Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States

Inference about genetic covariance matrices using multiple-trait models is often hindered by lack of information. This leads to imprecise estimates of genetic parameters and of breeding values. Patterns in a genetic covariance matrix can be exploited to reduce the number of parameters and to increase quality of inferences. A structural model for genetic covariances was developed and fitted to milk yield data in five regions of the United States. This was compared with a standard multiple-trait analysis using a deviance information criterion, a measure of quality of fit. Data consisted of 3,465,334 Holstein first-lactation records from daughters of 43,755 sires in five regions of the United States (Midwest, Northeast, Northwest, Southeast, Southwest). Parameters of the structural model included an intercept and effects of measures of genetic and of management similarity on genetic covariances. Genetic similarity depended on the number of records contributed by sires that were common to a pair of regions. Management similarity was a function of the quantity of concentrate used to produce 1000 kg of milk in each pair of regions. The structural and the multiple-trait models gave similar estimates of genetic covariances, but the number of parameters was 8 in the former vs. 15 in the latter. Hence, estimates of genetic covariances were more precise with the structural model. A deviance information criterion suggested a slight superiority of the multiple-trait model, although probably within sampling error. For both models, genetic correlations between milk yield in five regions of the United States were larger than 0.93.     

Short communication: Genetic parameters of production traits in Chinese Holsteins using a random regression test-day model

The objective of this study was to estimate genetic parameters of production traits in the first 3 parities in Chinese Holsteins. Data were a random sample of complete herds (109,005 test-day records of 9,706 cows from 54 herds) extracted from the original data set, which included 362,304 test-day records of 30,942 Holstein cows from 105 herds. A test-day animal model with multiple-trait random regression and the Gibbs sampling method were used for parameter estimation. Regression curves were modeled using Legendre polynomials of order 4. The multiple-trait analysis included milk, fat, and protein yield, and somatic cell score (SCS). Average daily heritabilities ranged between 0.222 and 0.346 for the yield traits and between 0.092 and 0.187 for SCS. Heritabilities were higher in the third lactation for all traits. Within-parity genetic correlations were very high among the yield traits (>0.806) and were close to zero between SCS and yield traits, especially for first-parity cows. Results were similar to previous literature estimates from studies that used the same model as applied to this study. The estimates found in this study will be used to perform breeding value estimation for national genetic evaluations in Chinese Holsteins.     

Short communication: Single-step genomic evaluation of milk production traits using multiple-trait random regression model in Chinese Holsteins

The objectives of this study were to evaluate the prediction performance of the single-step genomic BLUP method using a multi-trait random regression model in genomic evaluation for milk production traits of Chinese Holsteins, and investigate how parameters w, τ, and ω used in the construction of the combined relationship matrix (H) affected prediction accuracy and bias. A total of 2.8 million test-day records from 0.2 million cows were available for milk, protein, and fat yields. Pedigree information included 0.3 million animals and 7,577 of them were genotyped with medium-density single nucleotide polymorphism marker panels. Genotypes were imputed into Geneseek Genomic Profiler HD (GeneSeek, Lincoln, NE) including 77K markers. A reduced data set for evaluating models was extracted from the full data set by removing test-day records from the last 4 yr. Bull and cow validation populations were constructed for each trait. We evaluated the prediction performance of the multiple-trait multiple-lactation random regression single-step genomic BLUP (RR-ssGBLUP) models with different values of parameters w, τ, and ω in the H matrix, taking consideration of inbreeding. We compared RR-ssGBLUP with the multiple-trait multiple-lactation random regression model based on pedigree and genomic BLUP. De-regressed proofs for 305-d milk, protein, and fat yields averaged over 3 lactations, which were calculated from the full data set, were used for posteriori validations. The results showed that RR-ssGBLUP was feasible for implementation in breeding practice, and its prediction performance was superior to the other 2 methods in the comparison, including prediction accuracy and unbiasedness. For bulls, RR-ssGBLUP models with $w_{0.05}{\tau }_{2.0}{\omega }_{1.0},w_{0.05}{\tau }_{2.5}{\omega }_{1.0},$ and $w_{0.1}{\tau }_{1.6}{\omega }_{0.4}$ achieved the best performance for milk, protein, and fat yields, respectively. For cows, the RR-ssGBLUP with $w_{0.2}{\tau }_{1.6}{\omega }_{0.4}$ performed the best for all 3 traits. The H matrix constructed with larger τ and smaller ω gave better convergence in solving mixed model equations. Among different RR-ssGBLUP models, the differences in validation accuracy were small. However, the regression coefficient indicating prediction bias varied substantially. The increase of w and τ, and decrease of ω, led to an increase in the regression coefficient. The results demonstrated RR-ssGBLUP is a good alternative to the multi-step approach, but the optimal choice of parameters should be found via preliminary validation study to achieve the best performance.     

