritability ranged from 0.21 (birth weight) to 0.45 (weight at 6 years of age). The genetic and phenotypic correlations obtained with model PC3 were slightly higher than those estimated with model MV. In general, the reduced-rank model substantially decreased the number of parameters in the analyses without reducing the goodness-of-fit.

Parâmetros genéticos de relações de pesos, características de fertilidade e crescimento em vacas da raça Canchim

O objetivo neste trabalho foi estimar herdabilidade da idade ao primeiro parto (IPP), do escore de condição corporal ao primeiro parto (EPP), do escore de condição corporal ao parto (ECP), dos pesos à desmama (PD) e aos doze meses de idade (P12) e das relações de peso do bezerro à desmama pelo peso da vaca ao parto (RPP) e peso do primeiro bezerro à desmama pelo peso da vaca ao primeiro parto (RPPP) e as correlações genéticas de IPP, EPP, PD e P12 com RPPP, em um rebanho da raça Canchim. As médias a posteriori dos componentes de (co)variância foram obtidas por inferência bayesiana, em análises uni e bicaracterísticas. Os modelos estatísticos incluíram os efeitos aleatórios genético aditivos direto e materno, de ambiente permanente e residual, e os efeitos fixos de ano e mês de nascimento ou do parto, idade da vaca ao parto e sexo do bezerro, dependendo da característica. As médias a posteriori da herdabilidade, obtidas em análises unicararacterística, foram 0,12 (IPP); 0,36 (EPP); 0,18 (ECP); 0,50 (PD); 0,46 (P12); 0,16 (RPP) e 0,40 (RPPP), indicando que as características possuem variação genética aditiva suficiente para apresentar boa resposta à seleção massal, com exceção de IPP. As correlações genéticas de IPP (-0,61), EPP (-0,36), PD (-0,20) e P12 (-0,05) com RPPP sugerem que a seleção para reduzir a idade e o escore de condição corporal ao primeiro parto deve melhorar a produtividade das fêmeas no primeiro parto, mas a seleção para modificar pesos em idades jovens não promove mudanças na eficiência produtiva das matrizes.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was 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. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony.

Genetic parameters for type traits in Holstein cows in Brazil

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.

Análise genética de características de crescimento e perímetro escrotal em bovinos da raça Brangus

O objetivo deste trabalho foi estimar os parâmetros genéticos e a tendência genética de características de crescimento e perímetro escrotal em animais da raça Brangus. Dados de 6.340 animais, criados em cinco propriedades nas regiões Sul, Sudeste e Centro‑Oeste do Brasil, foram utilizados para avaliação de: perímetro escrotal (PE) ao sobreano e pesos ao nascer (PN), à desmama (P205), ao ano (P365) e ao sobreano (P550). Os componentes de covariância foram estimados por inferência bayesiana, sob modelo animal, com efeitos fixos de grupos de contemporâneos e de classe de idade da vaca ao parto, e efeitos aleatórios genético aditivo direto e residual. Os efeitos aleatórios genético materno e de ambiente permanente materno foram incluídos somente para PN e P205. O efeito linear da covariável idade do animal na mensuração foi considerado para todas as características analisadas, exceto PN. As médias observadas foram 33,6, 184,6, 235,9, 344,9 e 33,8 cm para PN, P205, P365, P550 e PE, respectivamente, e as tendências genéticas foram de ‑0,001, 0,107, 0,177, 0,217 kg por ano e 0,001 cm por ano. As estimativas das herdabilidades direta e materna variaram de 0,16 (PN) a 0,61 (PE) e de 0,08 (PN) a 0,09 (P205), indicativas de que as características avaliadas são passíveis de seleção para o melhoramento genético da raça Brangus.

Genetic associations between flight speed and growth traits in Nellore cattle1

The aim of the present study was to estimate genetic parameters for flight speed and its association with growth traits in Nellore beef cattle. The flight speed (FS) of 7,402 yearling animals was measured, using a device composed of a pair of photoelectric cells. Time interval data (s) were converted to speed (m/s) and faster animals were regarded as more reactive. The growth traits analyzed were weaning weight (WW), ADG from weaning to yearling age, and yearling scrotal circumference (SC). The (co)variance components were estimated using REML in a multitrait analysis applying an animal model. The model included random direct additive genetic and residual effects, fixed effects of contemporary groups, age of dam (classes), and age of animal as covariable. For WW, the model also included maternal genetic and permanent environmental random effects. The direct heritability estimate for FS was 0.26 ± 0.05 and direct heritability estimates for WW, SC, and ADG were 0.30 ± 0.01, 0.48 ± 0.02, and 0.19 ± 0.01, respectively. Estimates of the genetic correlation between FS and the growth traits were -0.12 ± 0.07 (WW), -0.13 ± 0.08 (ADG), and -0.11 ± 0.07 (SC). Although the values were low, these correlations showed that animals with better temperaments (slower FS) tended to present better performance. It is possible to infer that longterm selection for weight and scrotal circumference can promote a positive genetic response in the temperament of animals. Nevertheless, to obtain faster genetic progress in temperament, it would be necessary to perform direct selection for such trait. Flight speed is an easily measured indicator of temperament and can be included as a selection criterion in breeding programs for Nellore cattle.

