International genomic evaluation methods for dairy cattle

Background

Genomic evaluations are rapidly replacing traditional evaluation systems used for dairy cattle selection. Higher reliabilities from larger genotype files promote cooperation across country borders. Genomic information can be exchanged across countries using simple conversion equations, by modifying multi-trait across-country evaluation (MACE) to account for correlated residuals originating from the use of foreign evaluations, or by multi-trait analysis of genotypes for countries that use the same reference animals.

Methods

Traditional MACE assumes independent residuals because each daughter is measured in only one country. Genomic MACE could account for residual correlations using daughter equivalents from genomic data as a fraction of the total in each country and proportions of bulls shared. MACE methods developed to combine separate within-country genomic evaluations were compared to direct, multi-country analysis of combined genotypes using simulated genomic and phenotypic data for 8,193 bulls in nine countries.

Results

Reliabilities for young bulls were much higher for across-country than within-country genomic evaluations as measured by squared correlations of estimated with true breeding values. Gains in reliability from genomic MACE were similar to those of multi-trait evaluation of genotypes but required less computation. Sharing of reference genotypes among countries created large residual correlations, especially for young bulls, that are accounted for in genomic MACE.

Conclusions

International genomic evaluations can be computed either by modifying MACE to account for residual correlations across countries or by multi-trait evaluation of combined genotype files. The gains in reliability justify the increased computation but require more cooperation than in previous breeding programs.     

Principal component approach in variance component estimation for international sire evaluation

Background

The dairy cattle breeding industry is a highly globalized business, which needs internationally comparable and reliable breeding values of sires. The international Bull Evaluation Service, Interbull, was established in 1983 to respond to this need. Currently, Interbull performs multiple-trait across country evaluations (MACE) for several traits and breeds in dairy cattle and provides international breeding values to its member countries. Estimating parameters for MACE is challenging since the structure of datasets and conventional use of multiple-trait models easily result in over-parameterized genetic covariance matrices. The number of parameters to be estimated can be reduced by taking into account only the leading principal components of the traits considered. For MACE, this is readily implemented in a random regression model.

Methods

This article compares two principal component approaches to estimate variance components for MACE using real datasets. The methods tested were a REML approach that directly estimates the genetic principal components (direct PC) and the so-called bottom-up REML approach (bottom-up PC), in which traits are sequentially added to the analysis and the statistically significant genetic principal components are retained. Furthermore, this article evaluates the utility of the bottom-up PC approach to determine the appropriate rank of the (co)variance matrix.

Results

Our study demonstrates the usefulness of both approaches and shows that they can be applied to large multi-country models considering all concerned countries simultaneously. These strategies can thus replace the current practice of estimating the covariance components required through a series of analyses involving selected subsets of traits. Our results support the importance of using the appropriate rank in the genetic (co)variance matrix. Using too low a rank resulted in biased parameter estimates, whereas too high a rank did not result in bias, but increased standard errors of the estimates and notably the computing time.

Conclusions

In terms of estimation''s accuracy, both principal component approaches performed equally well and permitted the use of more parsimonious models through random regression MACE. The advantage of the bottom-up PC approach is that it does not need any previous knowledge on the rank. However, with a predetermined rank, the direct PC approach needs less computing time than the bottom-up PC.     

Binational evaluation of type traits from Germany and France with a single-trait MACE animal model

