Potential effects of hormonal synchronized breeding on genetic evaluations of fertility traits in dairy cattle: A simulation study

About 30% of producers use hormone protocols to synchronize ovulation and perform timed artificial insemination (AI) in Canada. Days from calving to first service (CTFS) and first service to conception (FSTC) become masked phenotypes leading to biased genetic evaluations of cows for these fertility traits. The objectives of this study were to (1) demonstrate and quantify the potential amount of bias in genetic evaluations, and (2) find a procedure that could remove the bias. Simulation was used for both objectives. The proposed solution was to identify cows that have been treated by hormone protocols, make their CTFS and FSTC missing, and perform a multiple trait analysis including traits that have high genetic correlations with CTFS and FSTC, and which are not affected by the hormone protocols themselves. A total of 12 scenarios (S1-S12) were tested, changing the percentage of herds and cows that were randomly selected to be under timed AI. Cows that were given hormone protocols had CTFS of 86 d and FSTC of 0, which were used in genetic evaluation. Four criteria were used to indirectly measure the presence of bias: (1) the correlation between true (TBV) and estimated (EBV) breeding values (accuracy); (2) the differences in the mean EBV of top 25, 50, and 75 sires; (3) changes in correlation between TBV and EBV rankings; and (4) the changes in mean EBV over the simulated generations. All criteria changed unfavorably and proportionally to the increased use of timed AI. The accuracy within each class of animals (cows, dams, or sires) decreased proportionally with increased use of timed AI, varying from 0.32 (S12) to 0.52 (S1) for bull EBV for CTFS. The average EBV of the top sires (best 25, 50, 75, or 100 sires) approached population average EBV values when increasing the number of treated animals. The sire rank correlation between EBV and TBV within simulated scenarios was smaller for scenarios with more synchronized animals, going from 0.38 (S12) to 0.67 (S1). The long-term use of hormonal synchronized cows clearly decreased the mean EBV over generations in the population for CTFS and FSTC. The inclusion of genetically correlated traits in a multiple trait model was effective in removing the bias due to the presence of hormonal synchronized cows. However, given the constraints within the simulation, it is important that further investigation with real data is conducted to determine the true effect of including timed AI records within genetic evaluations of fertility traits in dairy cattle.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

Necessary changes to improve animal models

Animal models evolved from sire models and inherited some issues that affected sire models. Those issues include definition and treatment of contemporary groups, accounting for time trends and dealing with animals having unknown parents. The assumptions and limitations of the animal model need to be kept in mind. This review of the animal model will discuss the issues and will recommend enhancements to animal models for future applications.

A method for the prediction of multitrait breeding values for use in stochastic simulation to compare progeny-testing schemes, with large progeny groups for proven sires

A method of approximating estimated breeding values (EBV) from a multivariate distribution of true breeding values (TBV) and EBV is proposed for use in large-scale stochastic simulation of alternative breeding schemes with a complex breeding goal. The covariance matrix of the multivariate distributions includes the additive genetic (co)variances and approximated prediction error (co)variances at different selection stages in the life of the animal. The prediction error (co)variance matrix is set up for one animal at a time, utilizing information on the selection candidate and its offspring, the parents, as well as paternal and maternal half- sibs. The EBV are a regression on TBV taking individual uncertainty into account, but with additional 'free' variation drawn at random. With the current information included in the calculation of the prediction error variance of a selection candidate, it is concluded that the method can be used to optimize progeny-testing schemes, where the progeny-tested sires are utilized with large progeny groups, e.g. through artificial insemination.

Adaptive immune response, survival, and somatic cell score between postpartum Holstein and Norwegian Red × Holstein first-calf heifers

The objectives of this study were to evaluate antibody (AMIR) and cell-mediated immune responses (CMIR), survival, and somatic cell score (SCS) between purebred Holstein (HO) and crossbred Norwegian Red × Holstein (NRHO) first-calf heifers postpartum. Additionally, immune response traits observed as calves in a previous study were correlated with their immune response traits as first-calf heifers. Heifers, previously immunized as calves, were bled and reimmunized 6 to 9 d postcalving with known type 1 and type 2 antigens and human serum albumin (HSA). Seven days later, heifers were rebled, and background skinfold measurements of the tail fold were taken. Intradermal injections of PBS and type 1 antigen were administered on either side of the tail fold. On d 9 final skinfold measurements were taken and used to assess delayed-type hypersensitivity (DTH) as an indicator of CMIR. Blood samples were also collected for a final time on d 14 from heifers that received the antigen HSA. Serum was obtained from blood collected on d 0, 7, and 14 and analyzed by ELISA to assess AMIR. Data on survival and somatic cell count, which was converted to SCS, were obtained from CanWest Dairy Herd Improvement (DHI). All SCS, survival, and immune response data were analyzed using general linear models to determine significance between HO and NRHO first-calf heifers. To determine residual correlations between immune response traits observed in calves to their responses as first-calf heifers, residuals were obtained from models, and correlations between traits were determined using PROC CORR in SAS. Results showed NRHO had a greater primary IgG antibody response to HSA and greater tertiary IgG antibody response to the type 2 antigen compared with HO. Crossbreds (NRHO)also had significantly greater DTH response (P < 0.05) and, in general, greater survival from calving to 100 d in milk (dim), 100 to 305 dim, calving to 305 dim, and age at immune response testing as calf to 305 dim. No difference was observed between breeds for SCS. Results also showed most correlations between calf and first-calf heifer immune response traits were found to be positive and significant (P < 0.05). In conclusion, NRHO heifers have greater survival, which likely relates at least in part to increases in aspects of both AMIR and CMIR and could indicate that crossbred heifers have enhanced disease resistance.