Genetic parameters for tunisian holsteins using a test-day random regression model

Genetic parameters of milk, fat, and protein yields were estimated in the first 3 lactations for registered Tunisian Holsteins. Data included 140,187; 97,404; and 62,221 test-day production records collected on 22,538; 15,257; and 9,722 first-, second-, and third-parity cows, respectively. Records were of cows calving from 1992 to 2004 in 96 herds. (Co)variance components were estimated by Bayesian methods and a 3-trait-3-lactation random regression model. Gibbs sampling was used to obtain posterior distributions. The model included herd × test date, age × season of calving × stage of lactation [classes of 25 days in milk (DIM)], production sector × stage of lactation (classes of 5 DIM) as fixed effects, and random regression coefficients for additive genetic, permanent environmental, and herd-year of calving effects, which were defined as modified constant, linear, and quadratic Legendre coefficients. Heritability estimates for 305-d milk, fat and protein yields were moderate (0.12 to 0.18) and in the same range of parameters estimated in management systems with low to medium production levels. Heritabilities of test-day milk and protein yields for selected DIM were higher in the middle than at the beginning or the end of lactation. Inversely, heritabilities of fat yield were high at the peripheries of lactation. Genetic correlations among 305-d yield traits ranged from 0.50 to 0.86. The largest genetic correlation was observed between the first and second lactation, potentially due to the limited expression of genetic potential of superior cows in later lactations. Results suggested a lack of adaptation under the local management and climatic conditions. Results should be useful to implement a BLUP evaluation for the Tunisian cow population; however, results also indicated that further research focused on data quality might be needed.     

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 0.5 million 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.     

Prediction accuracies and genetic parameters for test-day traits from genomic and pedigree-based random regression models with or without heat stress interactions

The aim of this study was to compare genetic (co)variance components and prediction accuracies of breeding values from genomic random regression models (gRRM) and pedigree-based random regression models (pRRM), both defined with or without an additional environmental gradient. The used gradient was a temperature-humidity index (THI), considered in statistical models to investigate possible genotype by environment (G×E) interactions. Data included 106,505 test-day records for milk yield (MY) and 106,274 test-day records for somatic cell score (SCS) from 12,331 genotyped Holstein Friesian daughters of 522 genotyped sires. After single nucleotide polymorphism quality control, all genotyped animals had 40,468 single nucleotide polymorphism markers. Test-day traits from recording years 2010 to 2015 were merged with temperature and humidity data from the nearest weather station. In this regard, 58 large-scale farms from the German federal states of Berlin-Brandenburg and Mecklenburg-West Pomerania were allocated to 31 weather stations. For models with a THI gradient, additive genetic variances and heritabilities for MY showed larger fluctuations in dependency of DIM and THI than for SCS. For both traits, heritabilities were smaller from the gRRM compared with estimates from the pRRM. Milk yield showed considerably larger G×E interactions than SCS. In genomic models including a THI gradient, genetic correlations between different DIM × THI combinations ranged from 0.26 to 0.94 for MY. For SCS, the lowest genetic correlation was 0.78, estimated between SCS from the last DIM class and the highest THI class. In addition, for THI × THI combinations, genetic correlations were smaller for MY compared with SCS. A 5-fold cross-validation was used to assess prediction accuracies from 4 different models. The 4 different models were gRRM and pRRM, both modeled with or without G×E interactions. Prediction accuracy was the correlation between breeding values for the prediction data set (i.e., excluding the phenotypic records from this data set) with respective breeding values considering all phenotypic information. Prediction accuracies for sires and for their daughters were largest for the gRRM considering G×E interactions. Such modeling with 2 covariates, DIM and THI, also allowed accurate predictions of genetic values at specific DIM. In comparison with a pRRM, the effect of a gRRM with G×E interactions on gain in prediction accuracies was stronger for daughters than for sires. In conclusion, we found stronger effect of THI alterations on genetic parameter estimates for MY than for SCS. Hence, gRRM considering THI especially contributed to gain in prediction accuracies for MY.     

