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.     

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on 1/6/2010orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.     

Multiple-trait random regression models for the estimation of genetic parameters for milk,fat, and protein yield in buffaloes

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21–0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal.     

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.     

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.     

Genetic parameters for test-day yield of milk, fat and protein in buffaloes estimated by random regression models

The test-day yields of milk, fat and protein were analysed from 1433 first lactations of buffaloes of the Murrah breed, daughters of 113 sires from 12 herds in the state of S?o Paulo, Brazil, born between 1985 and 2007. For the test-day yields, 10 monthly classes of lactation days were considered. The contemporary groups were defined as the herd-year-month of the test day. Random additive genetic, permanent environmental and residual effects were included in the model. The fixed effects considered were the contemporary group, number of milkings (1 or 2 milkings), linear and quadratic effects of the covariable cow age at calving and the mean lactation curve of the population (modelled by third-order Legendre orthogonal polynomials). The random additive genetic and permanent environmental effects were estimated by means of regression on third- to sixth-order Legendre orthogonal polynomials. The residual variances were modelled with a homogenous structure and various heterogeneous classes. According to the likelihood-ratio test, the best model for milk and fat production was that with four residual variance classes, while a third-order Legendre polynomial was best for the additive genetic effect for milk and fat yield, a fourth-order polynomial was best for the permanent environmental effect for milk production and a fifth-order polynomial was best for fat production. For protein yield, the best model was that with three residual variance classes and third- and fourth-order Legendre polynomials were best for the additive genetic and permanent environmental effects, respectively. The heritability estimates for the characteristics analysed were moderate, varying from 0·16±0·05 to 0·29±0·05 for milk yield, 0·20±0·05 to 0·30±0·08 for fat yield and 0·18±0·06 to 0·27±0·08 for protein yield. The estimates of the genetic correlations between the tests varied from 0·18±0·120 to 0·99±0·002; from 0·44±0·080 to 0·99±0·004; and from 0·41±0·080 to 0·99±0·004, for milk, fat and protein production, respectively, indicating that whatever the selection criterion used, indirect genetic gains can be expected throughout the lactation curve.     

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.     

Genotype by heat stress interactions for production and functional traits in dairy cows from an across-generation perspective

The aim of this study was to analyze time-lagged heat stress (HS) effects during late gestation on genetic co(variance) components in dairy cattle across generations for production, female fertility, and health traits. The data set for production and female fertility traits considered 162,492 Holstein Friesian cows from calving years 2003 to 2012, kept in medium-sized family farms. The health data set included 69,986 cows from calving years 2008 to 2016, kept in participating large-scale co-operator herds. Production traits were milk yield (MKG), fat percentage (fat%), and somatic cell score (SCS) from the first official test-day in first lactation. Female fertility traits were the nonreturn rate after 56 d (NRR56) in heifers and the interval from calving to first insemination (ICFI) in first-parity cows. Health traits included clinical mastitis (MAST), digital dermatitis (DD), and endometritis (EM) in the early lactation period in first-parity cows. Meteorological data included temperature and humidity from public weather stations in closest herd distance. The HS indicator was the temperature-humidity index (THI) during dams' late gestation, also defined as in utero HS. For the genetic analyses of production, female fertility, and health traits in the offspring generation, a sire-maternal grandsire random regression model with Legendre polynomials of order 3 for the production and of order 2 for the fertility and health traits on prenatal THI, was applied. All statistical models additionally considered a random maternal effect. THI from late gestation (i.e., prenatal climate conditions), influenced genetic parameter estimates in the offspring generation. For MKG, heritabilities and additive genetic variances decreased in a wave-like pattern with increasing THI. Especially for THI >58, the decrease was very obvious with a minimal heritability of 0.08. For fat% and SCS, heritabilities increased slightly subjected to prenatal HS conditions at THI >67. The ICFI heritabilities differed marginally across THI [heritability (h²) = 0.02–0.04]. For NRR56, MAST, and DD, curves for heritabilities and genetic variances were U-shaped, with largest estimates at the extreme ends of the THI scale. For EM, heritability increased from THI 25 (h² = 0.13) to THI 71 (h² = 0.39). The trait-specific alterations of genetic parameters along the THI gradient indicate pronounced genetic differentiation due to intrauterine HS for NRR56, MAST, DD, and EM, but decreasing genetic variation for MKG and ICFI. Genetic correlations smaller than 0.80 for NRR56, MAST, DD, and EM between THI 65 with corresponding traits at remaining THI indicated genotype by environment interactions. The lowest genetic correlations were identified when considering the most distant THI. For MKG, fat%, SCS, and ICFI, genetic correlations throughout were larger than 0.80, disproving concerns for any genotype by environment interactions. Variations in genetic (co)variance components across prenatal THI may be due to epigenetic modifications in the offspring genome, triggered by in utero HS. Epigenetic modifications have a persistent effect on phenotypic responses, even for traits recorded late in life. However, it is imperative to infer the underlying epigenetic mechanisms in ongoing molecular experiments.     