Antibody and cell-mediated immune responses and survival between Holstein and Norwegian Red × Holstein Canadian calves

As an extension of a former study, the objectives of this study were to evaluate purebred Holstein (HO; n=140) and crossbred Norwegian Red × Holstein (NRFX; n=142) calves for antibody (AMIR) and cell-mediated immune responses (CMIR) as well as survival. Blood was collected on d 0, 14, and 21, and calves were immunized on d 0 and 14 with type 1 (Candida albicans) and type 2 (hen egg white lysozyme) antigens, which have been shown to induce CMIR and AMIR, respectively. Day 21 background skin-fold measurements of either side of the tail-fold were taken and intradermal injections of test (type 1 antigen) and control (phosphate saline buffer) were administered. Day 23 final skin-fold measurements were taken to assess delayed type hypersensitivity as an indicator of CMIR. Survival data were obtained from CanWest Dairy Herd Improvement. Statistical Analysis System general linear models were used to analyze all immune response and survival data and to determine statistical significance between breeds. Results showed that NRFX had greater primary IgM, IgG, IgG1, and secondary IgG1 antibody response, as well as greater primary IgG1:IgG2 ratio to the type 2 antigen compared with HO. The NRFX also had greater primary IgG1 and IgG2, and secondary IgG2 antibody response as well as greater primary IgG1:IgG2 ratio to the type 1 antigen. The NRFX calves had a tendency toward greater survival from age at immune response testing to calving. No difference was observed between breeds for other secondary antibody response traits or delayed type hypersensitivity. Results indicate NRFX have greater AMIR and therefore may have enhanced defense against extracellular pathogens. This may contribute to increased survival compared with HO. Both breeds, however, likely have similar defense against intracellular pathogens, because no differences in CMIR were observed. In general, these results may suggest that crossbreeding could improve resistance to certain diseases in dairy calves, resulting in decreased input costs to producers for crossbred calves compared with purebred calves. However, more research with larger sample sizes and different breeds should be conducted to confirm these results and obtain a complete picture of the benefits of crossbreeding on immune response traits in calves.

Test-day somatic cell score, fat-to-protein ratio and milk yield as indicator traits for sub-clinical mastitis in dairy cattle

Test-day (TD) records of milk, fat-to-protein ratio (F:P) and somatic cell score (SCS) of first-lactation Canadian Holstein cows were analysed by a three-trait finite mixture random regression model, with the purpose of revealing hidden structures in the data owing to putative, sub-clinical mastitis. Different distributions of the data were allowed in 30 intervals of days in milk (DIM), covering the lactation from 5 to 305 days. Bayesian analysis with Gibbs sampling was used for model inferences. Estimated proportion of TD records originated from cows infected with mastitis was 0.66 in DIM from 5 to 15 and averaged 0.2 in the remaining part of lactation. Data from healthy and mastitic cows exhibited markedly different distributions, with respect to both average value and the variance, across all parts of lactation. Heterogeneity of distributions for infected cows was also apparent in different DIM intervals. Cows with mastitis were characterized by smaller milk yield (down to -5 kg) and larger F:P (up to 0.13) and SCS (up to 1.3) compared with healthy contemporaries. Differences in averages between healthy and infected cows for F:P were the most profound at the beginning of lactation, when a dairy cow suffers the strongest energy deficit and is therefore more prone to mammary infection. Residual variances for data from infected cows were substantially larger than for the other mixture components. Fat-to-protein ratio had a significant genetic component, with estimates of heritability that were larger or comparable with milk yield, and was not strongly correlated with milk and SCS on both genetic and environmental scales. Daily milk, F:P and SCS are easily available from milk-recording data for most breeding schemes in dairy cattle. Fat-to-protein ratio can potentially be a valuable addition to SCS and milk yield as an indicator trait for selection against mastitis.

Cumulative permanent environmental effects for repeated records animal models

The assumption of a single permanent environmental (PE) effect contributing to every record made by an animal is questioned. An alternative model where new PE effects accumulate with each record made by an animal is proposed. An example is used to illustrate the differences between the traditional model and the proposed model.

Selection of locations of knots for linear splines in random regression test-day models

Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test-day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single- and multiple-trait test-day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness-of-fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test-day models when analysing milk production traits.