Binational genetic evaluation between Germany and France were performed for each type trait using a single-trait MACE (multiple across-country evaluation) model. Daughter yield deviations (DYD) of bulls having 30 equivalent daughter contributions or more were the data for parameter estimation. Full pedigree information of bulls was used via sire and dam relationships. In general, across-country genetic correlation estimates were in agreement with what is observed by Interbull. The estimated correlations were over 0.93 for stature, rump angle, udder depth, front teat placement, teat length and rear teat placement. These traits have been classified in both countries for a long period of time. However, some other type traits were included later in the French type classification system (most of them since 2000): chest width, body depth, angularity, rump width, rear leg rear view, fore udder and rear udder height. The estimated correlations for these traits were relatively low. In order to check changes in genetic correlations over time, data from bulls born until the end of 1995 were discarded. Higher genetic correlation estimates between both countries were obtained by using more recent data especially for traits having lower genetic correlation, e.g. body depth correlation increased from 0.55 to 0.83. Once genetic correlations were estimated, binational genetic evaluation between Germany and France were performed for each type trait using DYD of bulls. The rankings of bulls obtained from this evaluation had some differences with Interbull rankings but a similar proportion of bulls from each country was found. Finally, more computationally demanding binational evaluations were performed using yield deviations of cows for binational cow comparison. The rankings obtained were influenced by the number of daughters per bull and heritabilities used in each country.     

Genetic and phenotypic parameters for test day milk yield of Sahiwal cattle in the semi-arid tropics

A total of 19 376 test day (TD) milk yield records from the first three lactations of 1618 cows daughters of 162 sires were used to estimate genetic and phenotypic parameters and determine the relationship between daily milk yield and lactation milk yield in the Sahiwal cattle in Kenya. Variance components were estimated using animal models based on a derivative free restricted maximum likelihood procedure. Variance components were estimated using various univariate and multi-trait fixed regression test day models (TDM) that defined contemporary groups either based on the year-season of calving (YSCV) or on the year-season of TD milk sampling (YSTD). Variance components were influenced by CG which resulted in differences in heritability and repeatability estimates between TDM. Models considering YSTD resulted in higher additive genetic variances and lower residual variances compared with models in which YSCV was considered. Heritability estimates for daily yield ranged from 0.28 to 0.46, 0.38 to 0.52 and 0.33 to 0.52 in the first, second and third lactation, respectively. In the first and second lactation, the heritability estimates were highest between TD 2 and TD 4. Genetic correlations among daily milk yields ranged from 0.41 to 0.93, 0.50 to 0.83 and 0.43 to 86 in the first, second and third lactation, respectively. The phenotypic correlations were correspondingly lower. Genetic correlations were different from unit when fitting multi-trait TDM. Therefore, a multiple trait model would be more ideal in determining the genetic merit of dairy sires and bulls based on daily yield records. Genetic and phenotypic correlations between daily yield and lactation yields were high and positive. Genetic correlations ranged from 0.84 to 0.99, 0.94 to 1.00 and 0.94 to 0.97 in the first, second and third lactations, respectively. The corresponding phenotypic correlation estimates ranged from 0.50 to 0.85, 0.50 to 0.83 and 0.53 to 0.87. The high genetic correlation between daily yield and lactation yield imply that both traits are influenced by similar genes. Therefore daily yields records could be used in genetic evaluation in the Sahiwal cattle breeding programme.     

Genetic modelling of test day records in dairy sheep using orthogonal Legendre polynomials

Test day milk yields of three lactations in Sfakia sheep were analyzed fitting a random regression (RR) model, regressing on orthogonal polynomials of the stage of the lactation period, i.e. days in milk. Univariate (UV) and multivariate (MV) analyses were also performed for four stages of the lactation period, represented by average days in milk, i.e. 15, 45, 70 and 105 days, to compare estimates obtained from RR models with estimates from UV and MV analyses. The total number of test day records were 790, 1314 and 1041 obtained from 214, 342 and 303 ewes in the first, second and third lactation, respectively. Error variances and covariances between regression coefficients were estimated by restricted maximum likelihood. Models were compared using likelihood ratio tests (LRTs). Log likelihoods were not significantly reduced when the rank of the orthogonal Legendre polynomials (LPs) of lactation stage was reduced from 4 to 2 and homogenous variances for lactation stages within lactations were considered. Mean weighted heritability estimates with RR models were 0.19, 0.09 and 0.08 for first, second and third lactation, respectively. The respective estimates obtained from UV analyses were 0.14, 0.12 and 0.08, respectively. Mean permanent environmental variance, as a proportion of the total, was high at all stages and lactations ranging from 0.54 to 0.71. Within lactations, genetic and permanent environmental correlations between lactation stages were in the range from 0.36 to 0.99 and 0.76 to 0.99, respectively. Genetic parameters for additive genetic and permanent environmental effects obtained from RR models were different from those obtained from UV and MV analyses.     

