Random Regression Test Day Research Articles

Environmental sensitivity for milk yield in Luxembourg and Tunisian Holsteins by herd management level

Milk production data of Luxembourg and Tunisian Holstein cows were analyzed using herd management (HM) level. Herds in each country were clustered into high, medium, and low HM levels based on solutions of herd-test-date and herd-year of calving effects from national evaluations. Data from both populations included 730,810 test-day (TD) milk yield records from 87,734 first-lactation cows. A multi-trait, random regression TD model was used to estimate (co)variance components for milk yield within and across country HM levels. Additive genetic and permanent environmental variances of TD milk yields varied with management level in Tunisia and Luxembourg. Additive variances were smaller across HM levels in Tunisia than in Luxembourg, whereas permanent environmental variances were larger in Tunisian HM levels. Highest heritability estimates of 305-d milk yield (0.41 and 0.21) were found in high HM levels, whereas lowest estimates (0.31 and 0.12, respectively) were associated with low HM levels in both countries. Genetic correlations among Luxembourg HM levels were >0.96, whereas those among Tunisian HM levels were below 0.80. Respective rank orders of sires ranged from 0.73 to 0.83 across Luxembourg environments and from 0.33 to 0.42 across Tunisian HM levels indicating high re-ranking of sires in Tunisia and only a scaling effect in Luxembourg. Across-country environment analysis showed that estimates of genetic variance in the high, medium, and low classes of Tunisian environments were 45, 69, and 81% lower, respectively, than the estimate found in the high Luxembourg HM level. Genetic correlations among 305-d milk yields in Tunisian and Luxembourg HM environments ranged from 0.39 to 0.79. The largest estimated genetic correlation was found between the medium Luxembourg and high Tunisian HM levels. Rank correlations for common sires’ estimated breeding values among HM environments were low and ranged from 0.19 to 0.39, implying the existence of genotype by environment interaction. These results indicate that daughters of superior sires in Luxembourg have their genetic expression for milk production limited under Tunisian environments. Milk production of cows in the medium and low Luxembourg environments were good predictors of that of their paternal half-sisters in the high Tunisian HM level. Breeding decisions in low-input Tunisian environment should utilize semen from sires with daughters in similar production environments rather than semen of bulls proven in higher management levels.

Genetic evaluation of Australian dairy cattle for somatic cell scores using multi‐trait random regression test‐day model

A multi-trait (MT) random regression (RR) test day (TD) model has been developed for genetic evaluation of somatic cell scores for Australian dairy cattle, where first, second and third lactations were considered as three different but correlated traits. The model includes herd-test-day, year-season, age at calving, heterosis and lactation curves modelled with Legendre polynomials as fixed effects, and random genetic and permanent environmental effects modelled with Legendre polynomials. Residual variance varied across the lactation trajectory. The genetic parameters were estimated using asreml. The heritability estimates ranged from 0.05 to 0.16. The genetic correlations between lactations and between test days within lactations were consistent with most of the published results. Preconditioned conjugate gradient algorithm with iteration on data was implemented for solving the system of equations. For reliability approximation, the method of Tier and Meyer was used. The genetic evaluation system was validated with Interbull validation method III by comparing proofs from a complete evaluation with those from an evaluation based on a data set excluding the most recent 4 years. The genetic trend estimate was in the allowed range and correlations between the two sets of proofs were very high. Additionally, the RR model was compared to the previous test day model. The correlations of proofs between both models were high (0.97) for bulls with high reliabilities. The correlations of bulls decreased with increasing incompleteness of daughter performance information. The correlations between the breeding values from two consecutive runs were high ranging from 0.97 to 0.99. The MT RR TD model was able to make effective use of available information on young bulls and cows, and could offer an opportunity to breeders to utilize estimated breeding values for first and later lactations.

Improving the stability of test day model evaluation for production traits in the Italian Holstein

Genetic evaluation for production traits in the Holstein breed in Italy is based on a Random Regression Test Day Model (RRTDM) since November 2004. More specifically the model is a multiple lactation, multiple traits RRTDM, similar to the model used in Canada for official genetic evaluation. In order to improve stability, data were pre-adjusted for number of days pregnancy at test day and fixed regression curve effects include now the effect of year of production, four calving seasons instead of two and a general effect for days in milk (DIM) was added. The changes in the model improved stability of proofs over time, thus increasing the ability of the test day to accurately predict the breeding value of both bulls and cows. Trend validation results showed also improvements and residuals were positively affected by the changes. Trends in trait residuals previously detected with respect to DIM and month of calving did show a significant reduction. The new model was officially introduced in January 2009.