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

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

Short communication: effect of preadjusting test-day yields for stage of pregnancy on variance component estimation in Canadian Ayrshires

Preadjustment of phenotypic records is an alternative to accounting for the effect of pregnancy within the genetic evaluation model. Variance components used in the Canadian Test-Day Model may need to be re-estimated after preadjusting for pregnancy. The objective of this study was to assess the effect of preadjusting test-day yields on variance components and estimated breeding values using a random regression test-day model in a random sample of Ayrshire cows. A random sample of 981 Canadian Ayrshire cows from 18 complete herds (average of 54.5 cows/herd) was analyzed. Two data sets were created using the same animals, one with unadjusted milk, fat, and protein yields, and one data set with test-day records adjusted for pregnancy effects. Pregnancy effect estimates from a previous study were used for additive preadjustment of records. Variance components were estimated using both data sets. Results were very similar between the 2 data sets for all estimated genetic parameters (heritabilities, genetic, and permanent environmental correlations). The relative squared differences were very small: 0.05% for heritabilities, 0.20% for genetic correlations, and 0.18% for permanent environmental correlations. Furthermore, paired Student's t-tests showed that the differences between the genetic parameters of data sets adjusted and unadjusted for pregnancy effect were not significantly different from 0. Results from this study show that preadjusting data for pregnancy did not yield changes in covariance component estimates, thus suggesting that preadjusting test-day records could be a feasible solution to account for pregnancy in the Canadian Test-Day Model without changing the current model. Estimated breeding values (EBV) were calculated for both data sets to observe the impact of preadjusting for pregnancy. Overall, the largest changes in EBV seen when preadjusting for pregnancy (compared with unadjusted records) occurred for nonpregnant elite cows, whose EBV declined. Preadjusting for pregnancy before genetic evaluations improves the estimation of breeding values by adding the negative impact of pregnancy back onto pregnant cow test-day records, causing an increase in their production EBV.

Phenotypic analysis of pregnancy effect on milk, fat, and protein yields of Canadian Ayrshire, Jersey, Brown Swiss, and Guernsey breeds

Pregnancy has a negative impact on milk production in dairy cattle. Estimates of the effects of pregnancy are required in genetic evaluation models. Test-day records of Ayrshire, Jersey, Brown Swiss, and Guernsey breeds were analyzed phenotypically for the effect of pregnancy using 4 different models. Milk, fat, and protein yields were analyzed separately. The first model used a fourth-order Legendre polynomial regression on days in milk within classes of 10 d open. The second model fitted stage of pregnancy within days open classes to investigate the possible interaction between lactation stage and gestation stage. The third model included a fourth-order Legendre polynomial regression on days pregnant. In the fourth model, test-day records were divided into stage of pregnancy classes. Given that the effect of pregnancy was significant for all models, and that the adjusted R-squared values were consistent across the models, implying that the models for each trait fitted equally well within breeds, models were therefore compared based on the practicality of the results. Analysis of the first model indicated that milk production for cows with < or =180 d open tended to have low yields in the last part of lactation. Cows with longer days open, however, had proportionally higher milk yield throughout lactation, suggesting a possible confounding effect of production level with days open effects. Results from the analysis involving the second model illustrated that there was no apparent interaction between lactation stage and gestation stage. Results from the third and fourth models showed that milk and fat yields began to decline after about 4 mo of pregnancy for all breeds, and protein yield began to decline after about 2 mo of pregnancy for all breeds. A lack of records during the final 60 d of pregnancy (the typical dry period) severely limited the third model, as pregnancy effects could not be estimated accurately. This problem was lessened, however, with the fourth (stage of pregnancy) model, because test-day records for cows > or =210 d pregnant were grouped together, allowing for a moderate number of test-day records in the final class of days pregnant. Because the stage of pregnancy model showed a decline in production that increased as gestation progressed, and because there was not a lack of test-day records at the end of pregnancy, the fourth model provided the most realistic estimate of the effect of pregnancy on milk production. Further investigation is needed into the incorporation of stage of pregnancy effects into genetic evaluations.

Influence of population structure on estimates of direct and maternal parameters

The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (-0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates more than the proportion of dams with missing records. The correlation between two traits did not have an effect on the SE of the estimates. The proportion of dams without records and the correlation between direct and maternal effects had the strongest effects on bias of estimates. The largest biases were obtained when the proportion of dams without records was high, the correlation between direct and maternal effects was positive, and the direct variance was greater than the maternal variance, as would be the situation for most growth traits in livestock. Total bias in all parameter estimates for two traits was large in the same situations. Poor population structure can affect both bias and SE of estimates of the direct-maternal genetic correlation, and can explain some of the large negative estimates often obtained.

