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.     

Application of single-step single nucleotide polymorphism best linear unbiased predictor model with unknown-parent groups for type traits in Japanese Holsteins

The objectives of this study were to investigate the computational performance and the predictive ability and bias of a single-step SNP BLUP model (ssSNPBLUP) in genotyped young animals with unknown-parent groups (UPG) for type traits, using national genetic evaluation data from the Japanese Holstein population. The phenotype, genotype, and pedigree data were the same as those used in a national genetic evaluation of linear type traits classified between April 1984 and December 2020. In the current study, 2 data sets were prepared: the full data set containing all entries up to December 2020 and a truncated data set ending with December 2016. Genotyped animals were classified into 3 types: sires with classified daughters (S), cows with records (C), and young animals (Y). The computing performance and prediction accuracy of ssSNPBLUP were compared for the following 3 groups of genotyped animals: sires with classified daughters and young animals (SY); cows with records and young animals (CY); and sires with classified daughters, cows with records, and young animals (SCY). In addition, we tested 3 parameters of residual polygenic variance in ssSNPBLUP (0.1, 0.2, or 0.3). Daughter yield deviations (DYD) for the validation bulls and phenotypes adjusted for all fixed effects and random effects other than animal and residual (Y_adj) for the validation cows were obtained using the full data set from the pedigree-based BLUP model. The regression coefficients of DYD for bulls (or Y_adj for cows) on the genomic estimated breeding value (GEBV) using the truncated data set were used to measure the inflation of the predictions of young animals. The coefficient of determination of DYD on GEBV was used to measure the predictive ability of the predictions for the validation bulls. The reliability of the predictions for the validation cows was calculated as the square of the correlation between Y_adj and GEBV divided by heritability. The predictive ability was highest in the SCY group and lowest in the CY group. However, minimal difference was found in predictive abilities with or without UPG models using different parameters of residual polygenic variance. The regression coefficients approached 1.0 as the parameter of residual polygenic variance increased, but regression coefficients were mostly similar regardless of the use of UPG across the groups of genotyped animals. The ssSNPBLUP model, including UPG, was demonstrated as feasible for implementation in the national evaluation of type traits in Japanese Holsteins.     

Assessment of Poisson, logit, and linear models for genetic analysis of clinical mastitis in Norwegian Red cows

Clinical mastitis is typically coded as presence/absence during some period of exposure, and records are analyzed with linear or binary data models. Because presence includes cows with multiple episodes, there is loss of information when a count is treated as a binary response. The Poisson model is designed for counting random variables, and although it is used extensively in epidemiology of mastitis, it has rarely been used for studying the genetics of mastitis. Many models have been proposed for genetic analysis of mastitis, but they have not been formally compared. The main goal of this study was to compare linear (Gaussian), Bernoulli (with logit link), and Poisson models for the purpose of genetic evaluation of sires for mastitis in dairy cattle. The response variables were clinical mastitis (CM; 0, 1) and number of CM cases (NCM; 0, 1, 2, …). Data consisted of records on 36,178 first-lactation daughters of 245 Norwegian Red sires distributed over 5,286 herds. Predictive ability of models was assessed via a 3-fold cross-validation using mean squared error of prediction (MSEP) as the end-point. Between-sire variance estimates for NCM were 0.065 in Poisson and 0.007 in the linear model. For CM the between-sire variance was 0.093 in logit and 0.003 in the linear model. The ratio between herd and sire variances for the models with NCM response was 4.6 and 3.5 for Poisson and linear, respectively, and for model for CM was 3.7 in both logit and linear models. The MSEP for all cows was similar. However, within healthy animals, MSEP was 0.085 (Poisson), 0.090 (linear for NCM), 0.053 (logit), and 0.056 (linear for CM). For mastitic animals the MSEP values were 1.206 (Poisson), 1.185 (linear for NCM response), 1.333 (logit), and 1.319 (linear for CM response). The models for count variables had a better performance when predicting diseased animals and also had a similar performance between them. Logit and linear models for CM had better predictive ability for healthy cows and had a similar performance between them.     

