Genetic Evaluation Of Milk Yield Research Articles

Developing flexible models for genetic evaluations in smallholder crossbred dairy farms

The productivity of smallholder dairy farms is very low in developing countries. Important genetic gains could be realized using genomic selection, but genetic evaluations need to be tailored for lack of pedigree information and very small farm sizes. To accommodate this situation, we propose a flexible Bayesian model for the genetic evaluation of milk yield, which allows us to simultaneously account for nongenetic random effects for farms and varying SNP variance (BayesR model). First, we used simulations based on real genotype data from Indian crossbred dairy cattle to demonstrate that the proposed model can separate the true genetic and nongenetic parameters even for small farm sizes (2 cows on average) although with high standard errors in scenarios with low heritability. The accuracy of genomic genetic evaluation increased until farm size was approximately 5. We then applied the model to real data from 4,655 crossbred cows with 106,109 monthly test day milk records and 689,750 autosomal SNPs. We estimated a heritability of 0.16 (0.04) for milk yield and using cross-validation, a genomic estimated breeding value (GEBV) accuracy of 0.45 and bias (regression of phenotype on GEBV) of 1.04 (0.26). Estimated genetic parameters were very similar using BayesR, BayesC, and genomic BLUP approaches. Candidate genes near the top variants, IMMP2L and ARHGEF2, have been previously associated with milk protein composition, mastitis resistance, and milk cholesterol content. The estimated heritability and GEBV accuracy for milk yield are much lower than those from intensive or pasture-based systems in many countries. Further increases in the number of phenotyped and genotyped animals in farms with at least 2 cows (preferably 3-5, to allow for dropout of cows) are needed to improve the estimation of genetic effects in these smallholder dairy farms.

Impact of the Order of Legendre Polynomials in Random Regression Model on Genetic Evaluation for Milk Yield in Dairy Cattle Population.

The random regression test-day model has become the most commonly adopted model for routine genetic evaluations in dairy populations, which allows accurately accounting for genetic and environmental effects over lactation. The objective of this study was to explore appropriate random regression test-day models for genetic evaluation of milk yield in a Holstein population with a relatively small size, which is the common situation in regional or independent breeding companies to preform genetic evaluation. Data included 419,567 test-day records from 54,417 cows from the first lactation. Variance components and breeding values were estimated using a random regression test-day model with different orders (from first to fifth) of Legendre polynomials (LP) and accounted for homogeneous or heterogeneous residual variance across the lactation. Models were compared based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and predictive ability. In general, models with a higher order of LP showed better goodness of fit based on AIC and BIC values. However, models with third, fourth, and fifth order of LP led to similar estimates of genetic parameters and predictive ability. Models with assumption of heterogeneous residual variances achieved better goodness of fit but yielded similar predictive ability compared with those with assumption of homogeneous residual variances. Therefore, a random regression model with third order of LP is suggested to be an appropriate model for genetic evaluation of milk yield in local Chinese Holstein populations.

Bias and accuracy of dairy sheep evaluations using BLUP and SSGBLUP with metafounders and unknown parent groups

BackgroundBias has been reported in genetic or genomic evaluations of several species. Common biases are systematic differences between averages of estimated and true breeding values, and their over- or under-dispersion. In addition, comparing accuracies of pedigree versus genomic predictions is a difficult task. This work proposes to analyse biases and accuracies in the genetic evaluation of milk yield in Manech Tête Rousse dairy sheep, over several years, by testing five models and using the estimators of the linear regression method. We tested models with and without genomic information [best linear unbiased prediction (BLUP) and single-step genomic BLUP (SSGBLUP)] and using three strategies to handle missing pedigree [unknown parent groups (UPG), UPG with QP transformation in the {mathbf{H}} matrix (EUPG) and metafounders (MF)].MethodsWe compared estimated breeding values (EBV) of selected rams at birth with the EBV of the same rams obtained each year from the first daughters with phenotypes up to 2017. We compared within and across models. Finally, we compared EBV at birth of the rams with and without genomic information.ResultsWithin models, bias and over-dispersion were small (bias: 0.20 to 0.40 genetic standard deviations; slope of the dispersion: 0.95 to 0.99) except for model SSGBLUP-EUPG that presented an important over-dispersion (0.87). The estimates of accuracies confirm that the addition of genomic information increases the accuracy of EBV in young rams. The smallest bias was observed with BLUP-MF and SSGBLUP-MF. When we estimated dispersion by comparing a model with no markers to models with markers, SSGBLUP-MF showed a value close to 1, indicating that there was no problem in dispersion, whereas SSGBLUP-EUPG and SSGBLUP-UPG showed a significant under-dispersion. Another important observation was the heterogeneous behaviour of the estimates over time, which suggests that a single check could be insufficient to make a good analysis of genetic/genomic evaluations.ConclusionsThe addition of genomic information increases the accuracy of EBV of young rams in Manech Tête Rousse. In this population that has missing pedigrees, the use of UPG and EUPG in SSGBLUP produced bias, whereas MF yielded unbiased estimates, and we recommend its use. We also recommend assessing biases and accuracies using multiple truncation points, since these statistics are subject to random variation across years.