Estimativas de componentes de (co)variância para peso e escores visuais de conformação frigorífica em bovinos Nelore

Estimaram-se os componentes de (co)variância e herdabilidade da conformação frigorífica à desmama (CFD), conformação frigorífica ao sobreano (CFS), peso à desmama (PD) e peso ao sobreano (PS) de animais Nelore, e as correlações genéticas entre essas características. Um modelo animal multicaracterística foi proposto para analisar 6.397 informações de peso e escores visuais de conformação frigorífica, obtidas à desmama e ao sobreano. Esse modelo incluiu os efeitos aleatórios genético aditivo direto, genético aditivo materno, ambiente permanente materno e residual, além dos efeitos fixos de grupo contemporâneo e das covariáveis idade da mãe ao parto - para peso e conformação frigorífica à desmama e ao sobreano - e idade do animal à data da avaliação - para conformação frigorífica, à desmama e ao sobreano. As herdabilidades estimadas para CFD, CFS, PD e PS foram, respectivamente, 0,13, 0,25, 0,22 e 0,29. Correlações genéticas positivas e de alta magnitude entre as características de peso e as características de avaliação visual sugerem que a seleção para uma delas pode resultar em resposta indireta na outra. A característica de conformação frigorífica pode ser selecionada em idade mais precoce em razão da correlação genética alta e positiva entre mensurações feitas nas duas idades estudadas.

Genetic parameters for test-day yield of milk, fat and protein in buffaloes estimated by random regression models

The test-day yields of milk, fat and protein were analysed from 1433 first lactations of buffaloes of the Murrah breed, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, born between 1985 and 2007. For the test-day yields, 10 monthly classes of lactation days were considered. The contemporary groups were defined as the herd-year-month of the test day. Random additive genetic, permanent environmental and residual effects were included in the model. The fixed effects considered were the contemporary group, number of milkings (1 or 2 milkings), linear and quadratic effects of the covariable cow age at calving and the mean lactation curve of the population (modelled by third-order Legendre orthogonal polynomials). The random additive genetic and permanent environmental effects were estimated by means of regression on third- to sixth-order Legendre orthogonal polynomials. The residual variances were modelled with a homogenous structure and various heterogeneous classes. According to the likelihood-ratio test, the best model for milk and fat production was that with four residual variance classes, while a third-order Legendre polynomial was best for the additive genetic effect for milk and fat yield, a fourth-order polynomial was best for the permanent environmental effect for milk production and a fifth-order polynomial was best for fat production. For protein yield, the best model was that with three residual variance classes and third- and fourth-order Legendre polynomials were best for the additive genetic and permanent environmental effects, respectively. The heritability estimates for the characteristics analysed were moderate, varying from 0·16±0·05 to 0·29±0·05 for milk yield, 0·20±0·05 to 0·30±0·08 for fat yield and 0·18±0·06 to 0·27±0·08 for protein yield. The estimates of the genetic correlations between the tests varied from 0·18±0·120 to 0·99±0·002; from 0·44±0·080 to 0·99±0·004; and from 0·41±0·080 to 0·99±0·004, for milk, fat and protein production, respectively, indicating that whatever the selection criterion used, indirect genetic gains can be expected throughout the lactation curve.

Hierarchical Bayesian modeling of heterogeneous cluster‐ and subject‐level associations between continuous and binary outcomes in dairy production

The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square-root-free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd-level and residual cow-level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects.

Covariate Pharmacokinetic Model Building in Oncology and its Potential Clinical Relevance

When modeling pharmacokinetic (PK) data, identifying covariates is important in explaining interindividual variability, and thus increasing the predictive value of the model. Nonlinear mixed-effects modeling with stepwise covariate modeling is frequently used to build structural covariate models, and the most commonly used software-NONMEM-provides estimations for the fixed-effect parameters (e.g., drug clearance), interindividual and residual unidentified random effects. The aim of covariate modeling is not only to find covariates that significantly influence the population PK parameters, but also to provide dosing recommendations for a certain drug under different conditions, e.g., organ dysfunction, combination chemotherapy. A true covariate is usually seen as one that carries unique information on a structural model parameter. Covariate models have improved our understanding of the pharmacology of many anticancer drugs, including busulfan or melphalan that are part of high-dose pretransplant treatments, the antifolate methotrexate whose elimination is strongly dependent on GFR and comedication, the taxanes and tyrosine kinase inhibitors, the latter being subject of cytochrome p450 3A4 (CYP3A4) associated metabolism. The purpose of this review article is to provide a tool to help understand population covariate analysis and their potential implications for the clinic. Accordingly, several population covariate models are listed, and their clinical relevance is discussed. The target audience of this article are clinical oncologists with a special interest in clinical and mathematical pharmacology.