Comparison of different models for genetic analysis of clinical mastitis in Austrian Fleckvieh dual-purpose cows

The performance of different models for genetic analyses of clinical mastitis in Austrian Fleckvieh dual-purpose cows was evaluated. The main objective was to compare threshold sire models (probit and logit) with linear sire and linear animal models using REML algorithm. For comparison, data were also analyzed using a Bayesian threshold sire model. The models were evaluated with respect to ranking of sires and their predictive ability in cross-validation. Only minor differences were observed in estimated variance components and heritability from Bayesian and REML probit models. Heritabilities for probit and logit models were 0.06 and 0.08, respectively, whereas heritabilities for linear sire and linear animal models were lower (0.02). Correlations among ranking of sires from threshold and linear sire models were high (>0.99), whereas correlations between any sire model (threshold or linear) and the linear animal model were slightly lower (0.96). The worst sires were ranked very similar across all models, whereas for the best sires some reranking occurred. Further, models were evaluated based on their ability to predict future data, which is one of the main concerns of animal breeders. The predictive ability of each model was determined by using 2 criteria: mean squared error and Pearson correlation between predicted and observed value. Overall, the 5 models did not differ in predictive ability. In contrast to expectations, sire models had the same predictive ability as animal models. Linear models were found to be robust toward departures from normality and performed equally well as threshold models.     

Genetic variance in micro-environmental sensitivity for milk and milk quality in Walloon Holstein cattle

Animals that are robust to environmental changes are desirable in the current dairy industry. Genetic differences in micro-environmental sensitivity can be studied through heterogeneity of residual variance between animals. However, residual variance between animals is usually assumed to be homogeneous in traditional genetic evaluations. The aim of this study was to investigate genetic heterogeneity of residual variance by estimating variance components in residual variance for milk yield, somatic cell score, contents in milk (g/dL) of 2 groups of milk fatty acids (i.e., saturated and unsaturated fatty acids), and the content in milk of one individual fatty acid (i.e., oleic acid, C18:1 cis-9), for first-parity Holstein cows in the Walloon Region of Belgium. A total of 146,027 test-day records from 26,887 cows in 747 herds were available. All cows had at least 3 records and a known sire. These sires had at least 10 cows with records and each herd × test-day had at least 5 cows. The 5 traits were analyzed separately based on fixed lactation curve and random regression test-day models for the mean. Estimation of variance components was performed by running iteratively expectation maximization-REML algorithm by the implementation of double hierarchical generalized linear models. Based on fixed lactation curve test-day mean models, heritability for residual variances ranged between 1.01 × 10⁻³ and 4.17 × 10⁻³ for all traits. The genetic standard deviation in residual variance (i.e., approximately the genetic coefficient of variation of residual variance) ranged between 0.12 and 0.17. Therefore, some genetic variance in micro-environmental sensitivity existed in the Walloon Holstein dairy cattle for the 5 studied traits. The standard deviations due to herd × test-day and permanent environment in residual variance ranged between 0.36 and 0.45 for herd × test-day effect and between 0.55 and 0.97 for permanent environmental effect. Therefore, nongenetic effects also contributed substantially to micro-environmental sensitivity. Addition of random regressions to the mean model did not reduce heterogeneity in residual variance and that genetic heterogeneity of residual variance was not simply an effect of an incomplete mean model.     

Genetic evaluation of susceptibility to clinical mastitis in Spanish Holstein cows

This study had 3 objectives: to estimate genetic parameters and predict sires’ transmitting abilities for clinical mastitis in a Spanish Holstein population, to propose a methodology for comparing models with different response variables by using a cost-based loss function, and to evaluate alternative genetic evaluation models by using this methodology. On-farm records for clinical mastitis from herds in 3 Spanish regions were analyzed as a binary trait (CM) and as number of episodes (NCM) per lactation. Linear and probit models were fitted for CM, whereas linear and Poisson models were used for NCM. Predictive ability of the models was evaluated by using the average predicted residual sum of squares from cross-validation and an alternative cost-based loss function. The loss function for model comparison was calculated by using average mastitis costs depending on the NCM and average cost per infected lactation. The average cost per infected lactation was $345.58, whereas the cost per lactation ranged from $204.86 to $985.44 for lactations with 1 to 5 cases, respectively. Management and hygiene practices on individual farms had a large impact on clinical mastitis because the herd-year variance was larger than that of other random effects considered. The sire variance was significantly different from zero, confirming that genetic variation exists for clinical mastitis. Estimates of heritability for CM using the linear and probit models were 0.07 and 0.10 on the underlying scale, respectively. For NCM, the estimate of heritability for the linear model was 0.10 and estimates for the Poisson model evaluated at the mean and the median of lambda on the underlying scale were 0.09 and 0.07, respectively. Regarding ranking of sires, the definition of response variable (CM or NCM) was of greater importance than the choice of statistical model. Cross-validation results indicated that models with the best fit for CM and NCM were the probit model and the linear model, respectively. However, a comparison across all models using the alternative cost-based loss function showed that using NCM as a response variable with a Poisson model provided the most accurate predictions of future costs associated with clinical mastitis.     

