Estimates of genetic parameters and eigenvector indices for milk production of Holstein cows

The objectives of the present study were to estimate genetic parameters of monthly test-day milk yield (TDMY) of the first lactation of Brazilian Holstein cows using random regression (RR), and to compare the genetic gains for milk production and persistency, derived from RR models, using eigenvector indices and selection indices that did not consider eigenvectors. The data set contained monthly TDMY of 3,543 first lactations of Brazilian Holstein cows calving between 1994 and 2011. The RR model included the fixed effect of the contemporary group (herd-month-year of test days), the covariate calving age (linear and quadratic effects), and a fourth-order regression on Legendre orthogonal polynomials of days in milk (DIM) to model the population-based mean curve. Additive genetic and nongenetic animal effects were fit as RR with 4 classes of residual variance random effect. Eigenvector indices based on the additive genetic RR covariance matrix were used to evaluate the genetic gains of milk yield and persistency compared with the traditional selection index (selection index based on breeding values of milk yield until 305 DIM). The heritability estimates for monthly TDMY ranged from 0.12 ± 0.04 to 0.31 ± 0.04. The estimates of additive genetic and nongenetic animal effects correlation were close to 1 at adjacent monthly TDMY, with a tendency to diminish as the time between DIM classes increased. The first eigenvector was related to the increase of the genetic response of the milk yield and the second eigenvector was related to the increase of the genetic gains of the persistency but it contributed to decrease the genetic gains for total milk yield. Therefore, using this eigenvector to improve persistency will not contribute to change the shape of genetic curve pattern. If the breeding goal is to improve milk production and persistency, complete sequential eigenvector indices (selection indices composite with all eigenvectors) could be used with higher economic values for persistency. However, if the breeding goal is to improve only milk yield, the traditional selection index is indicated.     

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.     

Genetic analysis of somatic cell score in Norwegian cattle using random regression test-day models

The dataset used in this analysis contained a total of 341,736 test-day observations of somatic cell scores from 77,110 primiparous daughters of 1965 Norwegian Cattle sires. Initial analyses, using simple random regression models without genetic effects, indicated that use of homogeneous residual variance was appropriate. Further analyses were carried out by use of a repeatability model and 12 random regression sire models. Legendre polynomials of varying order were used to model both permanent environmental and sire effects, as did the Wilmink function, the Lidauer-M?ntysaari function, and the Ali-Schaeffer function. For all these models, heritability estimates were lowest at the beginning (0.05 to 0.07) and higher at the end (0.09 to 0.12) of lactation. Genetic correlations between somatic cell scores early and late in lactation were moderate to high (0.38 to 0.71), whereas genetic correlations for adjacent DIM were near unity. Models were compared based on likelihood ratio tests, Bayesian information criterion, Akaike information criterion, residual variance, and predictive ability. Based on prediction of randomly excluded observations, models with 4 coefficients for permanent environmental effect were preferred over simpler models. More highly parameterized models did not substantially increase predictive ability. Evaluation of the different model selection criteria indicated that a reduced order of fit for sire effects was desireable. Models with zeroth- or first-order of fit for sire effects and higher order of fit for permanent environmental effects probably underestimated sire variance. The chosen model had Legendre polynomials with 3 coefficients for sire, and 4 coefficients for permanent environmental effects. For this model, trajectories of sire variance and heritability were similar assuming either homogeneous or heterogeneous residual variance structure.     

Genetic improvement in mastitis resistance: comparison of selection criteria from cross-sectional and random regression sire models for somatic cell score

Several selection criteria for reducing incidence of mastitis were developed from a random regression sire model for test-day somatic cell score (SCS). For comparison, sire transmitting abilities were also predicted based on a cross-sectional model for lactation mean SCS. Only first-crop daughters were used in genetic evaluation of SCS, and the different selection criteria were compared based on their correlation with incidence of clinical mastitis in second-crop daughters (measured as mean daughter deviations). Selection criteria were predicted based on both complete and reduced first-crop daughter groups (261 or 65 daughters per sire, respectively). For complete daughter groups, predicted transmitting abilities at around 30 d in milk showed the best predictive ability for incidence of clinical mastitis, closely followed by average predicted transmitting abilities over the entire lactation. Both of these criteria were derived from the random regression model. These selection criteria improved accuracy of selection by approximately 2% relative to a cross-sectional model. However, for reduced daughter groups, the cross-sectional model yielded increased predictive ability compared with the selection criteria based on the random regression model. This result may be explained by the cross-sectional model being more robust, i.e., less sensitive to precision of (co)variance components estimates and effects of data structure.     