Estimation of genetic parameters for test day records of dairy traits in the first three lactations

Application of test-day models for the genetic evaluation of dairy populations requires the solution of large mixed model equations. The size of the (co)variance matrices required with such models can be reduced through the use of its first eigenvectors. Here, the first two eigenvectors of (co)variance matrices estimated for dairy traits in first lactation were used as covariables to jointly estimate genetic parameters of the first three lactations. These eigenvectors appear to be similar across traits and have a biological interpretation, one being related to the level of production and the other to persistency. Furthermore, they explain more than 95% of the total genetic variation. Variances and heritabilities obtained with this model were consistent with previous studies. High correlations were found among production levels in different lactations. Persistency measures were less correlated. Genetic correlations between second and third lactations were close to one, indicating that these can be considered as the same trait. Genetic correlations within lactation were high except between extreme parts of the lactation. This study shows that the use of eigenvectors can reduce the rank of (co)variance matrices for the test-day model and can provide consistent genetic parameters.     

A simple method for genomic selection of moderately sized dairy cattle populations

An efficient algorithm for genomic selection of moderately sized populations based on single nucleotide polymorphism chip technology is described. A total of 995 Israeli Holstein bulls with genetic evaluations based on daughter records were genotyped for either the BovineSNP50 BeadChip or the BovineSNP50 v2 BeadChip. Milk, fat, protein, somatic cell score, female fertility, milk production persistency and herd-life were analyzed. The 400 markers with the greatest effects on each trait were first selected based on individual analysis of each marker with the genetic evaluations of the bulls as the dependent variable. The effects of all 400 markers were estimated jointly using a 'cow model,' estimated from the data truncated to exclude lactations with freshening dates after September 2006. Genotype probabilities for each locus were computed for all animals with missing genotypes. In Method I, genetic evaluations were computed by analysis of the truncated data set with the sum of the marker effects subtracted from each record. Genomic estimated breeding values for the young bulls with genotypes, but without daughter records, were then computed as their parent averages combined with the sum of each animal's marker effects. Method II genomic breeding values were computed based on regressions of estimated breeding values of bulls with daughter record on their parent averages, sum of marker effects and birth year. Method II correlations of the current breeding values of young bulls without daughter records in the truncated data set were higher than the correlations of the current breeding values with the parent averages for fat and protein production, persistency and herd-life. Bias of evaluations, estimated as a difference between the mean of current breeding values of the young bulls and their genomic evaluations, was reduced for milk production traits, persistency and herd-life. Bias for milk production traits was slightly negative, as opposed to the positive bias of parent averages. Correlations of Method II with the means of daughter records adjusted for fixed effects were higher than parent averages for fat, protein, fertility, persistency and herd-life. Reducing the number of markers included in the analysis from 400 to 300 did not reduce correlations of genomic breeding values for protein with current breeding values, but did slightly reduce correlations with means of daughter records. Method II has the advantages as compared with the method of VanRaden in that genotypes of cows can be readily incorporated into the Method II analysis, and it is more effective for moderately sized populations.     

Genetic and phenotypic parameters of lactations longer than 305 days (extended lactations)