Genetic parameters for fertility of dairy bulls

Genetic parameters for male fertility and fertility ratings of AI bulls were obtained by analyzing 298,013 service records of cows with successive calving records. Cows were mated to 746 service bulls, which were progeny of 126 sires. The model for variance component estimation accounted for fixed effects of herd-year-seasons, sire of the service bull, age of mates, and random effects of service bull and residual error. Estimates of variances of service bulls and residual error components for bull fertility indicated almost 10% of the phenotypic variation for fertility is among AI bulls. Best linear unbiased prediction of fertility ratings of individual bulls with inclusion of sire and maternal grandsire relationships on these data permitted the evaluation of 886 AI bulls for bull fertility. Heritability for bull fertility computed as twice the regression of son on sire was .158. Differences in fertility ratings of AI bulls ranged from -.29 to .19. Prediction of fertility of young AI bulls and more accurate rating of proven bulls might be useful to the industry.     

Genetic analysis of days from calving to first insemination and days open in Danish Holsteins using different models and censoring scenarios

The objectives of this study were to estimate genetic parameters and evaluate models for genetic evaluation of days from calving to first insemination (ICF) and days open (DO). Data including 509,512 first-parity records of Danish Holstein cows were analyzed using 5 alternative sire models that dealt with censored records in different ways: 1) a conventional linear model (LM) in which a penalty of 21 d was added to censored records; 2) a bivariate threshold-linear model (TLM), which included a threshold model for censoring status (0, 1) of the observations, and a linear model for ICF or DO without any penalty on censored records; 3) a right-censored linear model (CLM); 4) a Weibull proportional hazard model (SMW); and 5) a Cox proportional hazard model (SMC) constructed with piecewise constant baseline hazard function. The variance components for ICF and DO estimated from LM and TLM were similar, whereas CLM gave higher estimates of both additive genetic and residual components. Estimates of heritability from models LM, TLM, and CLM were very similar (0.102 to 0.108 for ICF, and 0.066 to 0.069 for DO). Heritabilities estimated using model SMW were 0.213 for ICF and 0.121 for DO in logarithmic scale. Using SMC, the estimates of heritability, defined as the log-hazard proportional factor for ICF and DO, were 0.013 and 0.009, respectively. Correlations between predicted transmitting ability from different models for sires with records from at least 20 daughters were far from unity, indicating that different models could lead to different rankings. The largest reranking was found between SMW and SMC, whereas negligible reranking was found among LM, TLM, and CLM. The 5 models were evaluated by comparing correlations between predicted transmitting ability from different data sets (the whole data set and 2 subsets, each containing half of the whole data set), for sires with records from at least 20 daughters, and χ² statistics based on predicted and observed daughter frequencies using a cross validation. The model comparisons showed that SMC had the best performance in predicting breeding values of the 2 traits. No significant difference was found among models LM, TLM, and CLM. The SMW model had a relatively poor performance, probably because the data are far from a Weibull distribution. The results from the present study suggest that SMC could be a good alternative for predicting breeding values of ICF and DO in the Danish Holstein population.     

Estimation of heterogeneous within-herd variance components using empirical Bayes methods: a simulation study.

Genetic evaluation using BLUP can accommodate heterogeneous variances if the necessary variance components are known; this may require estimation of variance components within each heterogeneous subclass. Properties of sire and residual variance estimates obtained by an empirical Bayes approach, which combines within-herd and prior estimates, were examined via simulation. Prior estimates were obtained using REML across herds, as if variances were homogeneous. Convergence was improved by incorporation of prior information such that variance component estimates could be obtained in within-herd situations for which a REML algorithm failed to converge. Accuracy of sire variance estimates was greatest when both within-herd and prior information were used, but improvement in accuracy of residual variance estimates associated with incorporation of prior information was minimal. Correlations between sires' standardized true transmitting abilities and PTA that used empirical Bayes variance estimates were larger than those obtained when heterogeneity was ignored. Proportions of sires selected, based on standardized PTA, from environments with differing genetic and residual variances became more uniform as the relative weight placed on within-herd data in variance estimation increased. Thus, useful variance component estimates can be obtained within individual herds by using empirical Bayes methods with across-herd estimates as prior information; this may allow prediction of breeding values that are less influenced by heterogeneous variances.     

