L. El Faro

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.

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.

Random regression models to estimate genetic parameters for test-day milk yield in Brazilian Murrah buffaloes

The objective of this work was to estimate covariance functions for additive genetic and permanent environmental effects and, subsequently, to obtain genetic parameters for buffalos test-day milk production using random regression models on Legendre polynomials (LPs). A total of 17 935 test-day milk yield (TDMY) from 1433 first lactations of Murrah buffaloes, calving from 1985 to 2005 and belonging to 12 herds located in São Paulo state, Brazil, were analysed. Contemporary groups (CGs) were defined by herd, year and month of milk test. Residual variances were modelled through variance functions, from second to fourth order and also by a step function with 1, 4, 6, 22 and 42 classes. The model of analyses included the fixed effect of CGs, number of milking, age of cow at calving as a covariable (linear and quadratic) and the mean trend of the population. As random effects were included the additive genetic and permanent environmental effects. The additive genetic and permanent environmental random effects were modelled by LP of days in milk from quadratic to seventh degree polynomial functions. The model with additive genetic and animal permanent environmental effects adjusted by quintic and sixth order LP, respectively, and residual variance modelled through a step function with six classes was the most adequate model to describe the covariance structure of the data. Heritability estimates decreased from 0.44 (first week) to 0.18 (fourth week). Unexpected negative genetic correlation estimates were obtained between TDMY records at first weeks with records from middle to the end of lactation, being the values varied from -0.07 (second with eighth week) to -0.34 (1st with 42nd week). TDMY heritability estimates were moderate in the course of the lactation, suggesting that this trait could be applied as selection criteria in milking buffaloes.

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.

Efeito da idade de exposição de novilhas à reprodução sobre estimativas de herdabilidade da idade ao primeiro parto em bovinos Nelore

Heritability estimates of age at first calving (AFC) were obtained from four different data sets from Nellore heifers. The first set (AFCI) had information about heifers (n= 6,222) which were exposed only at 24 months of age. The second (AFC2) data set used all heifers (n= 15,746) with information about AFC. The third set (AFC3) included a restricted number of heifers (n= 9,524), which were exposed earlier to reproduction at 18 months of age. The fourth set (AFC4) had information about all heifers born on herd (n= 40,954). Analyses included as fixed effects the contemporary group and linear and quadratic effects of age of dam. Estimates of heritability for AFC1, AFC2, AFC3 and AFC4 were, respectively, 0.00, 0.11, 0.20 and 0.36. Age at first calving was affected by reproductive management.

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.

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.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

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.

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.