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 association of clinical mastitis with test-day somatic cell score and milk yield during first lactation of Finnish Ayrshire cows

In this study the genetic association during lactation of 2 clinical mastitis (CM) traits: CM1 (7 d before to 30 d after calving) and CM2 (31 to 300 d after calving) with test-day somatic cell score (SCS) and milk yield (MY) was assessed using multitrait random regression sire models. The data analyzed were from 27,557 first-lactation Finnish Ayrshire cows. Random regressions on second- and third-order Legendre polynomials were used to model the daily genetic and permanent environmental variances of test-day SCS and MY, respectively, while only the intercept term was fitted for CM. Results showed that genetic correlations between CM and the test-day traits varied during lactation. Genetic correlations between CM1 and CM2 and test-day SCS during lactation varied from 0.41 to 0.77 and from 0.34 to 0.71, respectively. Genetic correlations of test-day MY with CM1 and CM2 ranged from 0.13 to 0.51 and from 0.49 to 0.66, respectively. Correlations between CM1 and SCS were strongest during early lactation, whereas correlations between CM2 and SCS were strongest in late lactation. Genetic correlations lower than unity indicate that CM and SCS measure different aspects of the trait mastitis. Milk yield in early lactation was more strongly correlated with both CM1 and CM2 than milk yield in later lactation. This suggests that selection for higher lactation MY through selection on increased milk yield in early lactation will have a more deleterious effect on genetic resistance to mastitis than selection for higher yield in late lactation. The approach used in this study for the estimation of the genetic associations between test-day and CM traits could be used to combine information from traits with different data structures, such as test-day SCS and CM traits in a multitrait random regression model for the genetic evaluation of udder health.     

Use of test-day records beyond three hundred five days for estimation of three hundred five-day breeding values for production traits and somatic cell score of Canadian Holsteins

The Canadian Test-Day Model includes test-day (TD) records from 5 to 305 d in milk (DIM). Because 60% of Canadian Holstein cows have at least one lactation longer than 305 d, a significant number of TD records beyond 305 DIM could be included in the genetic evaluation. The aim of this study was to investigate whether TD records beyond 305 DIM could be useful for estimation of 305-d estimated breeding value (EBV) for milk, fat, and protein yields and somatic cell score. Data were 48,638,184 TD milk, fat, and protein yields and somatic cell scores from the first 3 lactations of 2,826,456 Canadian Holstein cows. All production traits were preadjusted for the effect of pregnancy. Subsets of data were created for variance-component estimation by random sampling of 50 herds. Variance components were estimated using Gibbs sampling. Full data sets were used for estimation of breeding values. Three multiple-trait, multiple-lactation random regression models with TD records up to 305 DIM (M305), 335 DIM (M335), and 365 DIM (M365) were fitted. Two additional models (M305a and M305b) used TD records up to 305 DIM and variance components previously estimated by M335 and M365, respectively. The effects common to all models were fixed effects of herd × test-date and DIM class, fixed regression on DIM nested within region × age × season class, and random regressions for additive genetic and permanent environmental effects. Legendre polynomials of order 6 and 4 were fitted for fixed and random regressions, respectively. Rapid increase of additive genetic and permanent environmental variances at extremes of lactations was observed with all 3 models. The increase of additive genetic and permanent environmental variances was at earlier DIM with M305, resulting in greater variances at 305 DIM with M305 than with M335 and M365. Model M305 had the best ability to predict TD yields from 5 through 305 DIM and less error of prediction of 305-d EBV than M335 and M365. Model M335 had smaller change of 305-d EBV of bulls over the period of 7 yr than did M305 and M365. Model M305a had the least error of prediction and change of 305-d EBV from all models. Therefore, the use of TD records of Holstein cows from 5 through 305 DIM and variance components estimated using records up to 335 DIM is recommended for the Canadian Test-Day Model.     

Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models

Genomic selection has been widely implemented in many livestock breeding programs, but it remains incipient in buffalo. Therefore, this study aimed to (1) estimate variance components incorporating genomic information in Murrah buffalo; (2) evaluate the performance of genomic prediction for milk-related traits using single- and multitrait random regression models (RRM) and the single-step genomic best linear unbiased prediction approach; and (3) estimate longitudinal SNP effects and candidate genes potentially associated with time-dependent variation in milk, fat, and protein yields, as well as somatic cell score (SCS) in multiple parities. The data used to estimate the genetic parameters consisted of a total of 323,140 test-day records. The average daily heritability estimates were moderate (0.35 ± 0.02 for milk yield, 0.22 ± 0.03 for fat yield, 0.42 ± 0.03 for protein yield, and 0.16 ± 0.03 for SCS). The highest heritability estimates, considering all traits studied, were observed between 20 and 280 d in milk (DIM). The genetic correlation estimates at different DIM among the evaluated traits ranged from ?0.10 (156 to 185 DIM for SCS) to 0.61 (36 to 65 DIM for fat yield). In general, direct selection for any of the traits evaluated is expected to result in indirect genetic gains for milk yield, fat yield, and protein yield but also increase SCS at certain lactation stages, which is undesirable. The predicted RRM coefficients were used to derive the genomic estimated breeding values (GEBV) for each time point (from 5 to 305 DIM). In general, the tuning parameters evaluated when constructing the hybrid genomic relationship matrices had a small effect on the GEBV accuracy and a greater effect on the bias estimates. The SNP solutions were back-solved from the GEBV predicted from the Legendre random regression coefficients, which were then used to estimate the longitudinal SNP effects (from 5 to 305 DIM). The daily SNP effect for 3 different lactation stages were performed considering 3 different lactation stages for each trait and parity: from 5 to 70, from 71 to 150, and from 151 to 305 DIM. Important genomic regions related to the analyzed traits and parities that explain more than 0.50% of the total additive genetic variance were selected for further analyses of candidate genes. In general, similar potential candidate genes were found between traits, but our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the traits across parities. These results contribute to a better understanding of the genetic architecture of milk production traits in dairy buffalo and reinforce the relevance of incorporating genomic information to genetically evaluate longitudinal traits in dairy buffalo. Furthermore, the candidate genes identified can be used as target genes in future functional genomics studies.     

Genetic parameters of milking frequency and milk production traits in Canadian Holsteins milked by an automated milking system

Twice-a-day milking is currently the most frequently used milking schedule in Canadian dairy cattle. However, with an automated milking system (AMS), dairy cows can be milked more frequently. The objective of this study was to estimate genetic parameters for milking frequency and for production traits of cows milked within an AMS. Data were 141,927 daily records of 953 primiparous Holstein cows from 14 farms in Ontario and Quebec. Most cows visited the AMS 2 (46%) or 3 (37%) times a day. A 2-trait [daily (24-h) milking frequency and daily (24-h) milk yield] random regression daily animal model and a multiple-trait (milk, fat, protein yields, somatic cell score, and milking frequency) random regression test-day animal model were used for the estimation of (co)variance components. Both models included fixed effect of herd × test-date, fixed regressions on days in milk (DIM) nested within age at calving by season of calving, and random regressions for additive genetic and permanent environmental effects. Both fixed and random regressions were fitted with fourth-order Legendre polynomials on DIM. The number of cows in the multiple-trait test-day model was smaller compared with the daily animal model. Heritabilities from the daily model for daily (24-h) milking frequency and daily (24-h) milk yield ranged between 0.02 and 0.08 and 0.14 and 0.20, respectively. Genetic correlations between daily (24-h) milk yield and daily (24-h) milking frequency were largest at the end of lactation (0.80) and smallest in mid-lactation (0.27). Heritabilities from the test-day model for test-day milking frequency, milk, fat and protein yield, and somatic cell score were 0.14, 0.26, 0.20, 0.21, and 0.20, respectively. The genetic correlation was positive between test-day milking frequency and official test-day milk, fat, and protein yields, and negative between official test-day somatic cell score and test-day milking frequency.     

Genetic relationships of clinical mastitis,cystic ovaries,and lameness with milk yield and somatic cell score in first-lactation Canadian Holsteins