Predictive abilities of different statistical models for analysis of survival data in dairy cattle

The objective of this study was to compare alternative trait definitions and statistical models for genetic evaluation of survival in dairy cattle. Data from the first 5 lactations of 808,750 first-crop daughters of 3,064 Norwegian Red sires were analyzed. Seven sire models were used for genetic analyses: linear and threshold cross-sectional models for binary survival scores from first lactation; a linear multi-trait model for survival scores from the first 3 lactations; linear and threshold repeatability models for survival scores from the first 5 lactations; a Weibull frailty model for herd life in first lactation; and a Weibull frailty model for herd life in the first 5 lactations. The models were compared to assess predictive ability of sire estimated breeding values with respect to average survival 365 d after first calving for second-crop daughters (not included in calculation of predicted transmitting abilities) of 375 elite sires. Generally, the linear multi-trait model analyzing survival in the first 3 lactations as correlated traits gave more-accurate predicted sire breeding values compared with both linear and Weibull frailty models using data from first lactation only, even when the latter models were extended to include data up to the sixth lactation. The Weibull frailty models did not improve predictive ability of sire estimated breeding values over what was obtained using a simple cross-sectional linear model for binary survival in first lactation.     

Genetic parameters and responses of linear type,yield traits,and somatic cell scores to divergent selection for predicted transmitting ability for type in Holsteins

The objective was to examine the direct and correlated responses of linear type, yield traits, and somatic cell scores (SCS) to divergent selection for predicted transmitting ability for type (PTAT) in Holsteins, while maintaining selection for yield traits across lines. For four generations, one-half of the University of Nebraska research Holstein herd was bred to Holstein sires with PTAT > 1.50 and the other half to sires with PTAT < 1.25, with nearly equal predicted transmitting abilities for yield traits for both groups. Estimates of genetic and residual correlations and heritabilities were obtained from REML estimates of (co)variance components. Model for type traits included fixed effect of date cows were classified, effects of age in days at freshening, and stage of lactation at classification. Year-season when cows freshened was fixed effect in model for yield and SCS. Animal genetic and residual effects were random. Final score, milk, fat, and protein yields, and SCS had heritability estimates of 0.38, 0.13,0.22, 0.09, and 0.38, respectively. Heritability estimates for type traits ranged from 0.04 to 0.52. Estimates of genetic correlations of final score with SCS and milk, fat, and protein yields were -0.64, 0.01, -0.18, and 0.06, respectively. Estimates of genetic correlations among linear type traits ranged from -0.77 to 1.00. Means of estimated breeding values for final score, stature, strength, body depth, fore udder attachment, rear udder height and width, udder cleft, udder depth, and front teat placement were significantly different between lines in the third generation. Milk, fat, and protein yields were not significantly different between lines in third generation, whereas SCS was significantly different. Estimate of genetic correlation between final score and SCS suggest that selection on PTAT would result in a change for SCS. In this study, divergent selection on PTAT of sires had a significant effect on udder and body traits, but little or no effect on feet and leg traits.     

Contemporary groups for genetic evaluations

Contemporary groups are used to remove biases from genetic evaluations due to differential effects such as management associated with the grouping. Numerous groups, however, can result in small numbers of records per subclass with associated loss of effective number of daughters for sire evaluation and increased prediction error variance. Thus, in practice, mean square error, bias squared plus prediction error variance, may be more meaningful than bias alone or prediction error variance. Considering contemporary groups as fixed removes bias due to association between effects corresponding to contemporary groups and sires. If contemporary groups are considered random, then effective number of daughters is increased at the expense of possible bias. Various compromises may be effective for increasing genetic gain. Arbitrary definition of contemporary groups can include herd-year-season of freshening, lactation number, registered or nonregistered, sampling or postsampling daughters, and special treatments among others. The assumption of homogeneous genetic and residual variances is likely to be incorrect. Alternative methods include simple transformations, a two-step transformation, and multiple trait modeling. Multiple trait analyses may include the assumption of genetic correlations of unity, common genetic and heterogeneous residual variances, and joint estimation of genetic values and variances.     