Heterogeneidade dos componentes de variância na produção de leite e seus efeitos nas estimativas de herdabilidade e repetibilidade

Avaliou-se a heterogeneidade dos componentes de variância e seu efeito nas estimativas de herdabilidade e repetibilidade da produção de leite de bovinos da raça Holandesa. Os rebanhos foram agrupados de acordo com o nível de produção (baixo, médio e alto) e avaliados na escala não transformada, raiz quadrada e logarítmica. Os componentes de variância foram estimados pelo método de máxima verossimilhança restrita. O modelo animal incluiu os efeitos fixos de rebanho-ano-estação e das covariáveis duração da lactação (efeito linear) e idade da vaca ao parto (efeito linear e quadrático) e os efeitos aleatórios genético aditivo direto, de ambiente permanente e residual. Na escala não transformada, todos os componentes de variância foram heterogêneos entre os três níveis de produção. Nesta escala, a variância residual e a fenotípica estavam associadas positivamente com o nível de produção enquanto que na escala logarítmica a associação foi negativa. A heterogeneidade da variância fenotípica e de seus componentes afetou mais as estimativas de herdabilidade que as da repetibilidade. A eficiência do processo de seleção para produção de leite poderá ser afetada pelo nível de produção em que forem estimados os parâmetros genéticos.

Inbreeding Depression on Semen Quality in Austrian Dual‐Purpose Simmental Bulls

Using pedigree data, the inbreeding coefficients of 715 Austrian dual-purpose Simmental (Fleckvieh) bulls stationed in two artificial insemination (AI) centres in Upper and Lower Austria were calculated and incorporated in statistical models for the analysis of semen quality. Five semen quality parameters (volume, concentration, motility, number of spermatozoa per ejaculate and percentage of viable spermatozoa) of approximately 30,000 ejaculates, used in two separate data sets, were investigated. The mixed model included the fixed effects age class of the bull, bull handler, semen collector, month and year of collection, number of collection per bull and day, time interval since last collection, the linear continuous effect of the inbreeding coefficient of the bull, interactions between age class and month, and age class and interval since last collection, respectively, as well as the random effect of the bull and the random residual effect. Non-linear effects of inbreeding were significant for motility only. Despite the quite low inbreeding coefficients (mean 1.3%), all semen quality traits showed inbreeding depression, in four of the five traits significantly in at least one of the data sets. The magnitude of inbreeding depression was small, which might partly be caused by the low inbreeding levels and a potential pre-selection of the bulls in the AI centres. However, monitoring of inbreeding depression on fertility traits is recommended to avoid unrecognized deterioration of such traits.

Estimating transformations for repeated measures modeling of continuous bounded outcome data

Continuous bounded outcome data are unlikely to meet the usual assumptions for mixed-effects models of normally distributed and independent subject-specific and residual random effects. Additionally, overly complicated model structures might be necessary to account adequately for non-drug (time-dependent) and drug treatment effects. A transformation strategy with a likelihood component for censoring is developed to promote the simplicity of model structures and to improve the plausibility of assumptions on the random effects. The approach is motivated by Health Assessment Questionnaire Disability Index (HAQ-DI) data from a study in subjects with rheumatoid arthritis and is evaluated using a simulation study.

Production systems, technical parameters and quality of bovine milk producers in southern Chile

Production information of 29 milk producers in the southern region of Chile was studied with the objective of characterizing and classifying different dairy production systems, evaluating various associations between quantitative and qualitative studied variables and analyzing the effect of the production system and the quality of bovine milk according to the month of the year that it was processed. The classification of production groups was based on the implementation of the exploratory multivariate technique, main components analysis and conglomerates or cluster analysis. The applied statistical model was: y ijk = µ + M i + SP + MSP + e ijk , where y ijk =dependent variables (fat, protein, count of somatic cells and colony forming units); µ=general average; M i =effect of i-th month; SP =effect of j-th productive system; MSP ij =month-productive system interaction; j eijk =random residual effect. The price per liter of milk paid to producer was discarded for the construction of groups, since they presented a low discriminatory power given a coefficient of less than 20 % variation. Different correlations between analyzed variables are discussed. Five production systems are described using the qualifying variables and original systems. In general, more intensive production systems presented lower values of fat (%) and protein (%), but showed greater superiority in the quality of sanitary milk than dairy farms with minor animal load. Regarding seasonality, as winter turns to spring, protein (%) associated with a decrease in the fat (%) increases, which determines an inverse relationship between both variables.

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.