Extent of linkage disequilibrium in Holstein cattle in North America

The success of fine-scale mapping and genomic selection depends mainly on the strength of linkage disequilibrium (LD) between markers and causal mutations. With Lewontin's measure of LD (known as D'), high levels of LD that extend over several million base pairs have been reported in livestock. However, this measure of LD can be strongly biased upward by small samples and by low allele frequencies. The aim of this study was to characterize the level and extent of LD in Holstein cattle in North America (Canada and the United States for purposes of this study) by using the squared correlation of the alleles at 2 loci (r(2)). The Affymetrix MegAllele GeneChip Bovine Mapping 10K single nucleotide polymorphism (SNP) array was used to genotype 821 bulls, from which 497 were used in the analysis of the extent of LD. A total of 5,564 SNP were used after filtering out SNP with more than 5% of Mendelian inconsistencies, with more than 20% missing genotypes, or with a minor allele frequency of less than 10%. Analysis of syntenic pairs revealed that useful LD (measured as r(2) > 0.3) occurred at distances shorter than 100 kb. Linkage disequilibrium decayed very rapidly, within a few hundred kilobase pairs. In addition, no substantial LD between unlinked loci was found. Using a sliding window analysis, we observed an irregular pattern of LD across the genome. These findings suggest that to capture useful LD, which is required for whole-genome fine mapping and genomic selection, a denser SNP map would be needed.

Application of robust procedures for estimation of breeding values in multiple-trait random regression test-day model

Robust procedures for estimation of breeding values were applied to multiple-trait random regression test-day (TD) model to reduce the influence of outliers on inferences. Robust estimation methods consisted of correcting selected observations (defined as outliers) in the process of solving mixed-model equations in such a way that 'new' observations gave residuals (actual observation minus predicted) within k residual standard deviations for a given day in milk in 305-day lactation. Data were 980,503 TD records on 63,346 Canadian Jersey cows. Milk, fat, protein and somatic cell score in the first three lactations were analysed jointly in the model that included fixed herd-TD effect and regressions within region-age-season of calving, and regressions with random coefficients for animal genetic and permanent environmental effects. All regressions were orthogonal polynomials of order 4. Robust procedures for k = 1.5, 2.0, 2.5, 2.75 and 3.0 were contrasted with the regular best linear unbiased prediction (BLUP) method in terms of numbers and distributions of outliers, and estimated breeding values (EBV) of animals. Distributions of outliers were similar across traits and lactations. Early days in milk (from 5 to 15) were associated with larger frequency of outliers compared with the remaining part of lactation. Several, computationally simple, robust methods (for k > 2.0) reduced the influence of outlier observations in the model and improved the overall model performance. Differences in rankings of animals from robust evaluations were small compared with the regular BLUP method. No clear associations between changes in EBV (rankings) of top animals from different methods and the occurrence of outliers were detected.

Strategy for applying genome-wide selection in dairy cattle

Animals can be genotyped for thousands of single nucleotide polymorphisms (SNPs) at one time, where the SNPs are located at roughly 1-cM intervals throughout the genome. For each contiguous pair of SNPs there are four possible haplotypes that could be inherited from the sire. The effects of each interval on a trait can be estimated for all intervals simultaneously in a model where interval effects are random factors. Given the estimated effects of each haplotype for every interval in the genome, and given an animal's genotype, a 'genomic' estimated breeding value is obtained by summing the estimated effects for that genotype. The accuracy of that estimator of breeding values is around 80%. Because the genomic estimated breeding values can be calculated at birth, and because it has a high accuracy, a strategy that utilizes these advantages was compared with a traditional progeny testing strategy under a typical Canadian-like dairy cattle situation. Costs of proving bulls were reduced by 92% and genetic change was increased by a factor of 2. Genome-wide selection may become a popular tool for genetic improvement in livestock.

Estimation of genetic effects in the presence of multicollinearity in multibreed beef cattle evaluation

Breed additive, dominance, and epistatic loss effects are of concern in the genetic evaluation of a multibreed population. Multiple regression equations used for fitting these effects may show a high degree of multicollinearity among predictor variables. Typically, when strong linear relationships exist, the regression coefficients have large SE and are sensitive to changes in the data file and to the addition or deletion of variables in the model. Generalized ridge regression methods were applied to obtain stable estimates of direct and maternal breed additive, dominance, and epistatic loss effects in the presence of multicollinearity among predictor variables. Preweaning weight gains of beef calves in Ontario, Canada, from 1986 to 1999 were analyzed. The genetic model included fixed direct and maternal breed additive, dominance, and epistatic loss effects, fixed environmental effects of age of the calf, contemporary group, and age of the dam x sex of the calf, random additive direct and maternal genetic effects, and random maternal permanent environment effect. The degree and the nature of the multicollinearity were identified and ridge regression methods were used as an alternative to ordinary least squares (LS). Ridge parameters were obtained using two different objective methods: 1) generalized ridge estimator of Hoerl and Kennard (R1); and 2) bootstrap in combination with cross-validation (R2). Both ridge regression methods outperformed the LS estimator with respect to mean squared error of predictions (MSEP) and variance inflation factors (VIF) computed over 100 bootstrap samples. The MSEP of R1 and R2 were similar, and they were 3% less than the MSEP of LS. The average VIF of LS, R1, and R2 were equal to 26.81, 6.10, and 4.18, respectively. Ridge regression methods were particularly effective in decreasing the multicollinearity involving predictor variables of breed additive effects. Because of a high degree of confounding between estimates of maternal dominance and direct epistatic loss effects, it was not possible to compare the relative importance of these effects with a high level of confidence. The inclusion of epistatic loss effects in the additive-dominance model did not cause noticeable reranking of sires, dams, and calves based on across-breed EBV. More precise estimates of breed effects as a result of this study may result in more stable across-breed estimated breeding values over the years.

