Random Regression Test-day Model Research Articles

Genotype × Environment Interaction for Milk Yield in Holsteins Using Luxembourg and Tunisian Populations

Test-day (TD) milk yield records of first-lactation Holstein cows in Luxembourg and Tunisia were analyzed using within-and between-country random regression TD models. Edited data used for within-country analysis included 661,453 and 281,913 TD records in Luxembourg and Tunisia, respectively. The joint data included 730,810 TD records of 87,734 cows and 231 common sires. Both data sets covered calving years 1995 to 2006. Fourth-order Legendre polynomials for random effects and a Gibbs sampling method were used to estimate variance components of lactation curve parameters in separate and joint analyses. Genetic variances of the first 3 coefficients from Luxembourg data were 46 to 69% larger than corresponding estimates from the Tunisian data. Inversely, the Tunisian permanent environment variances for the same coefficients were 52 to 65% larger than the Luxembourg ones. Posterior mean heritabilities of 305-d milk yield and persistency, defined as estimated breeding values (EBV) at 280 days in milk-EBV at 80 days in milk, from between-country analysis were 0.42 and 0.12 and 0.19 and 0.08 in Luxembourg and Tunisia, respectively. Heritability estimates for the same traits from within-country analyses, mainly from the Tunisian data, were lower than those from the joint analysis. Genetic correlations for 305-d milk yield and persistency between countries were 0.60 and 0.36. Product moment and rank correlations between EBV of common sires for 305-d milk yield and persistency from within-country analyses were 0.38 and 0.41 and 0.27 and 0.26, respectively. Differences between genetic variances found in both countries reflect different milk production levels. Moreover, low genetic and rank correlations suggest different ranking of sires in the 2 environments, which implies the existence of a genotype × environment interaction for milk yield in Holsteins.

A General Method to Validate Breeding Value Prediction Software

The validity of national genetic evaluations depends on the quality of input data, on the model of analysis, and on the correctness of genetic evaluation software. A general strategy was developed to validate national breeding value prediction software: performances from a real data file were replaced with simulated ones, created from simulated fixed and random effects and residuals in such a way that BLUP estimates from the evaluation software must be equal to the simulated effects. This approach was implemented for a multiple-trait model and a random regression test-day model. An example was presented on test-day observations analyzed with a random regression animal model including a lactation curve described as a sum of fixed polynomial regression and fixed spline regression on days in milk, and with genetic and permanent environmental effects modeled by using Legendre polynomials of order 2. Residuals had heterogeneous variances, and phantom parent groups were included. This method can be easily extended to other linear models. The comparison of genetic evaluation results with simulated true effects is used to demonstrate the great efficiency and usefulness of the proposed method.

Variance Components for Test-Day Milk, Fat, and Protein Yield, and Somatic Cell Score for Analyzing Management Information

Test-day (TD) models are used in most countries to perform national genetic evaluations for dairy cattle. The TD models estimate lactation curves and their changes as well as variation in populations. Although potentially useful, little attention has been given to the application of TD models for management purposes. The potential of the TD model for management use depends on its ability to describe within- or between-herd variation that can be linked to specific management practices. The aim of this study was to estimate variance components for milk yield, milk component yields, and somatic cell score (SCS) of dairy cows in the Ragusa and Vicenza areas of Italy, such that the most relevant sources of variation can be identified for the development of management parameters. The available data set contained 1,080,637 TD records of 42,817 cows in 471 herds. Variance components were estimated with a multilactation, random-regression, TD animal model by using the software adopted by NRS for the Dutch national genetic evaluation. The model comprised 5 fixed effects [region×parity×days in milk (DIM), parity×year of calving×season of calving×DIM, parity×age at calving×year of calving, parity×calving interval×stage of pregnancy, and year of test×calendar week of test] and random herd×test date, regressions for herd lactation curve (HCUR), the animal additive genetic effect, and the permanent environmental effect by using fourth-order Legendre polynomials. The HCUR variances for milk and protein yields were highest around the time of peak yield (DIM 50 to 150), whereas for fat yield the HCUR variance was relatively constant throughout first lactation and decreased following the peak around 40 to 90 DIM for lactations 2 and 3. For SCS, the HCUR variances were relatively small compared with the genetic, permanent environmental, and residual variances. For all the traits except SCS, the variance explained by random herd×test date was much smaller than the HCUR variance, which indicates that the development of management parameters should focus on between-herd parameters during peak lactation for milk and milk components. For SCS, the within-herd variance was greater than the between-herd variance, suggesting that the focus should be on management parameters explaining variances at the cow level. The present study showed clear evidence for the benefits of using a random regression TD model for management decisions.