Genetic evaluation of milk yield and milk composition of Saudi Aradi and Damascus goats

The aim of the present study was to evaluate the effects of various non-genetic factors on milk production traits and to estimates its' heritability and variance component in milk production trait among Saudi Aradi and Damascus goats. A total number of 213 (98 Aradi and 115 Damascus goats) was classified according to breed, season, year, and type of birth. Data were analyzed statistically. The variation in milk yield (MY) were moderate (32.80 %), while variations in fat (F %) and protein (P %) were low (fat 17.67 % and protein 19.75 %). The genetic groups had a significant (P≤0.05) effect on milk yield and highly significant on (F % and P %, (P≤0.01)). Damascus goats had higher than Aradi in milk yield, fat and protein. Milk yield and fat% during seasons were not significant differ. Milk protein% during Summer/Spring season (S2) had a significant higher (P≤0.01) than at during Winter/Autumn (S1). The highest fat% (P≤0.05) found in year 2009. Triplets had higher (P≤0.01) effect on milk yield than twins or single. However, there were no significant differences between type of births for protein% and fat%. Damascus had higher heritability estimates (0.45) than Aradi goats (0.29) for milk yield. Also, for protein%, the heritability estimates of Damascus had higher heritability estimates (0.69) than Aradi goats (0.37). But the heritability for fat % in Aradi (0.23) was similar to that in Damascus goats (0.22). In conclusions, the percentage of genetic variance component in Aradi goats is low so that the best programs for the genetic improvement in the Aradi goats could be upgraded through crossing with Damascus goats.

Effect of calving age on genetic evaluation of milk yield in Holstein cattle

The aim of this study was to evaluate the effect of including calving age (CA) on genetic evaluation models for Holstein cattle. The evaluated models included the permanent environment, the sire-herd interactions, and the animals and residual effects as random. The fixed effects included the average production of milk, fat, and protein and the herd-year-season effect. The analyzed data included 603,521 records of milk production (in kg) corresponding to 438,098 animals from 527 herds. Additionally, there were 179,122 records of fat and protein components, corresponding to 148,930 animals from 137 herds. The records were classified by first lactation only (FL) and all available lactations (AL) for validation test (VT). The FL records corresponded to 275,487 milk production records with a mean of 10,874.1 ± 2773.9kg at a mean CA of 25.6 ± 4.2months. For FL, the milk components consisted of 78,955 records with a mean fat production of 392.86 ± 89.9kg, a mean protein production of 362.8 ± 74.9kg and a mean CA of 25.2 ± 4.1months. For AL, the number of records was 603,521 for milk production with a mean of 10,802.8 ± 2905.9kg and a mean CA of 35.6 ± 11.5months. For the milk components, there were 179,122 records with a mean of 36.1 ± 9.5months for CA and 388.3 ± 98.4kg and 356.7 ± 82.6kg for fat and protein, respectively. Three models were compared: the base model (M0) described above, and two alternative models that included CA in a linear and quadratic form (M1 and M2, respectively). Estimations of the variance components (VC) and breeding value (BV) were obtained using a repeatability animal model, with the same phenotypic and pedigree information used for all models. To select the best fit model for the data, a likelihood ratio test (LRtest) was used. A validation test (VT) was also applied to each model to evaluate the consistency of the genetic trends for females with information on AL and FL. The inclusion of CA in its linear form (M1) was the model that achieved the best results in the LRtest and an acceptable value for the VT. These results show that CA improves the model fit for BV prediction and reliability.