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.

Transmission disequilibrium test for quantitative trait loci detection in livestock populations

The performance of several transmission disequilibrium tests (TDT) for detection of quantitative trait loci (QTL) in data structures typical of outbred livestock populations were investigated. Factorial mating designs were simulated with 10 sires mated to either 50 or 200 dams, each family having five or eight full sibs. A single marker and QTL, both bi-allelic, were simulated using a disequilibrium coefficient based on complete initial disequilibrium and 50 generations of recombination [i.e. D = D(0)(1 - theta)50], where theta is the recombination fraction between marker and QTL. The QTL explained either 10% (small QTL) or 30% (large QTL) of the genetic variance for a trait with heritability of 0.3. Methods were: TDT for QTL (Q-TDT; both parents known), 1-TDT (only one parent known) and sibling-based TDT (S-TDT; neither parent known, but sibs available). All were found to be effective tests for association and linkage between the QTL and a tightly linked marker (theta < 0.02) in these designs. For a large QTL, theta = 0.01, and five full sibs per family, the empirical power for Q-TDT, 1-TDT and S-TDT was 0.966, 0.602 and 0.974, respectively, in a large population, versus 0.700, 0.414 and 0.654, respectively, in a small population. For a small QTL effect, theta = 0.01, large population the empirical power of these tests were 0.709, 0.287 and 0.634. The power of Q-TDT, 1-TDT and S-TDT was satisfactory for large populations, for QTL with large effects and for five full sibs per family. The 1-TDT based on a linear model was more powerful than the normal 1-TDT. The empirical power for Q-TDT and 1-TDT with a linear model was 0.978 and 0.995 respectively. TDT based on analogous linear models, incorporating the polygenic covariance structure, provided only small increases in power compared with the usual TDT for QTL.

Joint International Evaluation of Milking Shorthorn Dairy Cattle for Production Traits

Pedigree information and test-day records for the first 3 parities of Milking Shorthorn dairy cattle from 5 countries were analyzed. After editing, the data included 1,018,528 test-day records from 68,653 cows. A multiple-lactation random regression test-day model with Legendre polynomials of order 4 and a Bayesian method were used to estimate variance components for both single and multiple-countries. Fixed effects included herd-test-day class and regressions on DIM within age at calving-parity-season of calving. Random effects included animal genetic, permanent environmental, and residual effects. Average daily heritabilities from single country analyses ranged from 0.33 to 0.47 for milk yield and from 0.37 to 0.45 for protein yield across lactations and countries. Common sires (66) and their daughters were identified for creating a connected data set for simultaneous (co)variance component estimation of milk yield across all 5 countries. Between-country genetic correlations were low, with values from 0.08 to 0.46 and standard deviations from 0.08 to 0.12. Estimated breeding values for milk were generated for each animal using the same test-day animal model. Correlations among country estimated breeding values were higher than genetic correlations. Top 100 bull lists were generated on the scale of each country, and genetic progress was assessed. Future evaluation with increased genetic ties among countries may facilitate international comparison of Milking Shorthorns.

Estimation of genetic parameters for lactational milk yields using two-dimensional random regressions on parities and days in milk in Chinese Simmental cattle

A two-dimensional random regression model with regressions on days in milk (DIM) and parity number was applied to lactational milk yields in Chinese Simmental cattle. Random regressions were fitted for additive genetic and permanent environmental effects using a two-dimensional polynomial on DIM and parity number. A total of 4340 lactational milk yields from Chinese Simmental cattle which calved between 1980 and early 2000 were used in this study. Variance components were estimated using Bayesian methodology via Gibbs sampling. Variances of random regression coefficients associated with all terms of the polynomials were significant. A covariance function showed that heritabilities of lactational milk yields between 200 and 400 DIM over parities varied between 0.25 and 0.45. Heritabilities of 305-day milk yields from 1st to 6-8th parities were 0.28, 0.30, 0.32 0.32, 0.32, and 0.31, respectively. Ratios of permanent environment variances to total variances at each DIM were greater than corresponding heritabilities. Generally, genetic correlations were higher between lactational milk yields with similar DIM and parity number.