The objective of this study was to investigate the genetic relationships of the 3 most frequently reported dairy cattle diseases (clinical mastitis, cystic ovaries, and lameness) with test-day milk yield and somatic cell score (SCS) in first-lactation Canadian Holstein cows using random regression models. Health data recorded by producers were available from the National Dairy Cattle Health System in Canada. Disease traits were defined as binary traits (0 = healthy, 1 = affected) based on whether or not the cow had at least one disease case recorded within 305 d after calving. Mean frequencies of clinical mastitis, cystic ovaries, and lameness were 12.7, 8.2, and 9.1%, respectively. For genetic analyses, a Bayesian approach using Gibbs sampling was applied. Bivariate linear sire random regression model analyses were carried out between each of the 3 disease traits and test-day milk yield or SCS. Random regressions on second-degree Legendre polynomials were used to model the daily sire additive genetic and cow effects on test-day milk yield and SCS, whereas only the intercept term was fitted for disease traits. Estimated heritabilities were 0.03, 0.03, and 0.02 for clinical mastitis, cystic ovaries, and lameness, respectively. Average heritabilities for milk yield were between 0.41 and 0.49. Average heritabilities for SCS ranged from 0.10 to 0.12. The average genetic correlations between daily milk yield and clinical mastitis, cystic ovaries, and lameness were 0.40, 0.26, and 0.23, respectively; however, the last estimate was not statistically different from zero. Cows with a high genetic merit for milk yield during the lactation were more susceptible to clinical mastitis and cystic ovaries. Estimates of genetic correlations between daily milk yield and clinical mastitis were moderate throughout the lactation. The genetic correlations between daily milk yield and cystic ovaries were near zero at the beginning of lactation and were highest at mid and end lactation. The average genetic correlation between daily SCS and clinical mastitis was 0.59 and was consistent throughout the lactation. The average genetic correlation between daily SCS and cystic ovaries was near zero (−0.01), whereas a moderate, but nonsignificant, correlation of 0.27 was observed between SCS and lameness. Unfavorable genetic associations between milk yield and diseases imply that production and health traits should be considered simultaneously in genetic selection.     

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.     

Adjustment for heterogeneous covariance due to herd milk yield by transformation of test-day random regressions

A method of accounting for differences in covariance components of test-day milk records was developed based on transformation of regressions for random effects. Preliminary analysis indicated that genetic and nongenetic covariance structures differed by herd milk yield. Differences were found for phenotypic covariances and also for genetic, permanent environmental, and herd-time covariances. Heritabilities for test-day milk yield tended to be lower at the end and especially at the start of lactation; they also were higher (maximum of ∼25%) for high-yield herds and lower (maximum of 15%) for low-yield herds. Permanent environmental variances were on average 10% lower in high-yield herds. Relative herd-time variances were ∼10% at start of lactation and then began to decrease regardless of herd yield; high-yield herds increased in midlactation followed by another decrease, and medium-yield herds increased at the end of lactation. Regressors for random regression effects were transformed to adjust for heterogeneity of test-day yield covariances. Some animal reranking occurred because of this transformation of genetic and permanent environmental effects. When genetic correlations between environments were allowed to differ from 1, some additional animal re-ranking occurred. Correlations of variances of genetic and permanent-environmental regression solutions within herd, test-day, and milking frequency class with class mean milk yields were reduced with adjustment for heterogeneous covariance. The method suggests a number of innovative solutions to issues related to heterogeneous covariance structures, such as adjusted estimates in multibreed evaluation.     

Experience with a test-day model

The Canadian Test-Day Model is a 12-trait random regression animal model in which traits are milk, fat, and protein test-day yields, and somatic cell scores on test days within each of first three lactations. Test-day records from later lactations are not used. Random regressions (genetic and permanent environmental) were based on Wilmink's three parameter function that includes an intercept, regression on days in milk, and regression on an exponential function to the power -0.05 times days in milk. The model was applied to over 22 million test-day records of over 1.4 million cows in seven dairy breeds for cows first calving since 1988. A theoretical comparison of test-day model to 305-d complete lactation animal model is given. Each animal in an analysis receives 36 additive genetic solutions (12 traits by three regression coefficients), and these are combined to give one estimated breeding value (EBV) for each of milk, fat, and protein yields, average daily somatic cell score and milk yield persistency (for bulls only). Correlation of yield EBV with previous 305-d lactation model EBV for bulls was 0.97 and for cows was 0.93 (Holsteins). A question is whether EBV for yield traits for each lactation should be combined into one overall EBV, and if so, what method to combine them. Implementation required development of new methods for approximation of reliabilities of EBV, inclusion of cows without test day records in analysis, but which were still alive and had progeny with test-day records, adjustments for heterogeneous herd-test date variances, and international comparisons. Efforts to inform the dairy industry about changes in EBV due to the model and recovering information needed to explain changes in specific animals' EBV are significant challenges. The Canadian dairy industry will require a year or more to become comfortable with the test-day model and to realize the impact it could have on selection decisions.     

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.     