Test-day or 305-day milk yield for genetic evaluation of Gir cattle

Abstract: The objective of this work was to compare genetic evaluations of milk yield in the Gir breed, in terms of breeding values and their accuracy, using a random regression model applied to test-day records or the traditional model (TM) applied to estimates of 305-day milk yield, as well as to predict genetic trends for parameters of interest. A total of 10,576 first lactations, corresponding to 81,135 test-day (TD) records, were used. Rank correlations between the breeding values (EBVs) predicted with the two models were 0.96. The percentage of animals selected in common was 67 or 82%, respectively, when 1 or 5% of bulls were chosen, according to EBVs from random regression model (RRM) or TM genetic evaluations. Average gains in accuracy of 2.7, 3.0, and 2.6% were observed for all animals, cows with yield record, and bulls (sires of cows with yield record), respectively, when the RRM was used. The mean annual genetic gain for 305-day milk yield was 56 kg after 1993. However, lower increases in the average EBVs were observed for the second regression coefficient, related to persistency. The RRM applied to TD records is efficient for the genetic evaluation of milk yield in the Gir dairy breed.

Contemporary group alternatives for genetic evaluation of milk yield in small populations of dairy cattle

In the present study, different random regression models, focussed on the nature of the effect of the contemporary group, fixed or random, were compared for genetic evaluation of test-day milk yield in dairy Gir breed, whose herds are characterised by relatively reduced numbers of cows. Cows were assigned to the same contemporary group if they were tested in the same herd, year and month. In one of the evaluated models, the contemporary group was investigated as a fixed effect and a clustering procedure was adopted to group herd-year subclasses in order to, at the end of the process, all contemporary groups contained at least three cows. The models were compared by the quality of fit, the accuracy of the predicted breeding values and their estimates of genetic parameters. The clustering procedure did not significantly improve the accuracy of predicted breeding values. Moreover, the fit to the data for this model was negatively affected. Therefore, this strategy should not be further implemented. The model including the herd-calving period effect and contemporary group treated as random effect showed similar characteristics to its equivalent, where the contemporary group was modelled as a fixed effect. However, the fit to the data for this model was slightly worse. Thus, the results suggest a random regression model including the herd-calving period effect and the fixed effect of contemporary group for the genetic evaluations of production traits in dairy Gir cattle. These findings could be extended to small dairy cattle populations whose herds are small-sized.

Estimation of genetic parameters for test-day milk yield in Khuzestan buffalo

Abstract: The objective of this work was to estimate covariance functions for additive genetic and permanent environmental effects, as well as to obtain genetic parameters for buffalo test-day milk yield using random regression models on Legendre polynomials (LPs). A total of 2,538 test-day milk yield (TDMY) records from 516 first lactation records of Khuzestan buffalo, calving from 1993 to 2009 and belonging to 150 herds located in the state of Khuzestan, Iran, were analyzed. The residual variances were modeled through a step function with 1, 5, 6, 9, and 19 classes. The additive genetic and permanent environmental random effects were modeled by LPs of days in milk using quadratic to septic polynomial functions. The model with additive genetic and animal permanent environmental effects adjusted by cubic and third order LP, respectively, and with the residual variance modeled through a step function with nine classes was the most adequate one to describe the covariance structure. The model with the highest significant log-likelihood ratio test (LRT) and with the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC) was considered to be the most appropriate one. Unexpected negative genetic correlation estimates were obtained between TDMY records of the twenty-fifth and thirty-seventh week (-0.03). Genetic correlation estimates were generally higher, close to unity, between adjacent weeks during the middle of lactation. Random regression models can be used for routine genetic evaluation of milk yield in Khuzestan buffalo.