Estimates of Genetic Parameters for Canadian Holstein Female Reproduction Traits

Age at first insemination, days from calving to first insemination, number of services, first-service nonreturn rate to 56 d, days from first service to conception, calving ease, stillbirth, gestation length, and calf size of Canadian Holstein cows were jointly analyzed in a linear multiple-trait model. Traits covered a wide spectrum of aspects related to reproductive performance of dairy cows. Other frequently used fertility characteristics, like days open or calving intervals, could easily be derived from the analyzed traits. Data included 94,250 records in parities 1 to 6 on 53,158 cows from Ontario and Quebec, born in the years 1997 to 2002. Reproductive characteristics of heifers and cows were treated as different but genetically correlated traits that gave 16 total traits in the analysis. Repeated records for later parities were modeled with permanent environmental effects. Direct and maternal genetic effects were included in linear models for traits related to calving performance. Bayesian methods with Gibbs sampling were used to estimate covariance components of the model and respective genetic parameters. Estimates of heritabilities for fertility traits were low, from 3% for nonreturn rate in heifers to 13% for age at first service. Interval traits had higher heritabilities than binary or categorical traits. Service sire, sire of calf, and artificial insemination technician were important (relative to additive genetic) sources of variation for nonreturn rate and traits related to calving performance. Fertility traits in heifers and older cows were not the same genetically (genetic correlations in general were smaller than 0.9). Genetic correlations (both direct and maternal) among traits indicated that different traits measured different aspects of reproductive performance of a dairy cow. These traits could be used jointly in a fertility index to allow for selection for better fertility of dairy cattle.

Genetic Relationships Between Persistency and Reproductive Performance in First-Lactation Canadian Holsteins

The main objective of this study was to estimate genetic relationships between lactation persistency and reproductive performance in first lactation. Relationships with day in milk at peak milk yield and estimated 305-d milk yield were also investigated. The data set contained 33,312 first-lactation Canadian Holsteins with first-parity reproductive, persistency, and productive information. Reproductive performance traits included age at first insemination, nonreturn rate at 56 d after first insemination as a virgin heifer and as a first-lactation cow, calving difficulty at first calving and calving interval between first and second calving. Lactation persistency was defined as the Wilmink b parameter for milk yield and was calculated by fitting lactation curves to test day records using a multiple-trait prediction procedure. An 8-trait genetic analysis was performed using the Variance Component Estimation package (VCE 5) via Gibbs sampling to estimate genetic parameters for all traits. Heritabilities of persistency, day in milk at peak milk yield and estimated 305-d milk yield were 0.18, 0.09 and 0.45, respectively. Heritabilities of reproduction were low and ranged from 0.03 to 0.19. The highest heritability was for age at first insemination. Heifer reproductive traits were lowly genetically correlated, whereas cow reproductive traits were moderately correlated. Heifers younger than average when first inseminated and/or conceived successfully at first insemination tended to have a more persistent first lactation. First lactation was more persistent if heifers had difficulty calving (r(g) = 0.43), or conceived successfully at first insemination in first lactation (r(g) = 0.32) or had a longer interval between first and second calving (r(g) = 0.17). Estimates of genetic correlations of reproductive performance with estimated 305-d milk yield were different in magnitude, but similar in sign to those with persistency (0.02 to 0.51).

Random Regression Test-Day Models with Residuals Following a Student's-t Distribution

First-lactation milk yield test-day records of Canadian Holsteins were analyzed by single-trait random regression test-day models that assumed normal or Student's-t distribution for residuals. Objectives were to test the performance of the robust statistical models that use heavy-tailed distributions for the residual effect. Models fitted were: Gaussian, Student's-t, and Student's-t with fixed number of degrees of freedom (equal to 5, 15, 30, 100 or 1000) for the t distribution. Bayesian methods with Gibbs sampling were used to make inferences about overall model plausibility through Bayes factors, posterior means for covariance components, estimated breeding values for regression coefficients, solutions for permanent environmental regressions, and residuals of the models. Bayes factors favored Student's-t model with the posterior mean of degrees of freedom equal to 2.4 over all other models, indicating very strong departure from normality. Number of outliers in Student's-t model was reduced by 35% in comparison with the Gaussian model. Differences in covariance components for regression coefficients between models were small, and rankings of animals based on additive genetic merit for the first two regression coefficients (total yield and persistency) were similar. Results from the Gaussian and Student's-t models with fixed degrees of freedom become more alike (smaller departures from normality for Student's-t models) with increasing number of degrees of freedom for the t-distributions. For any pair of Student's-t models, the one with the smaller number of degrees of freedom for the t-distribution was shown to be superior. Similarly, number of outliers increased with increasing degrees of freedom for the t distribution.

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

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

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

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

Bayesian inference for categorical traits with an application to variance component estimation

We implemented statistical models of Bayesian inference that included direct and maternal genetic effects for genetic parameter estimation of categorical traits by Gibbs sampling. The estimation errors and variances of estimates of animal versus sire and maternal grandsire models, of linear versus threshold models, of single-trait versus multiple-trait models, and of treating herd-year-season as fixed versus random effects in the model were compared. The results indicated that linear models yielded biased estimates of genetic parameters for categorical traits. The animal model was improper for analysis of categorical traits using a threshold model and the Gibbs sampler. Moreover, linear versus threshold models and animal versus sire-maternal grandsire models resulted in larger Monte Carlo errors and increased auto-correlations among posterior samples. Treating herd-year-seasons as random effects in the threshold models decreased the Monte Carlo error, auto-correlations, and the variances of estimates. Efficiency of the single-trait threshold sire model, as measured by the variance of the estimates, was lower than for a multiple-trait model that included a correlated continuous trait, but both estimates were unbiased. Therefore, the threshold single-trait sire and maternal grandsire model is a feasible alternative to the multiple-trait model for analysis of variance components of categorical traits affected by direct and maternal genetic factors.