Genetic parameters across lactation for feed intake,fat- and protein-corrected milk,and liveweight in first-parity Holstein cattle

Breeding values for dry matter intake (DMI) are important to optimize dairy cattle breeding goals for feed efficiency. However, generally, only small data sets are available for feed intake, due to the cost and difficulty of measuring DMI, which makes understanding the genetic associations between traits across lactation difficult, let alone the possibility for selection of breeding animals. However, estimating national breeding values through cheaper and more easily measured correlated traits, such as milk yield and liveweight (LW), could be a first step to predict DMI. Combining DMI data across historical nutritional experiments might help to expand the data sets. Therefore, the objective was to estimate genetic parameters for DMI, fat- and protein-corrected milk (FPCM) yield, and LW across the entire first lactation using a relatively large data set combining experimental data across the Netherlands. A total of 30,483 weekly records for DMI, 49,977 for FPCM yield, and 31,956 for LW were available from 2,283 Dutch Holstein-Friesian first-parity cows between 1990 and 2011. Heritabilities, covariance components, and genetic correlations were estimated using a multivariate random regression model. The model included an effect for year-season of calving, and polynomials for age of cow at calving and days in milk (DIM). The random effects were experimental treatment, year-month of measurement, and the additive genetic, permanent environmental, and residual term. Additive genetic and permanent environmental effects were modeled using a third-order orthogonal polynomial. Estimated heritabilities ranged from 0.21 to 0.40 for DMI, from 0.20 to 0.43 for FPCM yield, and from 0.25 to 0.48 for LW across DIM. Genetic correlations between DMI at different DIM were relatively low during early and late lactation, compared with mid lactation. The genetic correlations between DMI and FPCM yield varied across DIM. This correlation was negative (up to −0.5) between FPCM yield in early lactation and DMI across the entire lactation, but highly positive (above 0.8) when both traits were in mid lactation. The correlation between DMI and LW was 0.6 during early lactation, but decreased to 0.4 during mid lactation. The highest correlations between FPCM yield and LW (0.3–0.5) were estimated during mid lactation. However, the genetic correlations between DMI and either FPCM yield or LW were not symmetric across DIM, and differed depending on which trait was measured first. The results of our study are useful to understand the genetic relationship of DMI, FPCM yield, and LW on specific days across lactation.     

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.     

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications.     

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

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

Modeling lactation curves and estimation of genetic parameters for first lactation test-day records of French Holstein cows

Several functions were used to model the fixed part of the lactation curve and genetic parameters of milk test-day records to estimate using French Holstein data. Parametric curves (Legendre polynomials, Ali-Schaeffer curve, Wilmink curve), fixed classes curves (5-d classes), and regression splines were tested. The latter were appealing because they adjusted the data well, were relatively insensitive to outliers, were flexible, and resulted in smooth curves without requiring the estimation of a large number of parameters. Genetic parameters were estimated with an Average Information REML algorithm where the average information matrix and the first derivatives of the likelihood functions were pooled over 10 samples. This approach made it possible to handle larger data sets. The residual variance was modeled as a quadratic function of days in milk. Quartic Legendre polynomials were used to estimate (co)variances of random effects. The estimates were within the range of most other studies. The greatest genetic variance was in the middle of the lactation while residual and permanent environmental variances mostly decreased during the lactation. The resulting heritability ranged from 0.15 to 0.40. The genetic correlation between the extreme parts of the lactation was 0.35 but genetic correlations were higher than 0.90 for a large part of the lactation. The use of the pooling approach resulted in smaller standard errors for the genetic parameters when compared to those obtained with a single sample.     

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.     

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.     

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.     

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.     