Genetic Improvement of Total Milk Yield and Total Lactation Persistency of the First Three Lactations in Dairy Cattle

The objective of this study was to compare 6 selection criteria in terms of 3-parity total milk yield and 9 selection criteria in terms of total net merit (H) comprising 3-parity total milk yield and total lactation persistency. The 6 selection criteria compared were as follows: first-parity milk estimated breeding value (EBV; M1), first 2-parity milk EBV (M2), first 3-parity milk EBV (M3), first-parity eigen index (EI1), first 2-parity eigen index (EI2), and first 3-parity eigen index (EI3). The 9 selection criteria compared in terms of H were M1, M2, M3, EI1, EI2, EI3, and first-parity, first 2-parity, and first 3-parity selection indices (I1, I2, and I3, respectively). In terms of total milk yield, selection on M3 or EI3 achieved the greatest genetic response, whereas selection on EI1 produced the largest genetic progress per day. In terms of total net merit, selection on I3 brought the largest response, whereas selection EI1 yielded the greatest genetic progress per day. A multiple-lactation random regression test-day model simultaneously yields the EBV of the 3 lactations for all animals included in the analysis even though the younger animals do not have the opportunity to complete the first 3 lactations. It is important to use the first 3 lactation EBV for selection decision rather than only the first lactation EBV in spite of the fact that the first-parity selection criteria achieved a faster genetic progress per day than the 3-parity selection criteria. Under a multiple-lactation random regression animal model analysis, the use of the first 3 lactation EBV for selection decision does not prolong the generation interval as compared with the use of only the first lactation EBV. Thus, it is justified to compare genetic response on a lifetime basis rather than on a per-day basis. The results suggest the use of M3 or EI3 for genetic improvement of total milk yield and the use of I3 for genetic improvement of total net merit H. Although this study deals with selection for 3-parity milk production, the same principle applies to selection for lifetime milk production.

Multiplicative random regression model for heterogeneous variance adjustment in genetic evaluation for milk yield in Simmental

A multiplicative random regression (M-RRM) test-day (TD) model was used to analyse daily milk yields from all available parities of German and Austrian Simmental dairy cattle. The method to account for heterogeneous variance (HV) was based on the multiplicative mixed model approach of Meuwissen. The variance model for the heterogeneity parameters included a fixed region x year x month x parity effect and a random herd x test-month effect with a within-herd first-order autocorrelation between test-months. Acceleration of variance model solutions after each multiplicative model cycle enabled fast convergence of adjustment factors and reduced total computing time significantly. Maximum Likelihood estimation of within-strata residual variances was enhanced by inclusion of approximated information on loss in degrees of freedom due to estimation of location parameters. This improved heterogeneity estimates for very small herds. The multiplicative model was compared with a model that assumed homogeneous variance. Re-estimated genetic variances, based on Mendelian sampling deviations, were homogeneous for the M-RRM TD model but heterogeneous for the homogeneous random regression TD model. Accounting for HV had large effect on cow ranking but moderate effect on bull ranking.

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.