Number of inseminations to conception in Holstein cows using censored records and time-dependent covariates

Three methodologies that accommodate censoring or time-dependent covariates were used to estimate variance components for number of inseminations to conception. Data included 80,071 lactation records and 143,927 artificial inseminations in 47,509 Spanish Holstein cows. Up to 4 inseminations to conception, along with their respective censoring information, were analyzed. An ordinal-censored threshold model (CTM), a sequential threshold model (STM), and a grouped survival analysis via a discrete proportional hazards model (DPH) were implemented. Sire variance estimates on the liability scale were 0.016 and 0.010 for CTM and STM, respectively, and 0.012 for DPH on the logarithmic scale. Heritability estimates on the liability scale were 0.050 and 0.038 with CTM and STM, respectively. All models led to similar rankings of sires, and the strong correlations (0.97 to 0.98) between methodologies suggested robustness in ranking of sires of cows. Service sire variance estimates were 0.021 for both CTM and STM; DPH led to an approximate service sire variance of 0.020. Rankings for service sires between methodologies ranged from 0.76 to 0.90. These lower values are most likely due to differences in the treatment of time-dependent covariates.The STM had greater predictive ability of daughter fertility at first insemination than the other methodologies. However, the CTM predicted daughter fertility more accurately in subsequent inseminations. The DPH and STM had a similar predictive ability of daughter fertility in second and subsequent inseminations.     

Effect of parentage misidentification on estimates of genetic parameters for milk yield in the Mediterranean Italian buffalo population

The objective of this study was to evaluate the effect of parentage misidentification on estimation of genetic parameters for the Italian buffalo population for milk yield from 45,194 lactation records of 23,104 Italian buffalo cows. Animals were grouped into 10 data sets in which sires and dams were DNA identified, or reported from the pedigree, or unknown. A derivative-free restricted maximum likelihood method was used to estimate components of variance with a repeatability model. The model contained age at calving nested within parity and days from calving to conception as linear covariates, herd-year-seasons as fixed effects, and additive genetic, permanent environmental, and temporary environmental effects as random effects. Estimates of heritability (±SE) ranged from 0.00 ± 0.099 (sires and dams as reported in the pedigree) to 0.39 ± 0.094 (sires DNA identified and dams as reported in the pedigree). When identification of sires was as reported in the pedigree, estimates of heritability were close to zero. These small estimates indicate that a large proportion of reported paternity is incorrect. When sires are unknown and dams are DNA identified, the proportion of variance due to sires seems to be captured in the estimate of permanent environmental variance as a fraction of phenotypic variance. Therefore, as heritability decreased, permanent environmental variance increased about the same amount. Data sets with dams identified from pedigree and sires DNA identified showed the largest estimate of heritability (0.39), which was essentially the same as when dams were DNA identified (0.38). This result supports that most dams are correctly reported from the pedigree. Genetic progress should be much greater with bulls DNA identified because of greater heritability, but without artificial insemination and progeny testing, progress would be slow and would depend mostly on selection of sires based on dam estimated breeding values. Implementation of artificial insemination programs and DNA testing to identify sires are the keys for increasing genetic progress in the Italian buffalo population.     

A comparison of alternative methods for predicting the carcass composition of crossbred lambs of different breeds and crosses

Carcass data for a total of 2808 lambs from three breed trials were used to evaluate a series of linear measurements, visual scores and the proportions of tissues in joints as predictors of carcass composition. The trials involved crossbred lambs out of different dam types by sires of the main British meat breeds and by Ile de France, Oldenburg and Texel sires. Each trial was carried out over a number of years and involved approximately equal numbers of female and castrated male lambs. Potential predictors were examined in terms of the precision of prediction and in terms of the robustness of prediction equations to differences in sire breed and sex. The overall standard deviation (s.d.) of carcass lean percentage averaged over trials was 4·3. Combinations of simple measurements, including visual fat scores, percentage perinephric and retroperitoneal fat in carcass and M. longissimus dimensions achieved a residual s.d. of 2·5 for carcass lean percentage. The application of an overall prediction equation to individual sire breed means resulted in considerable bias (predicted-actual lean percentage): the mean square deviation was 0·75. In comparison, the sex differences were relatively unimportant. The precision of sample joints was examined in relation to their cost of dissection. The best end neck and shoulder joints offered a high level in relation to cost: typical residual s.d. were 1·5 for carcass lean percentage. Joints and combination of joints with high predictive precision tended to have equations that were robust to differences between sire breeds.     