Random herd curves in a test-day model for milk, fat, and protein production of dairy cattle in The Netherlands

With random regression models, genetic parameters of test-day milk production records of dairy cattle can be estimated directly from the data. However, several researchers that used this method have reported unrealistically high variances at the borders of the lactation trajectory and low genetic correlations between beginning and end of lactation. Recently, it has been proposed to include herd-specific regression curves in the random regression model. The objective was to study the effect of including random herd curves on estimated genetic parameters. Genetic parameters were estimated with 2 models; both included random regressions for the additive genetic and permanent environmental effect, whereas the second model also included a random regression effect for herd x 2-yr period of calving. All random regressions were modeled with fourth-order Legendre polynomials. Bayesian techniques with Gibbs sampling were used to estimate all parameters. The data set comprised 857,255 test-day milk, fat, and protein records from lactations 1, 2, and 3 of 43,990 Holstein cows from 544 herds. Genetic variances estimated by the second model were lower in the first 100 d and at the end of the lactation, especially in lactations 2 and 3. Genetic correlations between d 50 and the end of lactation were around 0.25 higher in the second model and were consistent with studies where lactation stages are modeled as different traits. Subsequently, estimated heritabilities for persistency were up to 0.14 lower in the second model. It is suggested to include herd curves in a random regression model when estimating genetic parameters of test-day production traits in dairy cattle.     

Genotype by environment interaction for somatic cell score across bulk milk somatic cell count and days in milk

The objective of this paper was to investigate the importance of a genotype × environment interaction (G × E) for somatic cell score (SCS) across levels of bulk milk somatic cell count (BMSCC), number of days in milk (DIM), and their interaction. Variance components were estimated with a model including random regressions for each sire on herd test-day BMSCC, DIM, and the interaction of BMSCC and DIM. The analyzed data set contained 344,029 test-day records of 24,125 cows, sired by 182 bulls, in 461 herds comprising 13,563 herd test-days. In early lactation, considerable G × E effects were detected for SCS, indicated by 3-fold higher genetic variance for SCS at high BMSCC compared with SCS at low BMSCC, and a genetic correlation of 0.72 between SCS at low and at high BMSCC. Estimated G × E effects were smaller during late lactation. Genetic correlations between SCS at the same level of BMSCC, across DIM, were between 0.43 and 0.89. The lowest genetic correlation between SCS measures on any 2 possible combinations of BMSCC and DIM was 0.42. Correlated responses in SCS across BMSCC and DIM were, on some occasions, less than half the direct response to selection in the response environment. Responses to selection were reasonably high among environments in the second half of the lactation, whereas responses to selection between environments early and late in lactation tended to be low. Selection for reduced SCS yielded the highest direct response early in lactation at high BMSCC.     

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 correlation patterns between somatic cell score and protein yield in the Italian Holstein-Friesian population

Genetic parameters for somatic cell score (SCS) in the Italian Holstein-Friesian population were estimated addressing the pattern of genetic correlation with protein yield in different parities (first, second, and third) and on different days in milk within each parity. Three approaches for parameter estimation were applied using random samples of herds from the national database of the Italian Holstein Association. Genetic correlations for lactation measures (305-d protein yield and lactation SCS) were positive in the first parity (0.31) and close to zero in the second (0.01) and third (0.09) parities. These results indicated that larger values of SCS were genetically associated with increased production. The second and third sets of estimates were based on random regression test-day models, modeling the shape of lactation curve with the Wilmink function and fourth-order Legendre polynomials, respectively. Genetic correlations from both random regression models showed a specific pattern associated with days in milk within and across parities. Estimates varied from positive to negative in the first and second parity, and from null to negative in the third parity. Patterns were similar for both random regression models. The average overall correlation between SCS and protein yield was zero or slightly positive in the first lactation and ranged from zero to negative in later lactations. Correlation estimates differed by parity and stage of lactation. They also demonstrated the dubiousness of applying a single genetic correlation measure between SCS and protein in setting selection strategies. Differences in magnitude and the sign of genetic correlations between SCS and yields across and within parities should be accounted for in selection schemes.     