Test-day milk yield and somatic cell count data over extended lactation (lactation to 540-600 days) were analysed considering part lactations as different traits and fitting random regression (RR) models. Data on Australian Jersey and Holstein Friesian (HF) were used to demonstrate the shape of the lactation curve and data on HF were used for genetic study. Test-day data from about 100 000 cows that calved between 1998 and 2005 were used for this study. In all analyses, a sire model was used.When part lactations were considered as different traits, protein yield early in the lactation (e.g. first 2 months) had a genetic correlation of about 0.8 with protein yield produced after 300 days of lactation. Genetic correlations between lactation stages that are adjacent to each other were high (0.9 or more) within parity. Across parities, genetic correlations were high for both protein and milk yield if they are within the same stage of lactation. Phenotypic correlations were lower than genetic correlations. Heritability of milk-yield traits estimated from the RR model varied from 0.15 at the beginning of the lactation to as high as 0.37 by the 4th month of lactation. All genetic correlations between different days in milk were positive, with the highest correlations between adjacent days in milk and decreasing correlations with increasing time-span. The pattern of genetic correlations between milk yield in the second 300 days (301 to 600 days of lactation) do not markedly differ from the pattern in the first 300 days of lactation. The lowest estimated genetic correlation was 0.15 between milk yield on days 45 and 525 of lactation. The result from this study shows that progeny of bulls with high estimated breeding values for yield traits and those that produce at a relatively high level in the first few months are the most likely candidates for use in herds favouring extended lactations.     

Genetic parameters for milk urea concentration and milk traits in Polish Holstein-Friesian cows

Milk urea concentration (MU) used by dairy producers for management purposes can be affected by selection for milk traits. To assess this problem, genetic parameters for MU in Polish Holstein-Friesian cattle were estimated for the first three lactations. The genetic correlation of MU with milk production traits, lactose percentage, fat to protein ratio (FPR) and somatic cell score (SCS) were computed with two 5-trait random regression test-day models, separately for each lactation. Data used for estimation (159,044 daily observations) came from 50 randomly sampled herds. (Co)variance components were estimated with the Bayesian Gibbs sampling method. The coefficient of variation for MU in all three parities was high (40–41 %). Average daily heritabilities of MU were 0.22 for the first parity and 0.21 for the second and third lactations. Average genetic correlations for different days in milk in the first three lactations between MU and other traits varied. They were small and negative for protein percentage (from ?0.24 to ?0.11) and for SCS (from ?0.14 to ?0.09). The weakest genetic correlation between MU and fat percentage, and between MU and lactose percentage were observed (from ?0.10 to 0.10). Negative average genetic correlation with the fat to protein ratio was observed only in the first lactation (?0.14). Genetic correlations with yield traits were positive and ranged from low to moderate for protein (from 0.09 to 0.33), fat (from 0.16 to 0.35) and milk yield (from 0.20 to 0.42). These results suggest that the selection on yield traits and SCS tends to increase MU slightly.     

Application of the covariance function approach with an iterative two-stage algorithm to the estimation of parameters of a random regression test day model for dairy production traits

The covariance function approach with an iterative two-stage algorithm of LIU et al. (2000) was applied to estimate parameters for the Polish Black-and-White dairy population based on a sample of 338 808 test day records for milk, fat, and protein yields. A multiple trait sire model was used to estimate covariances of lactation stages. A third-order Legendre polynomial was subsequently fitted to the estimated (co)variances to derive (co)variances of random regression coefficients for both additive genetic and permanent environment effects. Daily and 305-day heritability estimates obtained are consistent with several studies which used both fixed and random regression test day models. Genetic correlations between any two days in milk (DIM) of the same lactation as well as genetic correlations between the same DIM of two lactations were within a biologically acceptable range. It was shown that the applied estimation procedure can utilise very large data sets and give plausible estimates of (co)variance components.     