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.     

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.     

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.     

Exploring the use of random regression models with legendre polynomials to analyze measures of volume of ejaculate in Holstein bulls

Artificial insemination centers routinely collect records of quantity and quality of semen of bulls throughout the animals’ productive period. The goal of this paper was to explore the use of random regression models with orthogonal polynomials to analyze repeated measures of semen production of Spanish Holstein bulls. A total of 8,773 records of volume of first ejaculate (VFE) collected between 12 and 30 mo of age from 213 Spanish Holstein bulls was analyzed under alternative random regression models. Legendre polynomial functions of increasing order (0 to 6) were fitted to the average trajectory, additive genetic and permanent environmental effects. Age at collection and days in production were used as time variables. Heterogeneous and homogeneous residual variances were alternatively assumed. Analyses were carried out within a Bayesian framework. The logarithm of the marginal density and the cross-validation predictive ability of the data were used as model comparison criteria. Based on both criteria, age at collection as a time variable and heterogeneous residuals models are recommended to analyze changes of VFE over time. Both criteria indicated that fitting random curves for genetic and permanent environmental components as well as for the average trajector improved the quality of models. Furthermore, models with a higher order polynomial for the permanent environmental (5 to 6) than for the genetic components (4 to 5) and the average trajectory (2 to 3) tended to perform best. High-order polynomials were needed to accommodate the highly oscillating nature of the phenotypic values. Heritability and repeatability estimates, disregarding the extremes of the studied period, ranged from 0.15 to 0.35 and from 0.20 to 0.50, respectively, indicating that selection for VFE may be effective at any stage. Small differences among models were observed. Apart from the extremes, estimated correlations between ages decreased steadily from 0.9 and 0.4 for measures 1 mo apart to 0.4 and 0.2 for most distant measures for additive genetic and phenotypic components, respectively. Further investigation to account for environmental factors that may be responsible for the oscillating observations of VFE is 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.     

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.     

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.     

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.     

Effect of pregnancy on production traits of Canadian Holstein cows

Seven test-day models with different ways of accounting for the effect of pregnancy on production traits were compared by their residual variance, rank correlations of estimated breeding values of bulls and cows and number of nonpregnant cows in the top 500 for milk yield and milk persistency. Data were 22,546,696 first-parity test-day milk, fat, and protein yields and somatic cell score records of 2,677,862 Canadian Holstein heifers calved between 1988 and 2006. The first model fitted separate lactation curves to 8 days open classes and 1 curve to a nonpregnant cow class. Two other models adjusted for pregnancy by fitting the effect of month of pregnancy or stage of pregnancy. One model fitted regression on days pregnant. The remaining 3 models fitted interactions between stage of pregnancy and stage of lactation when conception occurred using either regression on days pregnant nested within days open or classes for specific stage of pregnancy and stage of lactation combination. All models were contrasted to a model without any adjustment for the effect of pregnancy. Both models that accounted for the effect of pregnancy and the model without the effect of pregnancy had similar residual variance. Adjusting for the effect of pregnancy did not cause reranking of sires for estimated breeding values for 305-d yield and persistency but influenced ranking of cows. Models that used days open for the effect of pregnancy overestimated breeding values of nonpregnant cows and cows with shorter days open. No interaction was found between stage of pregnancy and stage of lactation. Month of pregnancy and stage of pregnancy models, compared with the model without the effect of pregnancy, decreased overestimation of breeding values of nonpregnant cows and did not overestimate breeding values of cows with short days open like models fitting days open. Month of pregnancy and stage of pregnancy models are recommended for estimation of adjustment factors for the effect of pregnancy on production traits.     

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.     

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 analysis of body condition score in first-parity Danish Holstein cows