Genetic correlations between the cumulative pseudo-survival rate,milk yield,and somatic cell score during lactation in Holstein cattle in Japan using a random regression model

Trends in genetic correlations between longevity, milk yield, and somatic cell score (SCS) during lactation in cows are difficult to trace. In this study, changes in the genetic correlations between milk yield, SCS, and cumulative pseudo-survival rate (PSR) during lactation were examined, and the effect of milk yield and SCS information on the reliability of estimated breeding value (EBV) of PSR were determined. Test day milk yield, SCS, and PSR records were obtained for Holstein cows in Japan from 2004 to 2013. A random subset of the data was used for the analysis (825 herds, 205,383 cows). This data set was randomly divided into 5 subsets (162–168 herds, 83,389–95,854 cows), and genetic parameters were estimated in each subset independently. Data were analyzed using multiple-trait random regression animal models including either the residual effect for the whole lactation period (H0), the residual effects for 5 lactation stages (H5), or both of these residual effects (HD). Milk yield heritability increased until 310 to 351 d in milk (DIM) and SCS heritability increased until 330 to 344 DIM. Heritability estimates for PSR increased with DIM from 0.00 to 0.05. The genetic correlation between milk yield and SCS increased negatively to under ?0.60 at 455 DIM. The genetic correlation between milk yield and PSR increased until 342 to 355 DIM (0.53–0.57). The genetic correlation between the SCS and PSR was ?0.82 to ?0.83 at around 180 DIM, and decreased to ?0.65 to ?0.71 at 455 DIM. The reliability of EBV of PSR for sires with 30 or more recorded daughters was 0.17 to 0.45 when the effects of correlated traits were ignored. The maximum reliability of EBV was observed at 257 (H0) or 322 (HD) DIM. When the correlations of PSR with milk yield and SCS were considered, the reliabilities of PSR estimates increased to 0.31–0.76. The genetic parameter estimates of H5 were the same as those for HD. The rank correlation coefficients of the EBV of PSR between H0 and H5 or HD were greater than 0.9. Additionally, the reliabilities of EBV of PSR of H0 were similar to those for H5 and HD. Therefore, the genetic parameter estimates in H0 were not substantially different from those in H5 and HD. When milk yield and SCS, which were genetically correlated with PSR, were used, the reliability of PSR increased. Estimates of the genetic correlations between PSR and milk yield and between PSR and SCS are useful for management and breeding decisions to extend the herd life of cows.     

Estimated heterogeneity of phenotypic variance of test-day yield with a structural variance model

First-lactation test-day milk, fat, and protein yields from New York, Wisconsin, and California herds from 1990 through 2000 were adjusted additively for age and lactation stage. A random regression model with third-order Legendre polynomials for permanent environmental and genetic effects was used. The model included a random effect with the same polynomial regressions for 2 yr of calvings within herd (herd-time effect) to provide herd-specific lactation curves that can change every 2 yr. (Co)variance components were estimated using expectation-maximization REML simultaneously with phenotypic variances that were modeled using a structural variance model. Maximum heritability for test-day milk yield was estimated to be approximately 20% around 200 to 250 d in milk; heritabilities were slightly lower for test-day fat and protein yields. Herd-time effects explained 12 to 20% of phenotypic variance and had the greatest impact at start of lactation. Variances of test-day yields increased with time, subclass size, and milking frequency. Test month had limited influence on variance. Variance increased for cows in herds with low and high milk yields and for early and late lactation stages. Repeatabilities of variances observed for a given class of herd, test-day, and milking frequency were 14 to 17% across nested variance subclasses based on lactation stage.     

Genetic analyses of protein yield in dairy cows applying random regression models with time-dependent and temperature x humidity-dependent covariates

Data used in the present study included 1,095,980 first-lactation test-day records for protein yield of 154,880 Holstein cows housed on 196 large-scale dairy farms in Germany. Data were recorded between 2002 and 2009 and merged with meteorological data from public weather stations. The maximum distance between each farm and its corresponding weather station was 50 km. Hourly temperature-humidity indexes (THI) were calculated using the mean of hourly measurements of dry bulb temperature and relative humidity. On the phenotypic scale, an increase in THI was generally associated with a decrease in daily protein yield. For genetic analyses, a random regression model was applied using time-dependent (d in milk, DIM) and THI-dependent covariates. Additive genetic and permanent environmental effects were fitted with this random regression model and Legendre polynomials of order 3 for DIM and THI. In addition, the fixed curve was modeled with Legendre polynomials of order 3. Heterogeneous residuals were fitted by dividing DIM into 5 classes, and by dividing THI into 4 classes, resulting in 20 different classes. Additive genetic variances for daily protein yield decreased with increasing degrees of heat stress and were lowest at the beginning of lactation and at extreme THI. Due to higher additive genetic variances, slightly higher permanent environment variances, and similar residual variances, heritabilities were highest for low THI in combination with DIM at the end of lactation. Genetic correlations among individual values for THI were generally >0.90. These trends from the complex random regression model were verified by applying relatively simple bivariate animal models for protein yield measured in 2 THI environments; that is, defining a THI value of 60 as a threshold. These high correlations indicate the absence of any substantial genotype × environment interaction for protein yield. However, heritabilities and additive genetic variances from the random regression model tended to be slightly higher in the THI range corresponding to cows’ comfort zone. Selecting such superior environments for progeny testing can contribute to an accurate genetic differentiation among selection candidates.     