Genetic characteristics of Japanese Holstein cows based on multiple-lactation random regression test-day animal models

The first three lactation curves of the Japanese Holstein cows were analyzed using a random regression (RR) test-day model with a cubic Legendre polynomial fitted to each of the three parities. The first three eigenvectors of the additive genetic RR covariance matrix explained 77.8, 10.9, and 4.2% of the total variance of the three parities and are associated mainly with the level of milk yield, the linear increase, and the concave curve, respectively. On a lactational basis, as the parity increases, the contribution of the first eigenvector to a lactational variation decreases whereas the contribution of the second eigenvector increases sharply. This means that the impact of the first eigenvector on the level of milk production decreases across parity whereas the effect of the second eigenvector on the shape of the lactation curve increases across parity. The first lactation curve was the most persistent, followed by the second and the third lactation. Persistency and days to reach peak yield decrease as the parity increases (45, 40, and 36 days for the first three parities). Daily heritabilities within lactation were lower for the first parity than for the second or the third parity. The first three lactation curves possess distinctive genetic characteristics that merit consideration when combining the proofs of the first three lactations to select for lifetime production. Within- and between-parity genetic correlations between the constant and the linear RR coefficients were all positive, suggesting that raising the level of milk production in one parity would increase the linear slope in all parities, thus improving persistency. Within- and between-parity genetic correlations between the constant and the quadratic RR coefficients were all negative, implying that increasing the level of production in one parity would deepen and/or widen the concave curve in all parities, thus decreasing persistency. The linear and quadratic RR coefficients were negatively correlated within or between parities and thus have antagonistic effects on persistency.

Environmental Sensitivity of Milk Production in Extensive Environments: A Comparison of Simmental, Brown Swiss, and Tyrol Grey Using Random Regression Models

A total of 25,160 milk test-day records from 2,516 cows in first lactation of 3 dairy cattle breeds [Simmental (n=1,900), Brown Swiss (n=444), and Tyrol Grey (n=172)] in Kosovo were analyzed using nested repeatability and random regression test-day models with varying (co)variance structures. The different models were compared based on likelihood-based criteria. The best model was a second-order random regression model, with heterogeneous cow variance per breed and heterogeneous residual variance per lactation month and breed, which was used for further analysis. The highest milk production was found in Brown Swiss, followed by Simmental and Tyrol Grey. Substantial breed differences were found for the trajectories of cow and residual variances by month of lactation, with the highest variances found for Brown Swiss, followed by Simmental and Tyrol Grey. High cow and residual variances indicated a high degree of environmental sensitivity on the macro- and microenvironmental levels, respectively. Thus, these results indicate increased environmental sensitivity for breeds with higher genetic potential for milk production. These results support the conclusion that dairy cattle production under the current environmental conditions of Kosovo should be based on a breed with moderate production that is robust to the diet offered (e.g., Tyrol Grey).

Use of Herd Solutions from a Random Regression Test-Day Model for Diagnostic Dairy Herd Management

In a random regression test-day model, environmental effects in addition to individual animal factors can be included and analyzed. Moreover, instead of herd-year classification of the management groups, the herd-test-day classification within the model better accounts for month-to-month short-term environmental variation in production and somatic cell count (SCC) traits. The herd management levels of milk yield (milk deviation from whole-country mean, kilograms/day), protein and fat concentration (protein and fat deviation, %), and SCC (SCC deviation, 1,000 cells/mL) are used in the dairy herd management Web application “Maitoisa” (in English, “Milky”). This management tool helps to recognize several management problems. For recognition of systematic patterns and single unusual test-days, a monthly time-trend analysis was developed to smooth the random fluctuations and display the yearly production pattern. In addition to analyzing single test-day deviations from the mean, modeled herd solutions assist users in identifying repeated phenomena and enable the forecasting of the management pattern for the subsequent year. The solutions are displayed either as tables or graphs plotted by calendar months. In addition to management effects of the farmer's own herd, he or she can request country or region percentiles to be displayed in the graphs. The Web service has been offered to farmers and dairy advisors since 2001, and it has proved to be a powerful tool for herd monitoring and planning.