Depressão endogâmica na produção de leite no dia do controle de bovinos Gir leiteiro

Resumo: O objetivo deste trabalho foi estimar o efeito da endogamia sobre a produção de leite e sua persistência durante a lactação, em bovinos Gir leiteiro, bem como determinar o impacto de se considerar ou não o efeito da endogamia na avaliação genética dessa característica. Utilizaram-se 89.490 registros de produção no dia do controle, de 11.675 vacas em primeira lactação. O coeficiente e o incremento de endogamia individuais e o número equivalente de gerações completas de cada indivíduo foram computados. A depressão por endogamia foi estimada pela inclusão do efeito do incremento individual de endogamia, em um modelo de regressão aleatória. As soluções para a depressão por endogamia, de acordo com a classe de incremento individual de endogamia e a quinzena da lactação, variaram entre -1,238 e -0,135 kg, o que indica a redução da produção de leite com o aumento da endogamia. Em níveis mais elevados, a endogamia reduziu a persistência da produção de leite. A inclusão do efeito da endogamia no modelo de avaliação genética não afetou as estimativas de parâmetros genéticos e, praticamente, não alterou a predição dos valores genéticos e a classificação dos animais. Pode-se incluir o efeito da endogamia no modelo estatístico para a avaliação genética da característica produção de leite.

Combining different functions to describe milk, fat, and protein yield in goats using Bayesian multiple-trait random regression models.

We proposed multiple-trait random regression models (MTRRM) combining different functions to describe milk yield (MY) and fat (FP) and protein (PP) percentage in dairy goat genetic evaluation by using Bayesian inference. A total of 3,856 MY, FP, and PP test-day records, measured between 2000 and 2014, from 535 first lactations of Saanen and Alpine goats, including their cross, were used in this study. The initial analyses were performed using the following single-trait random regression models (STRRM): third- and fifth-order Legendre polynomials (Leg3 and Leg5), linear B-splines with 3 and 5 knots, the Ali and Schaeffer function (Ali), and Wilmink function. Heterogeneity of residual variances was modeled considering 3 classes. After the selection of the best STRRM to describe each trait on the basis of the deviance information criterion (DIC) and posterior model probabilities (PMP), the functions were combined to compose the MTRRM. All combined MTRRM presented lower DIC values and higher PMP, showing the superiority of these models when compared to other MTRRM based only on the same function assumed for all traits. Among the combined MTRRM, those considering Ali to describe MY and PP and Leg5 to describe FP (Ali_Leg5_Ali model) presented the best fit. From the Ali_Leg5_Ali model, heritability estimates over time for MY, FP. and PP ranged from 0.25 to 0.54, 0.27 to 0.48, and 0.35 to 0.51, respectively. Genetic correlation between MY and FP, MY and PP, and FP and PP ranged from -0.58 to 0.03, -0.46 to 0.12, and 0.37 to 0.64, respectively. We concluded that combining different functions under a MTRRM approach can be a plausible alternative for joint genetic evaluation of milk yield and milk constituents in goats.

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.

Genetic evaluation of milk yield in Alpine goats for the first four lactations using random regression models.

Random regression models have been used in evaluating test-day milk yield, providing accurate estimates of genetic values in animals. However, herd evaluation with only information from the first lactation may not be the best option from an economic perspective. Other factors should be taken into account, particularly other lactations. Our objective in this study was to analyze the genetic divergence between the first four lactations of Alpine goats. The RENPED software was used to perform descriptive statistics, check for errors in pedigree, recode the data, and for Pearson's and Spearman's correlations. The WOMBAT software was used to estimate the variance components and predict the breeding values. The CALC software was adopted to calculate the percentage of coincidence between the ranking of the animals and the animals kept in common at each lactation evaluation. The results show that selection using only the first lactation in small herds with a low degree of technology can be employed as a palliative measure, in view of the difficulty in evaluating all lactations. However, the selection of breeding goats and the production of catalogues should not be based only on the first lactation, because the results demonstrate inversions in the classification of the best breeders when other lactations are analyzed.