Test day-milk yields variance component estimation using repeatability or random regression models in the Rendena breed

This study has aimed to compare Repeatability (RP-TDm) and Random-Regression Test Day models (RR-TDm) in genetic evaluations of milk (M), fat (F) and protein (P) yields in Rendena breed. Variance estimations for Milk (M), Fat (F) and Protein (P) were obtained on a sample of 43,842 TD belonging to 2,692 animals controlled over 15 years (1990-2005). RP-TDm estimates of h2 were of 0.21 for M and 0.17 for both F and P, whereas RR-TDM provided a trend of h2 ranging from 0.15-0.34 for M, 0.15-0.31 for F and 0.10-0.24 for P. Both RP-TDm and RR-TDm results agreed with literature, even though RR-TDm provided a pattern of h2 along the lactation different from other studies, with the lowest h2 at the beginning and at the end of lactation. PSB, MAD and -2Log L parameters revealed lower power of RP-TDm as compare with the RR-TDm.

Inferring Genetic Parameters of Lactation in Tropical Milking Criollo Cattle with Random Regression Test-Day Models

This study inferred genetic and permanent environmental variation of milk yield in Tropical Milking Criollo cattle and compared 5 random regression test-day models using Wilmink's function and Legendre polynomials. Data consisted of 15,377 test-day records from 467 Tropical Milking Criollo cows that calved between 1974 and 2006 in the tropical lowlands of the Gulf Coast of Mexico and in southern Nicaragua. Estimated heritabilities of test-day milk yields ranged from 0.18 to 0.45, and repeatabilities ranged from 0.35 to 0.68 for the period spanning from 6 to 400 d in milk. Genetic correlation between days in milk 10 and 400 was around 0.50 but greater than 0.90 for most pairs of test days. The model that used first-order Legendre polynomials for additive genetic effects and second-order Legendre polynomials for permanent environmental effects gave the smallest residual variance and was also favored by the Akaike information criterion and likelihood ratio tests.

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.

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.

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.

Data transformation for rank reduction in multi-trait MACE model for international bull comparison

Since many countries use multiple lactation random regression test day models in national evaluations for milk production traits, a random regression multiple across-country evaluation (MACE) model permitting a variable number of correlated traits per country should be used in international dairy evaluations. In order to reduce the number of within country traits for international comparison, three different MACE models were implemented based on German daughter yield deviation data and compared to the random regression MACE. The multiple lactation MACE model analysed daughter yield deviations on a lactation basis reducing the rank from nine random regression coefficients to three lactations. The lactation breeding values were very accurate for old bulls, but not for the youngest bulls with daughters with short lactations. The other two models applied principal component analysis as the dimension reduction technique: one based on eigenvalues of a genetic correlation matrix and the other on eigenvalues of a combined lactation matrix. The first one showed that German data can be transformed from nine traits to five eigenfunctions without losing much accuracy in any of the estimated random regression coefficients. The second one allowed performing rank reductions to three eigenfunctions without having the problem of young bulls with daughters with short lactations.

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.

Heterogeneity of variance components for production traits in large‐scale dairy farms

The aim of this study was to estimate genetic parameters applying fixed regression and random regression test day models for protein yield using subsets stratified by herd size, average production level of herds in test day protein yield, and average age at first calving within herds. The data consisted of 64,394 Holstein cows located in one region in Eastern Germany including 690,553 first lactation test day production records. Estimates of variance components revealed heterogeneity of genetic variances across subsets and the highest additive genetic variances and heritabilities were found in larger herds with high production level and low age at first calving. Special cooperator herds for dairy cattle progeny testing programs will be a common practice in the near future. Suitable selection criteria for cooperator herds should consider genetic parameters, e.g. genetic variances and heritabilities within herds or subsets, to identify genetically superior sires as accurately as possible. As shown in the present study, the two‐step cluster analysis is an appropriate method to combine all desirable effects of herd parameters for a final selection of cooperator herds. One cluster included 44 large‐scale dairy farms with an average of 638 cows per farm and was also characterised by the highest protein yield, the lowest age at first calving, the highest heritability, and the highest additive genetic variance for test day protein yield within herds. A cluster analysis can be implemented in the work routine of dairy cattle breeding programs and delivers results in acceptable time. Rank correlations of estimated breeding values of bulls in different subsets as well as in different clusters were greater than 0.90, and therefore disprove any concerns for possible genotype by environment interaction between the test and the production environment. The permanent environment variance was slightly increased in strata indicating a better environment, whereas the residual variance component was similar for all subsets. There were no remarkable differences in genetic correlations between individual test days and test days 25 and 150, when analysing different subsets.

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.