Genetic parameters for a multiple-trait multiple-lactation random regression test-day model in Italian Holsteins

The objectives of this study were to estimate variance components for test-day milk, fat, and protein yields and average daily SCS in 3 subsets of Italian Holsteins using a multiple-trait, multiple-lactation random regression test-day animal model and to determine whether a genetic heterogeneous variance adjustment was necessary. Data were test-day yields of milk, fat, and protein and SCS (on a log₂ scale) from the first 3 lactations of Italian Holsteins collected from 1992 to 2002. The 3 subsets of data included 1) a random sample of Holsteins from all herds in Italy, 2) a random sample of Holsteins from herds using a minimum of 75% foreign sires, and 3) a random sample of Holsteins from herds using a maximum of 25% foreign sires. Estimations of variances and covariances for this model were achieved by Bayesian methods using the Gibbs sampler. Estimated 305-d genetic, permanent environmental, and residual variance was higher in herds using a minimum of 75% foreign sires compared with herds using a maximum of 25% foreign sires. Estimated average daily heritability of milk, fat, and protein yields did not differ among subsets. Heritability of SCS in the first lactation differed slightly among subsets and was estimated to be the highest in herds with a maximum of 25% foreign sire use (0.19 ± 0.01). Genetic correlations across lactations for milk, fat, and protein yields were similar among subsets. Genetic correlations across lactations for SCS were 0.03 to 0.08 higher in herds using a minimum of 75% or a maximum of 25% foreign sires, compared with herds randomly sampled from the entire population. Results indicate that adjustment for heterogeneous variance at the genetic level based on the percentage of foreign sire use should not be necessary with a multiple-trait random regression test-day animal model in Italy.     

Genetic line comparisons and genetic parameters for endoparasite infections and test-day milk production traits

Keeping dairy cows in grassland systems relies on detailed analyses of genetic resistance against endoparasite infections, including between- and within-breed genetic evaluations. The objectives of this study were (1) to compare different Black and White dairy cattle selection lines for endoparasite infections and (2) the estimation of genetic (co)variance components for endoparasite and test-day milk production traits within the Black and White cattle population. A total of 2,006 fecal samples were taken during 2 farm visits in summer and autumn 2015 from 1,166 cows kept in 17 small- and medium-scale organic and conventional German grassland farms. Fecal egg counts were determined for gastrointestinal nematodes (FEC-GIN) and flukes (FEC-FLU), and fecal larvae counts for the bovine lungworm Dictyocaulus viviparus (FLC-DV). The lowest values for gastrointestinal nematode infections were identified for genetic lines adopted to pasture-based production systems, especially selection lines from New Zealand. Heritabilities were low for FEC-GIN (0.05–0.06 ± 0.04) and FLC-DV (0.05 ± 0.04), but moderate for FEC-FLU (0.33 ± 0.06). Almost identical heritabilities were estimated for different endoparasite trait transformations (log-transformation, square root). The genetic correlation between FEC-GIN and FLC-DV was 1.00 ± 0.60, slightly negative between FEC-GIN and FEC-FLU (?0.10 ± 0.27), and close to zero between FLC-DV and FEC-FLU (0.03 ± 0.30). Random regression test-day models on a continuous time scale [days in milk (DIM)] were applied to estimate genetic relationships between endoparasite and longitudinal test-day production traits. Genetic correlations were negative between FEC-GIN and milk yield (MY) until DIM 85, and between FEC-FLU and MY until DIM 215. Genetic correlations between FLC-DV and MY were negative throughout lactation, indicating improved disease resistance for high-productivity cows. Genetic relationships between FEC-GIN and FEC-FLU with milk protein content were negative for all DIM. Apart from the very early and very late lactation stage, genetic correlations between FEC-GIN and milk fat content were negative, whereas they were positive for FEC-FLU. Genetic correlations between FEC-GIN and somatic cell score were positive, indicating similar genetic mechanisms for susceptibility to udder and endoparasite infections. The moderate heritabilities for FEC-FLU suggest inclusion of FEC-FLU into overall organic dairy cattle breeding goals to achieve long-term selection response for disease resistance.     

Short communication: Optimal random regression models for milk production in dairy cattle

Legendre polynomials of orders 3 to 8 in random regression models (RRM) for first-lactation milk production in Canadian Holsteins were compared statistically to determine the best model. Twenty-six RRM were compared using LP of order 5 for the phenotypic age-season groupings. Variance components of RRM were estimated using Bayesian estimation via Gibbs sampling. Several statistical criteria for model comparison were used including the total residual variance, the log likelihood function, Akaike's information criterion, the Bayesian information criterion, Bayes factors, an information-theoretic measure of model complexity, and the percentage relative reduction in complexity. The residual variance always picks the model with the most parameters. The log likelihood and information-theoretic measure picked the model with order 5 for additive genetic effects and order 7 for permanent environmental effects. The currently used model in Canada (order 5 for both additive and permanent environmental effects) was not the best for any single criterion, but was optimal when considering all criteria.     