Random regression models using Legendre orthogonal polynomials to evaluate the milk production of Alpine goats

The objective of this study was to identify the best random regression model using Legendre orthogonal polynomials to evaluate Alpine goats genetically and to estimate the parameters for test day milk yield. On the test day, we analyzed 20,710 records of milk yield of 667 goats from the Goat Sector of the Universidade Federal de Viçosa. The evaluated models had combinations of distinct fitting orders for polynomials (2-5), random genetic (1-7), and permanent environmental (1-7) fixed curves and a number of classes for residual variance (2, 4, 5, and 6). WOMBAT software was used for all genetic analyses. A random regression model using the best Legendre orthogonal polynomial for genetic evaluation of milk yield on the test day of Alpine goats considered a fixed curve of order 4, curve of genetic additive effects of order 2, curve of permanent environmental effects of order 7, and a minimum of 5 classes of residual variance because it was the most economical model among those that were equivalent to the complete model by the likelihood ratio test. Phenotypic variance and heritability were higher at the end of the lactation period, indicating that the length of lactation has more genetic components in relation to the production peak and persistence. It is very important that the evaluation utilizes the best combination of fixed, genetic additive and permanent environmental regressions, and number of classes of heterogeneous residual variance for genetic evaluation using random regression models, thereby enhancing the precision and accuracy of the estimates of parameters and prediction of genetic values.

Analyses of fixed effects for genetic evaluation of dairy cattle using test day records in Indonesia

Season, rainfall, day of rain, temperature, humidity, year and farm are fixed effects, which have been reported to influence milk yield. Those factors are often linked together to contribute to the variation of milk production. This research is addressed to study the fixed effect factors, including lactation curve, which should be considered for genetic evaluation of milk yield based on test day records of dairy cattle. The data were taken from four different farms, which were PT. Taurus Dairy Farm, BPPT Cikole, Bandang Dairy Farm, and BBPTU Baturraden. In total of 16806 test day records were evaluated, consisting of 9,302 at first and 7,504 at second lactation, respectively. The results indicated that fixed effects were very specific and the influences had different patterns for each farm. Consequently, in a genetic evaluation, these factors such as lactation, temperature, year, day of rain, and humidity need to be evaluated first. Ali-Schaeffer curve represented the most appropriate curve to use in the genetic evaluation of dairy cattle in Indonesia. Key words : Fixed Effects, Milk Production Curve, Test Day, Dairy Cattle

Valores genéticos para as produções de leite do dia do controle e da lactação na raça Holandesa com diferentes modelos estatísticos

Foram utilizados 263.390 registros de produção de leite do dia do controle (PDC) de 32.448 primeiras lactações de vacas da raça Holandesa paridas no período de 1991 a 2001 para predizer valores genéticos usando diferentes modelos estatísticos e a metodologia REML. Valores genéticos estimados utilizando-se três modelos de regressão aleatória (MRA) foram comparados àqueles estimados utilizando-se um modelo de repetibilidade (MRF) e um modelo para produção até 305 dias (P305). Nos modelos de regressão aleatória, duas curvas foram utilizadas para descrever a trajetória da lactação: a polinomial logarítmica (AS) e a exponencial (W), sob duas formas: padrão e com uma modificação para reduzir a amplitude das covariáveis e contornar problemas de convergência (W*). As covariâncias requeridas foram estimadas em análises prévias utilizando-se as mesmas funções de covariância e mesmos modelos. Os desvios-padrão (DP) das estimativas de valores genéticos (EVG) para touros foram similares para os MRA com as curvas AS, W* e MRF. Os desvios-padrão das estimativas de valores genéticos para vacas e touros foram maiores nos modelos para ajuste das PDC que naquele para ajuste da P305. A magnitude das diferenças dos desvios-padrão entre modelos dependeu do número de controle, no caso de vacas, e do número de filhas, no caso de touros. Os desvios-padrão para o modelo W foram maiores, contudo, problemas de convergência ocorreram na fase de estimação dos componentes de covariância, o que exige cautela na interpretação dos resultados deste modelo. As correlações das estimativas de valores genéticos de touros preditas com os modelos testados aumentaram com o aumento no número de progênies e variaram de 0,66 (P305-W) a 0,92 (P305-AS, P305-W*). A tendência genética foi maior para os MRA e menor para MRF em comparação a P305. Os MRA possibilitam mais informações sobre as EVG que MRF por possibilitarem avaliação genética para persistência da produção de leite na lactação. Os resultados indicam o MRA com a curva de AS como o melhor modelo de ajuste das PDC alternativamente ao ajuste da P305 para avaliação genética dos animais da raça Holandesa no Brasil.