Utilização dos polinômios de Legendre e da função de Wilmink em avaliações genéticas para persistência na lactação de animais da raça Holandesa

Os registros de produção de leite de 11.023 primeiras lactações de vacas da raça Holandesa pertencentes a 251 rebanhos distribuídos no estado de Minas Gerais foram usados para comparar os polinômios de Legendre e a função Wilmink em modelos de regressão aleatória (MRA) quanto aos seus efeitos na estimação de parâmetros genéticos e predição de valores genéticos para nove medidas de persistência na lactação e produção de leite até 305 dias. Os modelos de regressão aleatória ajustados aos controles leiteiros entre o sexto e o 305(0) dia de lactação incluíram o efeito de rebanho-ano-mês do controle, os parâmetros dos polinômios de Legendre de ordens 3 a 5 ou da função de Wilmink, para modelar as curvas fixas da regressão dentro das subclasses de idade-estação de parto da vaca e os parâmetros dos polinômios de Legendre de ordens 3 a 5, para modelar os efeitos aleatórios genético-aditivo e permanente de ambiente. Os testes do critério de informação de Akaike e Bayesiano indicaram o modelo com maior número de parâmetros como o que melhor se ajustou aos dados de produção de leite. Observaram-se grandes variações nas estimativas de herdabilidade para a maioria das medidas de persistência na lactação, com uso dos modelos que envolveram ajustes dos polinômios de Legendre. As estimativas de herdabilidade variaram de 0,11 a 0,33 para produção de leite ao longo da lactação, de 0,33 a 0,36 para a produção de leite até 305 dias e de 0,00 a 0,32 para persistência na lactação. As correlações genéticas entre persistência e produção de leite até 305 dias diferiram com o modelo e a medida de persistência. A utilização da função de Wilmink, comparada aos polinômios de Legendre, proporcionou mudanças expressivas na ordem dos animais quando classificados para persistência na lactação.

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.

Approximate accuracy of dairy cattle evaluation from multiple lactation random regression model for Polish Black-and-White cattle

A method is described to obtain approximate reliabilities for breeding values calculated with a multiple-lactation random regression test day model. The method was based on a concept of an equivalent number of progeny for animals with records, which is further used to derive reliabilities for related animals. The procedure accounted for the size of contemporary groups. Approximate reliabilities were calculated for estimated breeding values of the average milk yield in the first three lactations, using the data of daily milk yield of Polish Black-and-White cows in randomly selected herds. Results of approximation were analysed by comparison with corresponding exact reliabilities, obtained from the inverse of the coefficients matrix of the mixed model equations. High correlation of 0.98 for bulls between reliabilities from both methods and very low computer requirements facilitate the implementation of the approximate method into a routine genetic evaluation procedure.

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.

Relationship between lactation curve function and phenotypic variance in random regression Test Day models

RiassuntoRelazione tra modello della curva di lattazione e stima della varianza fenotipica nei modelli Test Day di regressione random. I dati della produzione giornaliera di latte di 780 vacche primipare di razza pezzata Rossa Italiana sono stati analizzati con diversi modelli di regressione random. Il tipo di modello influenza notevolmente la stima della varianza fenotipica, con le funzioni polinomiali che mostrano forti distorsioni delle stime nella parte iniziale e finale della lattazione. Anche la forma della curva di lattazione influenza i risultati, con un miglioramento delle stime quando l’analisi viene condotta separatamente entro curve di forma omogenea (standard o atipica).

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.

Prediction of Daily Milk, Fat, and Protein Production by a Random Regression Test-Day Model

Test-day genetic evaluation models have many advantages compared with those based on 305-d lactations; however, the possible use of test-day model (TDM) results for herd management purposes has not been emphasized. The aim of this paper was to study the ability of a TDM to predict production for the next test day and for the entire lactation. Predictions of future production and detection of outliers are important factors for herd management (e.g., detection of health and management problems and compliance with quota). Because it is not possible to predict the herd-test-day (HTD) effect per se, the fixed HTD effect was split into 3 new effects: a fixed herd-test month-period effect, a fixed herd-year effect, and a random HTD effect. These new effects allow the prediction of future production for improvement of herd management. Predicted test-day yields were compared with observed yields, and the mean prediction error computed across herds was found to be close to zero. Predictions of performance records at the herd level were even more precise. Discarding herds enrolled in milk recording for <1 yr and animals with very few tests in the evaluation file improved correlations between predicted and observed yields at the next test day (correlation of 0.864 for milk in first-lactation cows as compared with a correlation of 0.821 with no records eliminated). Correlations with the observed 305-d production ranged from 0.575 to 1 for predictions based on 0 to 10 test-day records, respectively. Similar results were found for second and third lactation records for milk and milk components. These findings demonstrate the predictive ability of a TDM.