Genetic parameters for milk production and persistency for Danish Holsteins estimated in random regression models using REML

(Co)variance components for milk, fat, and protein yield of 8075 first-parity Danish Holsteins (DH) were estimated in random regression models by REML. For all analyses, the fixed part of the model was held constant, whereas four different functions were applied to model the additive genetic effect and the permanent environment effect. Homogeneous residual variance was assumed throughout lactation. Univariate models were compared using a minimum of -2 ln(restricted likelihood) as the criterion for best fit. Heritabilities as a function of time were calculated from the estimated curve parameters from univariate analyses. Independent of the function applied and the trait in question, heritabilities were lowest in the beginning of the lactation. Heritabilities for persistency of fat yield were slightly higher than heritabilities for persistency of milk and protein yield. Genetic correlations between persistency and 305-d production were higher for protein and milk yield than for fat yield. Bivariate analyses between the production traits were carried out in sire models using the models with the best 3-parameter curve fit in the univariate analyses. Correlations between traits were calculated from covariance components for curve parameters estimated in bivariate analyses. Genetic correlations between milk and protein yield were higher than between milk and fat yield.     

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.     

Genetic parameters for functional traits in dairy cattle from daily random regression models

The objective of the research was to estimate genetic parameters, such as heritabilities and genetic correlations, using daily test day data for milk yield (MY), milking speed (MS), dry matter intake (DMI), and body weight (BW) using random regression methodology. Data were from first lactation dairy cows (n = 320) from the Chamau research farm of the Swiss Federal Institute of Technology, Switzerland over the period from April 1994 to 2004. All traits were recorded daily using automated machines. Estimated heritabilities (h²) varied from 0.18 to 0.30 (mean h² = 0.24) for MY, 0.003 to 0.098 (mean h² = 0.03) for MS, 0.22 to 0.53 (mean h² = 0.43) for BW, and 0.12 to 0.34 (mean h² = 0.23) for DMI. A permanent environmental effect was included in both the univariate and bivariate models, but was assumed constant in estimating some genetic correlations because of convergence problems. Estimated genetic correlations varied from 0.31 to 0.41 between MY and MS, from −0.47 to 0.29 between MY and DMI, from −0.60 to 0.54 between MY and BW, from 0.17 to 0.26 between MS and DMI, from −0.18 to 0.25 between MS and BW, and from −0.89 to 0.29 between DMI and BW. Genetic correlations for MY, MS, DMI, and BW from calving to midlactation decreased similarly to 0.40, 0.36, 0.14, and 0.36 and, at the end of the lactation, decreased to −0.06, 0.23, −0.07, and 0.09, respectively. Daily genetic variance-covariance of many functional traits are reported for the first time and will be useful when constructing selection indexes for more than one trait based on longitudinal genetic parameters.     

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).     

Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.     

Short communication: estimates of genetic parameters of body condition score in the first 3 lactations using a random regression animal model

The objective of this research was to estimate the genetic parameters of body condition score (BCS) in the first 3 lactations in Canadian Holstein dairy cattle using a multiple-lactation random regression animal model. Field staff from Valacta milk recording agency (Sainte-Anne-de-Bellevue, QC, Canada) collected BCS from Québec herds several times throughout each lactation. Approximately 32,000, 20,000, and 11,000 first-, second-, and third-parity BCS were analyzed, respectively, from a total of 75 herds. Body condition score was a moderately heritable trait over the lactation for parity 1, 2, and 3, with average daily heritabilities of 0.22, 0.26, and 0.30, respectively. Daily heritability ranged between 0.14 and 0.26, 0.19 and 0.28, and 0.24 and 0.33 for parity 1, 2, and 3, respectively. Genetic variance of BCS increased with days in milk within lactations. The low genetic variance in early lactation suggests that the evolution of the ability to mobilize tissue reserves in early lactation provided cattle with a major advantage, and is, therefore, somewhat conserved. The increasing genetic variance suggests that more genetic differences were related to how well cows recovered from the negative energy balance state. More specifically, increasing genetic variation as lactation progressed could be a reflection of genetic differences in the ability of cows to efficiently control the rate of mobilization of tissue reserves, which would not be crucial in early lactation. The shape of BCS curves was similar across parities. From first to third parity, differences included the progressively deeper nadir and faster rate of recovery of condition. Daily genetic correlations between parities were calculated from 5 to 305 DIM, and were summed and divided by 301 to obtain average daily genetic correlations. The average daily genetic correlations were 0.84 between parity 1 and 2, 0.83 between parity 1 and 3, and 0.86 between parity 2 and 3. Although not 1, these genetic correlations are still strong, so much of the variation observed in BCS was controlled by the same genes for each of the first 3 lactations. If a genetic evaluation for BCS is developed, regular collection of first-lactation BCS records should be sufficient for genetic evaluation.     

