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.     

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 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.     

Selection for milk production and persistency using eigenvectors of the random regression coefficient matrix

The purpose of this study was to investigate the relationships of the eigenvectors of the additive genetic random regression coefficient matrix (K) to selection responses and to determine how many eigenvectors are necessary in the breeding goal to explain the variation. The construction of various eigenvector indexes was based on the K matrix estimated from test-day records of Japanese Holstein cattle. The first (leading) eigenvector index produced constant responses for each day of lactation, indicating that the first eigenvector is responsible for scaling the lactation curve without altering its shape. Daily genetic responses to the second eigenvector index increased linearly as DIM increased. Genetic responses to the third eigenvector index were negative in mid-lactation but were positive in early and late lactation (concave curve). Genetic responses to the fourth and fifth eigenvector indexes hovered around zero across the lactation. The results suggest that both second and third eigenvectors account for the change in the shape of the lactation curve and there is little utility of the fourth and fifth eigenvectors in improving lactation milk or persistency. When the goal is to increase lactation milk yield alone, the index based on the first eigenvector produced a similar response to the index based on all 5 eigenvectors. When the goal is to improve both lactation milk yield and persistency, the index based on the first 3 eigenvectors achieved more than 99.9% of the genetic response to an index based on all 5 eigenvectors. The advantage of an eigenvector index over conventional selection based on total lactation milk yield increases with increasing economic weight assigned to persistency.     

Relationships between milk yield and somatic cell score in Canadian Holsteins from simultaneous and recursive random regression models

Multiple-trait random regression animal models with simultaneous and recursive links between phenotypes for milk yield and somatic cell score (SCS) on the same test day were fitted to Canadian Holstein data. All models included fixed herd test-day effects and fixed regressions within region-age at calving-season of calving classes, and animal additive genetic and permanent environmental regressions with random coefficients. Regressions were Legendre polynomials of order 4 on a scale from 5 to 305 d in milk (DIM). Bayesian methods via Gibbs sampling were used for the estimation of model parameters. Heterogeneity of structural coefficients was modeled across (the first 3 lactations) and within (4 DIM intervals) lactation. Model comparisons in terms of Bayes factors indicated the superiority of simultaneous models over the standard multiple-trait model and recursive parameterizations. A moderate heterogeneous (both across- and within-lactation) negative effect of SCS on milk yield (from −0.36 for 116 to 265 DIM in lactation 1 to −0.81 for 5 to 45 DIM in lactation 3) and a smaller positive reciprocal effect of SCS on milk yield (from 0.007 for 5 to 45 DIM in lactation 2 to 0.023 for 46 to 115 DIM in lactation 3) were estimated in the most plausible specification. No noticeable differences among models were detected for genetic and environmental variances and genetic parameters for the first 2 regression coefficients. The curves of genetic and permanent environmental variances, heritabilities, and genetic and phenotypic correlations between milk yield and SCS on a daily basis were different for different models. Rankings of bulls and cows for 305-d milk yield, average daily SCS, and milk lactation persistency remained the same among models. No apparent benefits are expected from fitting causal phenotypic relationships between milk yield and SCS on the same test day in the random regression test-day model for genetic evaluation purposes.     

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.     

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.     

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.     

Genetic parameters for body condition score, body weight, milk yield, and fertility estimated using random regression models

Genetic (co)variances between body condition score (BCS), body weight (BW), milk yield, and fertility were estimated using a random regression animal model extended to multivariate analysis. The data analyzed included 81,313 BCS observations, 91,937 BW observations, and 100,458 milk test-day yields from 8725 multiparous Holstein-Friesian cows. A cubic random regression was sufficient to model the changing genetic variances for BCS, BW, and milk across different days in milk. The genetic correlations between BCS and fertility changed little over the lactation; genetic correlations between BCS and interval to first service and between BCS and pregnancy rate to first service varied from -0.47 to -0.31, and from 0.15 to 0.38, respectively. This suggests that maximum genetic gain in fertility from indirect selection on BCS should be based on measurements taken in midlactation when the genetic variance for BCS is largest. Selection for increased BW resulted in shorter intervals to first service, but more services and poorer pregnancy rates; genetic correlations between BW and pregnancy rate to first service varied from -0.52 to -0.45. Genetic selection for higher lactation milk yield alone through selection on increased milk yield in early lactation is likely to have a more deleterious effect on genetic merit for fertility than selection on higher milk yield in late lactation.     

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).     

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.     

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.     

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.     