Genetics of heat tolerance for milk yield and quality in Holsteins

Tropical and sub-tropical climates are characterized by high temperature and humidity, during at least part of the year. Consequently, heat stress is common in Holstein cattle and productive and reproductive losses are frequent. Our objectives were as follows: (1) to quantify losses in production and quality of milk due to heat stress; (2) to estimate genetic correlations within and between milk yield (MY) and milk quality traits; and (3) to evaluate the trends of genetic components of tolerance to heat stress in multiple lactations of Brazilian Holstein cows. Thus, nine analyses using two-trait random regression animal models were carried out to estimate variance components and genetic parameters over temperature–humidity index (THI) values for MY and milk quality traits (three lactations: MY×fat percentage (F%), MY×protein percentage (P%) and MY×somatic cell score (SCS)) of Brazilian Holstein cattle. It was demonstrated that the effects of heat stress can be harmful for traits related to milk production and milk quality of Holstein cattle even though most herds were maintained in a modified environment, for example, with fans and sprinklers. For MY, the effect of heat stress was more detrimental in advanced lactations (−0.22 to −0.52 kg/day per increase of 1 THI unit). In general, the mean heritability estimates were higher for lower THI values and longer days in milk for all traits. In contrast, the heritability estimates for SCS increased with increasing THI values in the second and third lactation. For each trait studied, lower genetic correlations (different from unity) were observed between opposite extremes of THI (THI 47 v. THI 80) and in advanced lactations. The genetic correlations between MY and milk quality trait varied across the THI scale and lactations. The genotype×environment interaction due to heat stress was more important for MY and SCS, particularly in advanced lactations, and can affect the genetic relationship between MY and milk quality traits. Selection for higher MY, F% or P% may result in a poor response of the animals to heat stress, as a genetic antagonism was observed between the general production level and specific ability to respond to heat stress for these traits. Genetic trends confirm the adverse responses in the genetic components of heat stress over the years for milk production and quality. Consequently, the selection of Holstein cattle raised in modified environments in both tropical and sub-tropical regions should take into consideration the genetic variation in heat stress.     

Impact of bovine somatotropin on ranking for genetic value of dairy sires for milk yield traits and somatic cell score

Records of Holstein cows were used to examine how different models account for the effect of bovine somatotropin (bST) treatment on genetic evaluation of dairy sires for yield traits and somatic cell score. Data set 1 included 65,720 first-lactation records. Set 2 included 50,644 second-lactation records. Set 3 included 45,505 records for lactations three, four and five. Estimated breeding values (EBV) of sires were with three different animal models. With Model 1, bST administration was ignored. With Model 2, bST administration was used as a fixed effect. With Model 3, administration of bST was used to define the contemporary group (herd-year-month of calving-bST). Correlations for EBV of 1,366 sires with treated daughters between pairs of the three models were calculated for milk, fat and protein yields and somatic cell score for the three data sets. Correlations for EBV of sires between pairs of models for all traits ranged from 0.971 to 0.999. Fractions of sires with bST-treated progeny selected in common (top 10 to 15%) were 0.94 and usually greater for all pairs of models for all traits and parities. For this study, the method of statistical adjustment for bST treatment resulted in a negligible effect on genetic evaluations of sires when some daughters were treated with bST and suggests that selection of sires to produce the next generation of sires and cows might not be significantly affected by how the effect of bST is modeled for prediction of breeding values for milk, fat and protein yields and somatic cell score.     

Combining datasets in a dynamic residual feed intake model and comparison with linear model results in lactating Holstein cattle

A new method to estimate residual feed intake (RFI) was recently developed based on a multi-trait random regression model. This approach deals with the dynamic nature of the lactation, which is in contrast with classical linear approaches. However, an issue remains: pooling data across sites and years, which implies dealing with different (and sometimes unknown) diet energy contents. This will be needed for genomic evaluation. In this study, we tested whether merging two individual datasets into a larger one can lead to valuable results in comparison to analysing them on their own with the multi-trait random regression model. Three datasets were defined: the first one with 1 063 lactations, the second one with 205 lactations from a second farm and the third one combining the data of the two first datasets (1 268 lactations). The model was applied to the three datasets to estimate individual RFI as well as variance components and correlations between the four traits included in the model (fat and protein corrected milk production, BW, feed intake and body condition score), and a fixed month-year-farm effect was used to define the contemporary group. The variance components and correlations between animal effects of the four traits were very similar irrespective of the dataset used with correlations higher than 0.94 between the different datasets. The RFI estimates for animals from their single farm only were also very similar (r > 0.95) to the ones computed from the merged dataset (Dataset 3). This highlights that the contemporary group correction in the model adequately accounts for differences between the two feeding environments. The dynamic model can thus be used to produce RFI estimates from merged datasets, at least when animals are raised in similar systems. In addition, the 205 lactations from the second farm were also used to estimate the RFI with a linear approach. The RFI estimated by the two approaches were similar when the considered period was rather short (r = 0.85 for RFI for the first 84 days of lactation) but this correlation weakened as the period length grew (r = 0.77 for RFI for the first 168 days of lactation). This weakening in correlations between the two approaches when increasing the used time-period reflects that only the dynamic model permits the regression coefficients to evolve in line with the physiological changes through the lactation. The results of this study enlarge the possibilities of use for the dynamic RFI model.     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