Inverse of a Matrix of Relationships Due to Sires and Maternal Grandsires

The most important identifiable relationships among sires used in artificial insemination are due to common sires and maternal grandsires. A rapid method for finding the inverse of a numerator relationship matrix resulting from use of these two points in the pedigree has been developed. As a consequence, relationships among all sires to be evaluated can be incorporated easily into best linear unbiased prediction of future progeny of these sires.     

Multiple trait and random regression models using linear splines for genetic evaluation of multiple breed populations

This study aimed to verify if random regression models using linear splines (RRMLS) are suitable for identifying genetic parameters in multiple-breed populations and also to investigate whether an interaction exists between the breeding value (BV) of sires and their progeny breed group. Ten populations were simulated by crossing 2 breeds with distinct genetic variance and nonzero segregation variance. To obtain the genetic parameters, 2 models were used: a multiple-trait model (MULT), in which the trait was considered distinct when evaluated in each group (1/2P₁ + 1/2P₂, 5/8P₁ + 3/8P₂, and 3/4P₁ + 1/4P₂), and a RRMLS with the spline polynomial knots adjusted to these same groups. The genetic parameters estimated through MULT and RRMLS did not differ from the simulated values. The correlations between BV (simulated and estimated) of animals were high and varied from 0.74 to 0.76, which indicates the efficiency of using MULT and RRMLS for predicting BV. Using field data, the traits age at first calving (AFC), first lactation length (LL), and 305-d milk yield (MY-305) from a multiple-breed population of Holstein-Gyr cattle were analyzed. The BV of animals were modeled through RRMLS with 3, 5, and 7 knots, distributed in accordance with the fraction of Holstein breed in each progeny breed group. It was verified that RRMLS with 7 knots for adjusting mean trajectories and genetic effects, with homogeneous residual variance, best fit AFC and LL. For MY-305, the best fit for mean trajectory and genetic effects was the RRMLS with 5 knots and with homogeneous residual variance. The posterior means of heritability varied from 0.21 to 0.48, 0.21 to 0.38, and 0.10 to 0.33 for AFC, LL, and MY-305, respectively. Estimates from genetic parameters obtained by using RRMLS with field data showed that this model is a useful tool for genetic evaluations of populations formed by a great number of breed groups. An interaction occurred between the BV of sires and their progeny breed group, and the genetic parameters for AFC, LL, and MY-305 traits from a multiple-breed population depend on breed composition of the progeny from which the evaluations are based.     

Genetic parameters for first lactation milk yields at three levels of herd production

A multivariate linear model was used to estimate sire variance and covariance components and residual variance components for first lactation milk yield and logarithms of yield at three herd production levels using Restricted Maximum Likelihood with the Expectation-Maximization algorithm. Data for four separate analyses were 305-d, mature equivalent first lactation milk records from cows sired artificially in the northeastern United States that freshened in 1970, 1971, 1976, and 1984. Respective numbers of records for each year were 42,618, 40,207, 33,581, and 34,196. Corresponding numbers of sires were 298, 289, 305, and 313. Herd production level was defined by mean yield of all cows freshening in same herd-year-season. For untransformed records sire and residual components of variance increased as mean increased, both within and between years. Correlations between sire effects at different production levels were all above .85. Heritabilities increased as production level increased. These results indicate that it may be necessary to account for heterogeneous genetic and environmental variance in sire evaluations. For logarithms of yield, sire components of variance were similar for each of the three production levels within a year. Residual components for logarithms decreased as production level increased. Change in variance from one production level to another was considerably more for logarithms than for untransformed yields.     

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.     

Effect of sire of fetus on subsequent 90-day production of the Holstein dam

Data on calving ease and 90-day milk, fat, protein, fat percent, and protein percent were available on 8,817 Holstein cows enrolled in the Quebec Dairy Herd Analysis Service. These observations were distributed in 802 herds, and they represented 124 service sires. Estimates of the variance components associated with the service sire (sire of fetus) were obtained by Minimum Norm Quadratic Unbiased Estimation procedures. Two models were fitted; one model included herd, month of calving, age of cow, and sire of cow as fixed effects and service sire and residual as random effects, whereas a second model included calving ease as an additional fixed effect. Variance components and percentages of variance accounted for by service sire were similar under both models. Proportions of variance accounted for by service sire were 1.1, .3, .5, .2, and .3% for 90-day milk, fat, protein, fat percent, and protein percent.