Validation of single-step genomic BLUP random regression test-day models and SNP effects analysis on milk yield in French Saanen goats

The shape of the lactation curve is linked to an animal's health, feed requirements, and milk production throughout the year. Random regression models (RRM) are widely used for genetic evaluation of total milk production throughout the lactation and for milk yield persistency. Genomic information used with the single-step genomic BLUP method (ssGBLUP) substantially improves the accuracy of genomic prediction of breeding values in the main dairy cattle breeds. The aim of this study was to implement an RRM using ssGBLUP for milk yield in Saanen dairy goats in France. The data set consisted of 7,904,246 test-day records from 1,308,307 lactations of Saanen goats collected in France between 2000 and 2017. The performance of this type of evaluation was assessed by applying a validation step with data targeting candidate bucks. The model was compared with a nongenomic evaluation and a traditional evaluation that use cumulated performance throughout the lactation model (LM). The incorporation of genomic information increased correlations between daughter yield deviations (DYD) and estimated breeding values (EBV) obtained with a partial data set for candidate bucks. The LM and the RRM had similar correlation between DYD and EBV. However, the RRM reduced overestimation of EBV and improved the slope of the regression of DYD on EBV obtained at birth. This study shows that a genomic evaluation from a ssGBLUP RRM is possible in dairy goats in France and that RRM performance is comparable to a LM but with the additional benefit of a genomic evaluation of persistency. Variance of adjacent SNPs was studied with LM and RRM following the ssGBLUP. Both approaches converged on approximately the same regions explaining more than 1% of total variance. Regions associated with persistency were also found.     

Random regression analysis of milk yield and milk composition in the first and second lactations of Murciano-Granadina goats

Records from the milk recording scheme of Spanish Murciano-Granadina goats were studied to estimate genetic (co)variance components and breeding values throughout the first and second lactations. The data used consisted of 49,696 monthly test-day records of milk (MY), protein (PY), fat (FY), and dry matter (DMY) yields from 5,163 goats, distributed in 20 herds, offspring of 2,086 does and 206 bucks. These records were analyzed by 2-trait random regression models (RRM) and a repeatability test-day model (RTDM). At the middle of lactation, heritability estimates for MY, DMY, and FY obtained with RTDM were larger than those estimated with RRM, and the opposite was true for PY. The RRM estimates of heritability for MY, FY, and PY were very similar throughout the trajectories of both lactations. Heritability estimates for DMY decreased through the lactation period. The genetic correlations between the first and second lactation records estimated for all traits by RRM were positive and ranged from 0.43 to 0.80 throughout the lactation curves. The correlation between BV estimated with RTDM and RRM was 0.742 for MY and 0.664 for DMY. The RRM could be a useful alternative to RTDM for the prediction of BV in this breed.     

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.     

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.     

Recursive relationships between milk yield and somatic cell score of Canadian Holsteins from finite mixture random regression models

Finite mixture, multiple-trait, random regression animal models with recursive links between phenotypes for milk yield and somatic cell score (SCS) on the same test-day were applied to first lactation Canadian Holstein data. All models included fixed herd-test-day effects and fixed regressions within region-age at calving-season of calving classes, and animal additive genetic and permanent environmental regressions with random coefficients. Causal links between phenotypes for milk yield and SCS were fitted separately for records from healthy cows and cows with a putative, subclinical form of mastitis. Bayesian methods via Gibbs sampling were used for the estimation of model parameters. Bayes factors indicated superiority of the model with recursive link from milk to SCS over the reciprocal recursive model and the standard multiple-trait model. Differences between models measured by other, single-trait model comparison criteria (i.e., weighted mean squared error, squared bias, and correlation between observed and expected data) were negligible. Approximately 20% of test-day records were classified as originating from cows with mastitis in recursive mixture models. The proportion of records from cows infected with mastitis was largest at the beginning of lactation. Recursive mixture models exhibited different distributions of data from healthy and infected cows in different parts of lactation. A negative effect of milk to SCS (up to −0.15 score points for every kilogram of milk for healthy cows from 5 to 45 d in milk) was estimated for both mixture components (healthy and infected) in all stages of lactation for the most plausible model. The magnitude of this effect was stronger for healthy cows than for cows infected with mastitis. Different patterns of genetic and environmental correlations between milk and SCS for healthy and infected records were revealed, due to heterogeneity of structural coefficients between mixture components. Estimated breeding values for SCS from the best fitting model for sires of infected daughters were more related to estimated breeding values for the same trait from the regular multiple-trait model than evaluations for sires of mastitis-free cows.     

Genetic parameter estimation for milk yield over multiple parities and various lengths of lactation in Danish Jerseys by random regression models

The objectives of this study were to test for heterogeneity of genetic and environmental variance among completed and extended records from different lactations or different days in milk (DIM) and to build a model that accounts for this heterogeneity. A total of 147,457 305-d milk yield records from Danish Jersey cows calving between 1984 and early 1999 from two regions of Denmark were used in this study. Results showed that DIM and parity influenced parameters estimated from an animal model with repeated records. Therefore, the data were analyzed using random-regression models that allow the covariance between measurements to change gradually with DIM and parity. Random regressions were fitted for additive genetic effects and permanent environmental effects using second- or third-order normalized Legendre polynomials for DIM and parity. Variances of random-regression coefficients associated with all orders of the polynomials were significant. Based on these parameter estimates, a covariance function (CF) was defined. The CF showed that the heritability decreases over parities, but within each parity heritability increases with DIM, whereas variance of permanent environmental effects increases over parities and decreases with DIM. Generally, genetic correlations were higher between records with similar DIM and parity. The results indicate that there are problems with the extension procedure used to predict 305-d milk yields. Using the covariance functions estimated in this study, breeding values could be predicted that take into account the covariance structure between records from different parities and different DIM.