Application of robust procedures for estimation of breeding values in multiple‐trait random regression test‐day model

Robust procedures for estimation of breeding values were applied to multiple-trait random regression test-day (TD) model to reduce the influence of outliers on inferences. Robust estimation methods consisted of correcting selected observations (defined as outliers) in the process of solving mixed-model equations in such a way that 'new' observations gave residuals (actual observation minus predicted) within k residual standard deviations for a given day in milk in 305-day lactation. Data were 980,503 TD records on 63,346 Canadian Jersey cows. Milk, fat, protein and somatic cell score in the first three lactations were analysed jointly in the model that included fixed herd-TD effect and regressions within region-age-season of calving, and regressions with random coefficients for animal genetic and permanent environmental effects. All regressions were orthogonal polynomials of order 4. Robust procedures for k = 1.5, 2.0, 2.5, 2.75 and 3.0 were contrasted with the regular best linear unbiased prediction (BLUP) method in terms of numbers and distributions of outliers, and estimated breeding values (EBV) of animals. Distributions of outliers were similar across traits and lactations. Early days in milk (from 5 to 15) were associated with larger frequency of outliers compared with the remaining part of lactation. Several, computationally simple, robust methods (for k > 2.0) reduced the influence of outlier observations in the model and improved the overall model performance. Differences in rankings of animals from robust evaluations were small compared with the regular BLUP method. No clear associations between changes in EBV (rankings) of top animals from different methods and the occurrence of outliers were detected.

Fit of different functions to the individual deviations in random regression test day models for milk yield in dairy cattle

The shape of individual deviations of milk yield for dairy cattle from the fixed part of a random regression test day model (RRTDM) was investigated. Data were 53,217 TD records for milk yield of 6,229 first lactation Canadian Holsteins in Ontario. Data were fitted with a model that included the fixed effects of herd-testdate, DIM interval nested within age and season of calving. Residuals of the model were then fitted with the following functions: Ali and Schaeffer 5 parameter model, fourth-order Legendre Polynomials, and cubic spline with three, four or five knots. Result confirm the great variability of shape that can be found when individual lactation are modeled. Cubic splines gave better fitting pe4rformances although together with a marked tendency to yield aberrant estimates at the edge of the lactation trajectory.

The accuracy of test day model evaluation for the Italian Holstein

Genetic evaluation for production traits in the Holstein breed in Italy has been based on a Random Regression Test Day Model (RRTDM) since November 2004. More specifically, the model is a multiple lactation, multiple trait RRTDM, similar to the model used in Canada for official genetic evaluation.Fixed regression curve effect include time, region, age at calving, parity and season of calving. Last changes in the model included a new definition of the proof scale and of the genetic base.The accuracy of the model was assessed by analyzing residuals and testing Mendelian sampling trends. Residuals were normally distributed for all traits and had zero mean.Residual trends for all the effects included in the model were analyzed also for effects not included in the model like number of milkings per day and number of days pregnant at the test date. Mendelian sampling did not show any significant trend over time both for cows and bulls.

Linear and Curvilinear Effects of Inbreeding on Production Traits for Walloon Holstein Cows

The nonlinear effects of inbreeding were studied by comparing linear and curvilinear regression models of phenotypic performances on inbreeding coefficients for production traits (milk, fat, and protein yields) of Holstein cows in their first lactation. Three different regression models (linear, quadratic, and cubic) were introduced separately into a single-trait, single-lactation, random regression test-day model. The significance of the different regression coefficients was studied based on a t-test after estimation of error variances and covariances associated with the different regression coefficients. All of the tested regression coefficients were significantly different from 0. The traditional regression coefficients of milk, fat, and protein yields on inbreeding were, respectively, −22.10, −1.10, and −0.72kg for Holstein cows in their first lactation. However, the estimates of 305-d production losses for various classes of animals based on inbreeding coefficients showed that the effect of inbreeding was not a linear function of the percentage of inbreeding. The 305-d milk yield loss profiles attributable to inbreeding, obtained by the various regression models, were different. However, for inbreeding coefficients between 0 and 10%, these differences were small.

Genetic Analysis of Milk Production Traits of Polish Black and White Cattle Using Large-Scale Random Regression Test-Day Models