Genetic parameters for first and second lactation milk yields of Polish black and white cattle with random regression test-day models

Single- and two-trait random regression models were applied to estimate variance components of test-day records of milk, fat, and protein yields in the first and second lactation of Polish Black and White cattle. The model included fixed herd test-day effect, three covariates to describe lactation curve nested within age-season classes, and random regressions for additive genetic and permanent environmental effects. In two-parity models, each parity was treated as a separate trait. For milk and the two-parity model, heritabilities were in the range of 0.14 to 0.19 throughout first lactation and 0.10 to 0.16 throughout second lactation. For fat, heritabilities were within 0.11 to 0.16 and 0.11 to 0.22 throughout first and second lactations, respectively. For protein in the two-parity model, heritabilities were within 0.10 to 0.15 throughout most of first lactation and within 0.06 to 0.15 throughout the most of second lactation. For milk, genetic correlations between the first and second parities were 0.6 at the beginning of the lactation, rising to 0.9 in the middle, and 0.8 at the end of the lactation. For fat, the corresponding correlations were 0.6, 0.8, and 0.7, respectively, and for protein were 0.6, 0.8, and 0.8, respectively. Heritability estimates for all traits were flatter for the two-parity model. Relatively smooth genetic and permanent environmental variances with the two-parity model indicated that large swings of heritabilities could be artifacts of single-trait random regression models. High correlations between most of test day records across lactations suggested that a repeatability model could be considered as an alternative to a multiple-trait model to analyze multiple parities.     

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.     

Climate sensitivity of milk production traits and milk fatty acids in genotyped Holstein dairy cows

The aim of this study was the evaluation of climate sensitivity via genomic reaction norm models [i.e., to infer cow milk production and milk fatty acid (FA) responses on temperature-humidity index (THI) alterations]. Test-day milk traits were recorded between 2010 and 2016 from 5,257 first-lactation genotyped Holstein dairy cows. The cows were kept in 16 large-scale cooperator herds, being daughters of 344 genotyped sires. The longitudinal data consisted of 47,789 test-day records for the production traits milk yield (MY), fat yield (FY), and protein yield (PY), and of 20,742 test-day records for 6 FA including C16:0, C18:0, saturated fatty acids (SFA), unsaturated fatty acids (UFA), monounsaturated fatty acids (MUFA), and polyunsaturated fatty acids (PUFA). After quality control of the genotypic data, 41,057 SNP markers remained for genomic analyses. Meteorological data from the weather station in closest herd distance were used for the calculation of maximum hourly daily THI. Genomic reaction norm models were applied to estimate genetic parameters in a single-step approach for production traits and FA in dependency of THI at different lactation stages, and to evaluate the model stability. In a first evaluation strategy (New_sire), all phenotypic records from daughters of genotyped sires born after 2010 were masked, to mimic a validation population. In the second strategy (New_env), only daughter records of the new sires recorded in the most extreme THI classes were masked, aiming at predicting sire genomic estimated breeding values (GEBV) under heat stress conditions. Model stability was the correlation between GEBV of the new sires in the reduced data set with respective GEBV estimated from all phenotypic data. Among all test-day production traits, PY responded as the most sensitive to heat stress. As observed for the remaining production traits, genetic variances were quite stable across THI, but genetic correlations between PY from temperate climates with PY from extreme THI classes dropped to 0.68. Genetic variances in dependency of THI were very similar for C16:0 and SFA, indicating marginal climatic sensitivity. In the early lactation stage, genetic variances for C18:0, MUFA, PUFA, and UFA were significantly larger in the extreme THI classes compared with the estimates under thermoneutral conditions. For C18:0 and MUFA, PUFA, and UFA in the middle THI classes, genetic correlations in same traits from the early and the later lactation stages were lower than 0.50, indicating strong days in milk influence. Interestingly, within lactation stages, genetic correlations for C18:0 and UFA recorded at low and high THI were quite large, indicating similar genetic mechanisms under stress conditions. The model stability was improved when applying the New_env instead of New_sire strategy, especially for FA in the first stage of lactation. Results indicate moderately accurate genomic predictions for milk traits in extreme THI classes when considering phenotypic data from a broad range of remaining THI. Phenotypically, thermal stress conditions contributed to an increase of UFA, suggesting value as a heat stress biomarker. Furthermore, the quite large genetic variances for UFA at high THI suggest the consideration of UFA in selection strategies for improved heat stress resistance.