Estimates of correlations among yield traits and somatic cell score with different models to adjust for bovine somatotropin effects on Holstein dairy cows

Records of Holstein cows from the Dairy Records Processing Center at Raleigh, NC were edited to obtain three data sets: 65,720 first, 50,694 second, and 65,445 later lactations. Correlations among yield traits and somatic cell score were estimated with three different models: 1) bovine somatotropin (bST) administration ignored, 2) bST administration as a fixed effect and 3) administration of bST as part of the contemporary group (herd-year-month-bST). Heritability estimates ranged from 0.13 to 0.17 for milk, 0.12 to 0.20 for fat, 0.14 to 0.16 for protein yields, and 0.08 to 0.09 for somatic cell score. Estimates were less for later than first lactations. Estimates of genetic correlations among yields ranged from 0.35 to 0.85 with no important differences between estimates with the 3 models. Estimates for lactation 2 agreed with estimates for lactation 1. Estimates of genetic correlations for later lactations were generally greater than for lactations 1 and 2 except between milk and protein yields. Estimates of genetic correlations between yields and somatic cell score were mostly negative or small (-0.45 to 0.11). Estimates of environmental correlations among yield traits were similar with all models (0.77 to 0.97). Estimates of environmental correlations between yields and somatic cell score were negative (-0.22 to -0.14). Estimates of phenotypic correlations among yield traits ranged from 0.70 to 0.95. Estimates of phenotypic correlations between yields and somatic cell score were small and negative. For all three data sets and all traits, no important differences in estimates of genetic parameters were found for the two models that adjusted for bST and the model that did not.     

Genome-wide associations for investigating time-dependent genetic effects for milk production traits in dairy cattle

Phenotypic variation in milk production traits has been described over the course of a lactation as well as between different parities. The objective of this study was to investigate whether variation in production is affected by different loci across lactations. A genome-wide association study (GWAS) using a 50-k SNP chip was conducted in 152 divergent German Holstein Friesian cows to test for association with milk production traits over different lactations. The first four lactations were analysed regarding milk yield, fat, protein, lactose, milk urea nitrogen yield and content as well as somatic cell score. Two approaches were used: (i) Wilmink curve parameters were used to assess the genetic effects over the course of a lactation and (ii) test-day yield deviations (YD) were used as a normative approach for a GWAS. The significant effects were largest for markers affecting curve parameters for which there was a statistical power <0.8 of detection even in this small design. While significant markers for YDs were detected in this study, the power to detect effects of a similar magnitude was only 0.11, suggesting that many loci may have been missed with this approach in the present design. Furthermore, all significant effects were specific for a single lactation, leading to the conclusion that the variance explained by a certain locus changes from lactation to lactation. We confirm the common evidence that most production traits vary in the degree of persistency after the peak as a result of genetic influence.     

Milk yield persistency in Brazilian Gyr cattle based on a random regression model