Genetic parameters for milk, fat, and protein yield and persistency in the first 3 lactations of Polish Black and White cattle were estimated. A multiple-lactation model was applied with random herd-test-day effect, fixed regressions for herd-year and age-season of calving, and random regressions for the additive genetic and permanent environmental effects. Three data sets with slightly different edits on minimal number of days in milk and the size of herd-year class were used. Each subset included more than 0.5million test-day records and more than 58,000 cows. Estimates of covariance components and genetic parameters for each trait were obtained by Bayesian methods using the Gibbs sampler. Due to the large size and a good structure of the data, no differences in estimates were found when additional criteria for record selection were applied. More than 95% of the genetic variance for all traits and lactations was explained by the first 2 principal components, which were associated with the mean yield and lactation persistency. Heritabilities of 305-d milk yield in the first 3 lactations (0.18, 0.16, 0.17) were lower than those for fat (0.12, 0.11, 0.12) and protein (0.13, 0.14, 0.15). Estimates of daily heritabilities increased in general with days in milk for all traits and lactations, with no apparent abnormalities at the beginning or end of lactation. Genetic correlations between yields in different lactations ranged from 0.74 (fat yield in lactations 1 and 3) to 0.89 (milk yield in lactations 2 and 3). Persistency of lactation was defined as the linear regression coefficient of the lactation curve. Heritability of persistency increased with lactation number for all traits and genetic correlations between persistency in different lactations were smaller than those for 305d yield. Persistency was not genetically correlated with the total yield in lactation.

Comparison of Random Regression Test-Day Models for Polish Black and White Cattle

Test-day milk yields of first-lactation Black and White cows were used to select the model for routine genetic evaluation of dairy cattle in Poland. The population of Polish Black and White cows is characterized by small herd size, low level of production, and relatively early peak of lactation. Several random regression models for first-lactation milk yield were initially compared using the “percentage of squared bias” criterion and the correlations between true and predicted breeding values. Models with random herd-test-date effects, fixed age-season and herd-year curves, and random additive genetic and permanent environmental curves (Legendre polynomials of different orders were used for all regressions) were chosen for further studies. Additional comparisons included analyses of the residuals and shapes of variance curves in days in milk. The low production level and early peak of lactation of the breed required the use of Legendre polynomials of order 5 to describe age-season lactation curves. For the other curves, Legendre polynomials of order 3 satisfactorily described daily milk yield variation. Fitting third-order polynomials for the permanent environmental effect made it possible to adequately account for heterogeneous residual variance at different stages of lactation.

Joint International Evaluation of Milking Shorthorn Dairy Cattle for Production Traits

Pedigree information and test-day records for the first 3 parities of Milking Shorthorn dairy cattle from 5 countries were analyzed. After editing, the data included 1,018,528 test-day records from 68,653 cows. A multiple-lactation random regression test-day model with Legendre polynomials of order 4 and a Bayesian method were used to estimate variance components for both single and multiple-countries. Fixed effects included herd-test-day class and regressions on DIM within age at calving-parity-season of calving. Random effects included animal genetic, permanent environmental, and residual effects. Average daily heritabilities from single country analyses ranged from 0.33 to 0.47 for milk yield and from 0.37 to 0.45 for protein yield across lactations and countries. Common sires (66) and their daughters were identified for creating a connected data set for simultaneous (co)variance component estimation of milk yield across all 5 countries. Between-country genetic correlations were low, with values from 0.08 to 0.46 and standard deviations from 0.08 to 0.12. Estimated breeding values for milk were generated for each animal using the same test-day animal model. Correlations among country estimated breeding values were higher than genetic correlations. Top 100 bull lists were generated on the scale of each country, and genetic progress was assessed. Future evaluation with increased genetic ties among countries may facilitate international comparison of Milking Shorthorns.

불완전 검정일 기록이 RRTDM을 이용한 홀스타인 젖소의 유전평가에 미치는 영향

The purpose of this study was to find out the effects that daughters' incomplete lactation records affect sire's breeding values through genetic evaluation using RRTDM(random regression test-day model). First, we estimated genetic parameters and breeding values on sires having complete lactation records of daughter by RRTDM, second, we changed complete lactation records of specific sires into incomplete records by various methods. Third, the breeding values were compared between complete and incomplete records. Finally, this study aimed to find out the methods to minimize the estimation errors of young bulls' breeding values. Data used in this study were collected from the dairy herd improvement program, and a total of 97,562 records were composed of 10,929 first parity with both parents known, since 1999. Breeding values on the daughters from randomly chosen sires were calculated and compared with among 90 day, 150day, and 200 day's incomplete records. For milk yields, sire's ranks of breeding values used by complete lactation records were very different from sire's ranks of breeding values obtained by incomplete lactation records(Rank_90 cut, 150cut, 200 cut).The differences were also obtained between complete lactation records(per305_full) and incomplete lactation record (per_90 cut, 150cut, 200 cut) in breeding values regarding persistency. Especially, the differences between per_90 cut and per305_full were very large(from 1.8 kg to 145kg).