Genetic evaluation of dairy cattle with test-day models with autoregressive covariance structures and with a 305-d model

This study compared genetic evaluations from 3 test-day (TD) models with different assumptions about the environmental covariance structure for TD records and genetic evaluations from 305-d lactation records for dairy cows. Estimates of genetic values of 12,071 first-lactation Holstein cows were obtained with the 3 TD models using 106,472 TD records. The compound symmetry (CS) model was a simple test-day repeatability animal model with compound symmetry covariance structure for TD environmental effects. The AR_s and AR_e models also used TD records but with a first-order autoregressive covariance structure among short-term environmental effects or residuals, respectively. Estimates of genetic values with the TD models were also compared with those from a model using 305-d lactation records. Animals were genetically evaluated for milk, fat, and protein yields, and somatic cell score (SCS). The largest average estimates of accuracy of predicted breeding values were obtained with the AR_s model and the smallest were with the 305-d model. The 305-d model resulted in smaller estimates of correlations between average predicted breeding values of the parents and lactation records of their daughters for milk and protein yields and SCS than did the CS and AR_e models. Predicted breeding values with the 3 TD models were highly correlated (0.98 to 1.00). Predicted breeding values with 305-d lactation records were moderately correlated with those with TD models (0.71 to 0.87 for sires and 0.80 to 0.87 for cows). More genetic improvement can be achieved by using TD models to select for animals for higher milk, fat, and protein yields, and lower SCS than by using models with 305-d lactation records.     

Estimates of genetic parameters for single- and multiple-country test-day models

Single- and multiple-country random regression models were applied to estimate genetic parameters for first-lactation test-day milk yield of cows from four countries: Australia, Canada, Italy, and New Zealand. Selected countries represented a wide range of production systems and environments. Milk production in Canada and Italy is based mainly on intensive management systems, while Australia and New Zealand are largely based on rotational grazing. Legendre polynomials with five coefficients were used to model genetic and environmental lactation curves. Covariance components of lactation curve coefficients within and across countries, and selected functions of those, were estimated by Bayesian methods with Gibbs sampling, on selected subsets of data. Countries differed in both phenotypic and genetic parameters of lactation curves between d 5 and 305 of lactation. Principal component analysis of single-trait genetic and environmental covariance matrices showed, however, that the pattern of variability in test-day milk yield was very similar between countries. General level of milk production in lactation and persistency components accounted for more than 90% of the total variance. Estimated genetic correlations between countries for total yield in lactation ranged from 0.65 (Italy and New Zealand) to 0.83 (Australia and New Zealand), indicating a possibility of genotype by environment interaction for some pairs of countries.     

Genetic evaluation of bulls and cows with single- and multiple-country test-day models

First-lactation milk yield test-day records on cows from Australia, Canada, Italy, and New Zealand were analyzed by single- and multiple-country random regression models. Models included fixed effects of herd-test day and breed composition-age at calving-season of calving by days in milk, and random regressions with Legendre polynomials of order four for animal genetic and permanent environmental effects. Milk yields in different countries were defined as genetically different traits for the purpose of multiple-trait model. Estimated breeding values of bulls and cows from single- and multiple-trait models were compared within and across countries for two traits: total milk yield in lactation and lactation persistency, defined as the linear coefficient of animal genetic curve. Correlations between single- and multiple-trait evaluations within country for total yield were higher than 0.95 for bulls and close to 1 for cows. Correlations for lactation persistency were lower than respective correlations for total yield. Between country correlations for lactation yield ranged from 0.93 to 0.96, indicating different ranking of bulls on different country scales under multiple-trait model. Lactation persistency had in general lower between-country correlations, with the highest values for Canada-Italy and Australia-New Zealand pairs, for both single- and multiple-country models. Although multiple-country random regression test-day model was computationally feasible for four countries, the same would not be true for routine international genetic evaluation in the near future.