With the objective of evaluating measures of milk yield persistency, 27,000 test-day milk yield records from 3362 first lactations of Brazilian Gyr cows that calved between 1990 and 2007 were analyzed with a random regression model. Random, additive genetic and permanent environmental effects were modeled using Legendre polynomials of order 4 and 5, respectively. Residual variance was modeled using five classes. The average lactation curve was modeled using a fourth-order Legendre polynomial. Heritability estimates for measures of persistency ranged from 0.10 to 0.25. Genetic correlations between measures of persistency and 305-day milk yield (Y305) ranged from -0.52 to 0.03. At high selection intensities for persistency measures and Y305, few animals were selected in common. As the selection intensity for the two traits decreased, a higher percentage of animals were selected in common. The average predicted breeding values for Y305 according to year of birth of the cows had a substantial annual genetic gain. In contrast, no improvement in the average persistency breeding value was observed. We conclude that selection for total milk yield during lactation does not identify bulls or cows that are genetically superior in terms of milk yield persistency. A measure of persistency represented by the sum of deviations of estimated breeding value for days 31 to 280 in relation to estimated breeding value for day 30 should be preferred in genetic evaluations of this trait in the Gyr breed, since this measure showed a medium heritability and a genetic correlation with 305-day milk yield close to zero. In addition, this measure is more adequate at the time of peak lactation, which occurs between days 25 and 30 after calving in this breed.     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Abstract

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

Modelling QTL effect on BTA06 using random regression test day models

In statistical models, a quantitative trait locus (QTL) effect has been incorporated either as a fixed or as a random term, but, up to now, it has been mainly considered as a time-independent variable. However, for traits recorded repeatedly, it is very interesting to investigate the variation of QTL over time. The major goal of this study was to estimate the position and effect of QTL for milk, fat, protein yields and for somatic cell score based on test day records, while testing whether the effects are constant or variable throughout lactation. The analysed data consisted of 23 paternal half-sib families (716 daughters of 23 sires) of Chinese Holstein-Friesian cattle genotyped at 14 microsatellites located in the area of the casein loci on BTA6. A sequence of three models was used: (i) a lactation model, (ii) a random regression model with a QTL constant in time and (iii) a random regression model with a QTL variable in time. The results showed that, for each production trait, at least one significant QTL exists. For milk and protein yields, the QTL effect was variable in time, while for fat yield, each of the three models resulted in a significant QTL effect. When a QTL is incorporated into a model as a constant over time, its effect is averaged over lactation stages and may, thereby, be difficult or even impossible to be detected. Our results showed that, in such a situation, only a longitudinal model is able to identify loci significantly influencing trait variation.     

Isolating the cow-specific part of residual energy intake in lactating dairy cows using random regressions

The ability to properly assess and accurately phenotype true differences in feed efficiency among dairy cows is key to the development of breeding programs for improving feed efficiency. The variability among individuals in feed efficiency is commonly characterised by the residual intake approach. Residual feed intake is represented by the residuals of a linear regression of intake on the corresponding quantities of the biological functions that consume (or release) energy. However, the residuals include both, model fitting and measurement errors as well as any variability in cow efficiency. The objective of this study was to isolate the individual animal variability in feed efficiency from the residual component. Two separate models were fitted, in one the standard residual energy intake (REI) was calculated as the residual of a multiple linear regression of lactation average net energy intake (NEI) on lactation average milk energy output, average metabolic BW, as well as lactation loss and gain of body condition score. In the other, a linear mixed model was used to simultaneously fit fixed linear regressions and random cow levels on the biological traits and intercept using fortnight repeated measures for the variables. This method split the predicted NEI in two parts: one quantifying the population mean intercept and coefficients, and one quantifying cow-specific deviations in the intercept and coefficients. The cow-specific part of predicted NEI was assumed to isolate true differences in feed efficiency among cows. NEI and associated energy expenditure phenotypes were available for the first 17 fortnights of lactation from 119 Holstein cows; all fed a constant energy-rich diet. Mixed models fitting cow-specific intercept and coefficients to different combinations of the aforementioned energy expenditure traits, calculated on a fortnightly basis, were compared. The variance of REI estimated with the lactation average model represented only 8% of the variance of measured NEI. Among all compared mixed models, the variance of the cow-specific part of predicted NEI represented between 53% and 59% of the variance of REI estimated from the lactation average model or between 4% and 5% of the variance of measured NEI. The remaining 41% to 47% of the variance of REI estimated with the lactation average model may therefore reflect model fitting errors or measurement errors. In conclusion, the use of a mixed model framework with cow-specific random regressions seems to be a promising method to isolate the cow-specific component of REI in dairy cows.