Definition of subgroups for fixed regression in the test-day animal model for milk production ofHolsteincattle in theCzech Republic

The investigation was based on roughly 3.9, 2.7 and 1.7 million test-day records from first, second and third lactation, respectively, sampled from 596 200 Czech Holstein cows between the years 1991 and 2002. Breeding values were estimated from multi-lactation random-regression test-day models which contained the fixed effect of herd-test day, fixed regression on days in milk and random regressions on the animal level and the permanent environmental effect. Third degree Legendre polynomials (with four coefficients) were used for both the fixed and random regressions. The models differed in fixed regression. In Analysis I, 96 subclasses were defined according to age at calving, season and year of calving within lactation. In Analysis II, days open were additionally included as a grouping factor resulting in 480 subclasses. Rank correlations over 0.98 between both analyses were observed for breeding values for sires. Grouping according to Analysis I was recommended.  

Milk Loss and Treatment Costs Associated with Two Treatment Protocols for Clinical Mastitis in Dairy Cows ,

The objective of this study was to compare milk loss and treatment costs for cows with clinical mastitis that were given antibiotics in addition to supportive treatment or supportive treatment alone. Between January 1994 and January 1996, 116,876 daily milk records on 676 lactations were taken at the University of Illinois Dairy Research Farm. Clinical mastitis was diagnosed during 124 lactations with 25,047 daily milk records, and 1417 of the daily milk records were on days when clinical mastitis was present. Cows with clinical mastitis were randomly assigned to one of 2 treatment groups: N (supportive treatment only) or A (antibiotics in addition to supportive treatment). Extent of antibiotic and supportive treatment varied according to twice daily severity scores. Projected and actual daily milk yields were estimated utilizing a random regression test-day model, and the differences were summed over 305 d of lactation to estimate lactational milk yield loss. The actual amount of discarded milk was added to milk yield loss to determine total milk loss per lactation. A cost analysis that included milk loss and treatment costs was then performed. Cows with clinical mastitis that were given only supportive treatment lost 230±172kg (mean±standard error of mean [SEM]) more milk and incurred $94±51 (SEM) more cost per lactation than cows given antibiotics and supportive treatment. Cows given only supportive treatment showed a response pattern of 305-d milk yield loss and economic loss per lactation that varied 2 to 3 times as much as cows treated with antibiotics. Based on reduced milk loss, better reliability (less variable response), and lower economic loss, the addition of antibiotics to supportive treatment was more efficacious and cost effective than supportive treatment alone.

Derivation and Calculation of Approximate Reliabilities and Daughter Yield-Deviations of a Random Regression Test-Day Model for Genetic Evaluation of Dairy Cattle

Test-day milk, fat, protein yield, and somatic cell score (SCS) were analyzed separately using data from the first 3 lactations and a random regression model. Data used in the model were from Austria, Germany, and Luxembourg and from Holstein, Red, and Jersey dairy cattle. For reliability approximation, a multiple-trait effective daughter contribution (MTEDC) method was developed under general multiple trait models, including random regression test-day models, by extending the single-trait daughter equivalents concept. The MTEDC was applied to the very large dairy population, with about 15.5million animals. The calculation of reliabilities required less computer memory than the corresponding iteration program and a significantly lower computing time equivalent to 24 rounds of iteration. A formula for daughter-yield deviations was derived for bulls under multiple-trait models. Reliability associated with daughter-yield deviations was approximated using the MTEDC method. Both the daughter-yield deviation formula and associated reliability method were verified in a simulation study using the random regression test-day model. Correlations of lactation daughter-yield deviations with estimated breeding values calculated from a routine genetic evaluation were 0.996 for all bulls and 0.95 for young bulls having only daughters with short lactations.