The aim of this study was to test whether genetic components for body condition score (BCS) changed during lactation in first-parity Danish Holsteins. Data were extracted from the national conformation scoring system and consisted of 28,948 records from 3894 herds. Cows were scored once during lactation for BCS on a scale from 1 to 9 with increments of 1. The majority of records were made from d 30 to 150 of lactation. Mean BCS was 4.28 +/- 0.98. Body condition score was lowest in wk 8 to 10 from calving. A multivariate sire model with BCS recordings in six lactation stages treated as different traits was used to analyze the data. In addition, a random regression sire model was used to evaluate the changes in BCS as continuous functions of lactation stage. Estimates of heritability from the multivariate approach ranged from 0.14 to 0.29, and the estimated genetic correlations between BCS at different lactation stages were all higher than 0.82. The random regression model was based on Legendre polynomials (LP) specified on days in milk at scoring. To evaluate the change in mean BCS during lactation, the fixed part of the model included a fifth-order LP on the effect of days in milk at scoring. The highest order of fit used for the sire effect was a third-order LP, but based on likelihood ratio tests this could be reduced to a 0 order, i.e., a model with only the intercept term for the sire effect. This means that the genetic variation is constant over the investigated part of the lactation. Therefore, BCS can be considered the same trait during lactation, and a simple sire model can be used for prediction of breeding values.     

Within-herd heritability estimated with daughter-parent regression for yield and somatic cell score

Estimates of heritability within herd () that were generated with daughter-dam regression, daughter-sire regression, and REML were compared, and effects of adjusting lactation records for within-herd heritability on genetic evaluations were evaluated. Holstein records for milk, fat, and protein yields and somatic cell score (SCS) from the USDA national database represented herds in the US Northeast, Southeast, Midwest, and West. Four data subsets (457 to 499 herds) were randomly selected, and a large-herd subset included the 15 largest herds from the West and 10 largest herds from other regions. Subset heritabilities for yield and SCS were estimated assuming a regression model that included fixed covariates for effects of dam yield or SCS, sire predicted transmitting ability (PTA) for yield or SCS, herd-year-season of calving, and age within parity. Dam records and sire PTA were nested within herd as random covariates to generate within-herd heritability estimates that were regressed toward mean for the random subset. Heritabilities were estimated with REML using sire models (REML_SIRE), sire-maternal grandsire models (REML_MGS), and animal models (REML_ANIM) for each herd individually in the large-herd subset. Phenotypic variance for each herd was estimated from herd residual variance after adjusting for effects of year-season and age within parity. Deviations from herd-year-season mean were standardized to constant genetic variance across herds, and records were weighted according to estimated error variance to accommodate when estimating breeding values. Mean tended to be higher with daughter-dam regression (0.35 for milk yield) than with daughter-sire regression (0.24 for milk yield). Heritability estimates varied widely across herds (0.04 to 0.67 for milk yield estimated with daughter-dam regression), and deviated from subset means more for large herds than for small herds. Correlation with REML_ANIM was 0.68 for daughter-dam and was 0.45 for daughter-sire for milk yield. The correlation between daughter-sire and REML_MGS was greater than the correlation between daughter-dam and REML_MGS. Data adjustments had a minimal impact on breeding value bias. Within-herd heritability can be estimated rapidly using regression techniques with moderate accuracy, but adjusting lactation records for resulted in only a small improvement in the accuracy of genetic evaluations.     

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.     

Genomic prediction of lactation curves for milk,fat, protein,and somatic cell score in Holstein cattle

Application of random regression models (RRM) in a 2-step genomic prediction might be a feasible way to select young animals based on the complete pattern of the lactation curve. In this context, the prediction reliability and bias of genomic estimated breeding value (GEBV) for milk, fat, and protein yields and somatic cell score over days in milk (DIM) using a 2-step genomic approach were investigated. In addition, the effect of including cows in the training and validation populations was investigated. Estimated breeding values for each DIM (from 5 to 305 d) from the first 3 lactations of Holstein animals were deregressed and used as pseudophenotypes in the second step. Individual additive genomic random regression coefficients for each trait were predicted using RRM and genomic best linear unbiased prediction and further used to derive GEBV for each DIM. Theoretical reliabilities of GEBV obtained by the RRM were slightly higher than theoretical reliabilities obtained by the accumulated yield up to 305 d (P305). However, validation reliabilities estimated for GEBV using P305 were higher than for GEBV using RRM. For all traits, higher theoretical and validation reliabilities were estimated when incorporating genomic information. Less biased GEBV estimates were found when using RRM compared with P305, and different validation reliability and bias patterns for GEBV over time were observed across traits and lactations. Including cows in the training population increased the theoretical reliabilities and bias of GEBV; nonetheless, the inclusion of cows in the validation population does not seem to affect the regression coefficients and the theoretical reliabilities. In summary, the use of RRM in 2-step genomic prediction produced fairly accurate GEBV over the entire lactation curve for all analyzed traits. Thus, selecting young animals based on the pattern of lactation curves seems to be a feasible alternative in genomic selection of Holstein cattle for milk production traits.     

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.