Use of Multiple Traits Animal Model for Genetic Evaluation of Milk Yield and Age at First Calving of Holstein Friesian Cattle in Turkey

Use of Multiple Traits Animal Model for Genetic Evaluation of Milk Yield and Age at First Calving of Holstein Friesian Cattle in Turkey

Comparison of International Dairy Sire Evaluations from Meta-Analysis of National Estimated Breeding Values and Direct Analysis of Individual Animal Performance Records

Our objective was to assess the predictive ability of different methodologies for international genetic evaluation of milk yield and to determine the magnitude of differences in the resulting sire estimated breeding values (EBV). Data included first lactation records of 16,057,335 Holstein-sired cows from 237,049 herds in 14 countries. Meta-analysis of national sire EBV using the multiple-trait across country evaluation (MACE) procedure, single-trait analysis of individual animal performance records, multiple-trait analysis of individual animal performance records, and borderless herd cluster model were compared by assessing predictive ability. Comparisons were based on root mean square error of sire EBV from a subset of records from cows calving between 1990 and 1995 and corresponding pedigree indices for sires that received their first genetic evaluations in 1996 or 1997. The number of bulls first evaluated in 1996 or 1997 that were in common between the top 25, 100, and 250 for pedigree index and the top 25, 100, and 250 for EBV were also determined for each method. Average root mean square error of prediction was 10.3kg2 for the borderless single-trait model, 6.6kg2 for the borderless herd cluster model, and 6.7kg2 for both the borderless multiple-trait model and meta-analysis of national sire EBV using MACE. The mean numbers of common bulls among the top 25, 100, and 250, respectively, when selected on pedigree index and subsequent EBV were 11, 48, and 154 for the borderless single-trait model; 16, 66, and 176 for the borderless multiple-trait model; 16, 66, and 178 for the borderless herd cluster model; and 15, 66, and 178 for meta-analysis of national sire EBV using MACE. Rank correlations between sire EBV from different models ranged from 0.77 for the single-trait borderless model and the meta-analysis using MACE to 0.92 for the borderless multiple-trait and the borderless herd cluster models.

Genetic evaluation of milk yield under different milk recording schemes

Genetic evaluation of milk yield under different milk recording schemes

Model comparison for genetic evaluation of milk yield in Uruguayan Holsteins

Three models for genetic evaluation of milk yield of Uruguayan Holstein cattle were compared using 159 169 lactation records from 81 928 cows calving between 1989 and 1998. Model I included the effects of herd-year-season, parity by age group, additive genetic merit, permanent environment, and residual. Model II included all effects in Model I, as well as number of days open and length of the dry period. Model III included all factors in Model II, and it accommodated heterogeneity of variance within contemporary groups (CG) through a pre-adjustment of the data based on empirical Bayes estimates of the CG variance. Estimates of heritability for milk yield were 0.23, 0.24 and 0.25, and estimates of repeatability were 0.55, 0.56 and 0.57 for Models I, II and III, respectively. Models were contrasted by examining changes in sire ranking and by a cross-validation procedure, based on the ability of the models to predict first, second and later lactations. Data were divided into two subsets, and records from one subset were predicted using location parameters estimated from the other subset. A resampling procedure was used to minimise the dependency on the sample structure. Correspondence between observed and predicted values was assessed in terms of square root of empirical mean square errors of prediction, percentage squared bias and the coefficient of determination ‘ R 2’. Adjustment for heterogeneous CG variance had a marked effect on rankings of animals, especially elite cows, where correlations between solutions from Models I and II versus Model III ranged from 0.53 to 0.80. The percentage of animals selected in common by each pair of models decreased when selection intensity increased. Cross-validation analyses suggested that an assumption of heterogeneity of CG variance is tenable, especially in later lactations, whereas some doubts arise in first lactations, most probably due to the data structure used in the analyses.