Genetic parameters for test-day electrical conductivity of milk for first-lactation cows from random regression models

Electrical conductivity (EC) of milk has been introduced as an indicator trait for mastitis during the last few decades. The correlation of EC to mastitis, easy access to EC data, and the low cost of recording are properties that make EC a good indicator trait for mastitis. In this study, EC was measured daily during the lactation and available from 2101 first-lactation Holstein cows in 8 herds in the United States. Data were analyzed with an animal model that included herd-test-day, age at calving and days in milk (DIM) as fixed effects, and random additive genetic and permanent environmental effects. A repeatability model and 5 random regression (RR) models with increasing order of Legendre polynomials were used. The goodness of fit for the different models was evaluated based on several tests. Our results indicate that the best model was a RR model with a fourth-order Legendre polynomial for both additive genetic and permanent environmental effects. Heritability estimates obtained with this model were from 0.26 to 0.36. Due to the relatively high heritability obtained for EC of milk, EC might be a potential indicator trait to use in a breeding program designed to reduce the incidence of mastitis.     

Bivariate analysis of conception rates and test-day milk yields in Holsteins using a threshold-linear model with random regressions

The objective of this study was to estimate genetic correlations between conception rates (CR) and test-day (TD) milk yields in Holsteins for different days in milk (DIM) in small and large herds. The data included 217,213 first-parity service records of 94,984 cows in New York State between 1999 and 2003. The CR was defined as the outcome of a single insemination. Conception rate and TD milk were analyzed using a series of threshold-linear models with fixed effects that included herd-test-date for TD milk and herd-year for CR, age, service month, cubic regressions on DIM using Legendre polynomials and with random effects that included herd × sire interaction, sire additive genetic and permanent environments with quadratic random regressions on DIM, service sire for CR, and residual. Variance components were estimated using a Bayesian method via Gibbs sampling. Herds were categorized into small (≤80 cows) and large operations. Large herds produced a higher TD milk (34.0 vs. 30.8 kg), had lower CR (29.5 vs. 34.4%), began breeding earlier (75 vs. 92 d to first service), and had fewer days open (138 vs. 145 d). The average CR was 20% at 50 DIM, increased to about 38% at DIM 100, and then leveled off. Estimated genetic correlations between CR and TD milk stayed around −0.15 for small herds but changed from positive (0.3) at 60 DIM to negative (−0.3) at 120 DIM for large herds. Genetic correlations for CR between small and large herds were highest at 80 DIM and lowest at 140 DIM. The chi-square test showed that the frequency of service records was significantly different during a given week for 71% of large herds and for 15% of small herds, suggesting more timed artificial insemination services in large herds. For the top 15% of cows for milk, fertility peaked around 100 DIM in large herds and at around 100 and 170 DIM in small herds. It seems that optimum breeding practices in large herds of breeding cows earlier are already followed.     

Short communication: Genetic correlation and heritability of milk coagulation traits within and across lactations in Holstein cows using multiple-lactation random regression animal models

Genetic parameters of milk rennet coagulation time (RCT) and curd firmness (a₃₀) among the first 3 lactations in Holstein cows were estimated. The data set included 39,960 test-day records from 5,216 Estonian Holstein cows (the progeny of 306 sires), which were recorded from April 2005 to May 2010 in 98 herds across the country. A multiple-lactation random regression animal model was used. Individual milk samples from each cow were collected during routine milk recording. These samples were analyzed for milk composition and coagulation traits with intervals of 2 to 3 mo in each lactation (7 to 305 DIM) and from first to third lactation. Mean heritabilities were 0.36, 0.32, and 0.28 for log-transformed RCT [ln(RCT)] and 0.47, 0.40, and 0.62 for a₃₀ for parities 1, 2, and 3, respectively. Mean repeatabilities for ln(RCT) were 0.53, 0.55, and 0.56, but 0.59, 0.61, and 0.68 for a₃₀ for parities 1, 2 and 3, respectively. Mean genetic correlations between ln(RCT) and a₃₀ were −0.19, −0.14, and 0.02 for parities 1, 2, and 3, respectively. Mean genetic correlations were 0.91, 0.79, and 0.99 for ln(RCT), and 0.95, 0.94, and 0.94 for a₃₀ between parities 1 and 2, 1 and 3, and 2 and 3, respectively. Due to these high genetic correlations, we concluded that for a proper genetic evaluation of milk coagulation properties it is sufficient to record RCT and a₃₀ only in the first lactation.     

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 15.5 million 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.