Relationships between energy balance and health traits of dairy cattle in early lactation

The objective of the study was to calculate phenotypic relationships between energy balance in early lactation and health and reproduction in that lactation. Data were 26,701 daily records of dry matter intake and milk production, periodic measures of milk composition and body weight, and all health and reproductive information from 140 multiparous Holstein cows. Daily energy balance was calculated by multiplying feed intake by the concentration of energy of the ration and subtracting the amount of energy required for maintenance (based on parity and body weight) and for milk production (based on yield and concentrations of fat, protein, and lactose). Six measures of energy balance were defined: mean daily energy balance during the first 20, 50, and 100 d of lactation; minimum daily energy balance; days in negative energy balance; and total energy deficit. Measures of health were the numbers of occurrences of each of the following during lactation: all udder problems, mastitis, all locomotive problems, laminitis, digestive problems, and reproductive problems. Reproductive traits were the number of days to first observed estrus and number of inseminations. Several significant relationships between energy balance and health were observed. Increased digestive and locomotive problems were associated with longer and more extreme periods of negative energy balance.

Experience with a test-day model

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

Using recent versus complete pedigree data in genetic evaluation of a closed nucleus broiler line

Stochastic simulation was used to study the effect of using full data and pedigree structure vs more recent data and pedigree structure to obtain best linear unbiased predictors (BLUP) of breeding values for single trait selection. Simulations used heritabilities of 0.10 and 0.50, with a population structure of 20 sires each mated to two dams, each producing 10 progeny, with 11 hatches from an unselected base population under both discrete and overlapping generations. Selection of parents was based on BLUP of breeding values using an animal model. The use of the last two generations of data and pedigrees gave the same selection response as when using full data and pedigree structure, for both heritabilities. Under discrete generations with use of only the last generation data and pedigree, which is similar to phenotypic evaluation, response to selection decreased by 21 and 3.8% at Generation 10 compared to selection response when using the full data and pedigree for heritabilities of 0.10 and 0.50, respectively. Corresponding decreases in inbreeding were 72 and 37%. The amount of central processing unit time for genetic evaluation when using the last six, four, and two generations of data and pedigree was reduced to 70, 40, and 11% of that when using the full data set, for a heritability of 0.10 and discrete generations. Very similar values were observed for a heritability of 0.50 and also under overlapping generations.

Genetic evaluation for herd life in Canada

Methods were developed for the national genetic evaluation of herd life for Canadian Holstein sires. The genetic evaluations incorporate information from survival (direct herd life) and information from conformation traits that are related to herd life (indirect herd life) after adjustment for production in first lactation to remove the effect of culling for production. Direct genetic evaluations for herd life were based on survival in each of the first three lactations, which was analyzed using a multiple-trait animal model. Sire evaluations thus obtained for survival in each of the first three lactations were combined based on their economic weights into an overall sire evaluation for direct herd life. Sire evaluations for indirect herd life were based on an index of sire evaluations for mammary system, feet and legs, rump, and capacity. A multiple-trait sire model based on multiple-trait across country evaluation methodology was used to combine direct and indirect genetic evaluations for herd life into an overall genetic evaluation for herd life. Sire evaluations for herd life were expressed in estimated transmitting ability as the number of lactations and represent expected differences among daughters in functional herd life (number of lactations); the average functional herd life was set equal to three lactations. Estimated transmitting abilities were normally distributed and ranged from 2.31 to 3.43 lactations.

Comparison of possible covariates for use in a random regression model for analyses of test day yields

Random regression models have been proposed for the genetic evaluation of dairy cattle using test day records. Random regression models contain linear functions of fixed and random coefficients and a set of covariates to describe the shapes of lactation curves for groups of cows and for individual cows. Previous work has used a linear function of five covariates to describe lactation shape. This study compared the function of five covariates with a function of only three covariates in three random regression models. Comparisons of estimates of components of variances and covariances, as well as comparisons of EBV and their prediction errors for milk yield, were made among models. Small practical differences existed between models in all respects. The model using regressions with five covariates had a slight advantage for comparison of prediction error variances of daily yields.

Genetic evaluation of dairy cattle using test day yields and random regression model

A model for analyzing test day records that contains both fixed and random regression coefficients was applied to the genetic evaluation of first lactation data for Canadian Holstein dairy cows. Data were 5.1 million test day records with milk, fat, and protein yields from calvings between 1988 and 1995 from herds in four regions of Canada. Each evaluated animal received five predictions for each trait representing the random regression coefficients. From these solutions, a range of estimated breeding values for various parts of the lactation could be calculated. Three genetic measures of persistency were compared. Bulls could be selected for both yields and persistency of their daughters in whatever combination was desirable. Test day analyses could result in monthly genetic evaluations for yield traits.

Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins

A model that contains both fixed and random linear regressions is described for analyzing test day records of dairy cows. Estimation of the variances and covariances for this model was achieved by Bayesian methods utilizing the Gibbs sampler to generate samples from the marginal posterior distributions. A single-trait model was applied to yields of milk, fat, and protein of first lactation Holsteins. Heritabilities of 305-d lactation yields were 0.32, 0.28, and 0.28 for milk, fat, and protein, respectively. Heritabilities of daily yields were greater than for 305-d yields and varied from 0.40 to 0.59 for milk yield, 0.34 to 0.68 for fat yield, and 0.33 to 0.69 for protein yield. The highest heritabilities were within the first 10 d of lactation for all traits. Genetic correlations between daily yields were higher as the interval between tests decreased, and correlations of daily yields with 305-d yields were greatest during midlactation.

Multiple-trait prediction of lactation yields for dairy cows

A multiple-trait procedure is described for predicting 305-d lactation yields for milk, fat, and protein that incorporates information about standard lactation curves and covariances between yields for milk, fat, and protein. Test day yields are weighted by their relative variances, and standard lactation curves of cows from similar breed, region, lactation number, age, and season of calving are used for the estimation of lactation curve parameters for each cow. Accuracies of the test interval method and the multiple-trait procedure were comparable. In addition, the multiple-trait procedure can handle long intervals between test days as well as test days with milk only recorded and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

Factors influencing international comparisons of dairy sires

A method of dairy sire evaluation across multiple countries is described. Factors influencing this method are overestimation of genetic trends within countries, inclusion of evaluations of imported bulls, years of birth of the bulls included in the analysis, and estimates of genetic correlations between countries. Fall 1994 evaluations for milk, fat, and protein yields from Canada (4559 bulls), Germany (5894 bulls), and France (8419 bulls) were used to study the effect of these factors. After inclusion of ancestors there were 21,555 bulls in total. Eight data files were created based on combinations of three factors: 1) bulls born from 1970 to present versus bulls born from 1979 to present, 2) all bulls included versus imported bulls omitted, and 3) official Canadian evaluations for all lactations versus Canadian evaluations for first lactation only. Separate evaluations for two of the data files assumed a uniform genetic correlation of 0.995 between countries. Rankings of top bulls from analyses were affected by all factors to various degrees, depending on the country. Evaluations of imported bulls have an effect on bull rankings and probably should not be included. An assumed uniform genetic correlation between countries of 0.995 may not be appropriate. Proper methods and data for estimation of the genetic correlation between countries should be sought.

Genetic evaluation for somatic cell score with a test day model for multiple lactations

A multiple lactation model for test day data was applied to predict genetic merit for somatic cell scores of Canadian Holsteins. The model for genetic evaluation included a fixed effect for herd test date, fixed regressions on functions of days of lactation, random effects of permanent environment within lactation, random genetic effects on animal, and residual effects. Records from the first three lactations were used and treated as different traits. Procedures for this model, developed for national genetic evaluation for somatic cell score in Canada, were found to be practical. Use of starting values from the previous genetic evaluation reduced the number of rounds necessary to reach convergence. Test day models were compared with several single-trait models based on lactation average of somatic cell score in terms of computing efficiency and ranking of animals. Differences between EBV from the test day model and EBV from a repeatability model for lactation average were small for bulls with many daughters, but differences were large with EBV from a single-trait model for first lactation average of somatic cell count. Association were desirable for EBV for somatic cell score with EBV for some udder conformation traits, but undesirable for EBV for milk and protein yield.

Estimation of genetic parameters for test day records of somatic cell score

The present study estimated variance components for test day records of somatic cell score and production traits. Data consisted of 235,100 test day observations recorded between 1986 and 1994 on lactations 1 to 3 of 15,922 Holstein cows from 143 herds. Records were considered as repeated observations within a lactation and as different traits across lactations. The multiple-trait animal model for analysis included random animal additive genetic and permanent environment effects by lactation. Fixed effects included herd test date and a set of four covariables for days in lactation, estimated by parity, age, and season, which accounted for the shape of the lactation curve. Gibbs sampling chains were carried out separately for somatic cell score and milk production and fat and protein yields. Heritabilities of somatic cell score for lactations 1 to 3 were .09, .09, and .11, respectively. Genetic correlations between lactations were high (.88, .79, and .95 between lactations 1 and 2, 1 and 3, and 2 and 3, respectively). Correlations between permanent environment effects were smaller (.29, .19, and .46 between lactations 1 and 2, 1 and 3, and 2 and 3, respectively). Heritabilities and correlations between permanent environment effects were higher for production traits than for somatic cell score. Genetic correlations between lactations for production traits were similar to those for somatic cell score. Variances between lactations differed significantly, indicating that observations from different lactations should no be considered as repeated observations of the same trait.

Multiple-country comparison of dairy sires

A multiple-trait sire model was described in which yields of daughters in different countries were considered to be different traits. Such a model required estimates of genetic correlations among sire genetic effects in different countries. Observations were average daughter yield deviations, which were yields adjusted for all fixed effects within a country and for mate and animal permanent environmental effects. The methodology was described through a small example. Methods for estimating genetic covariances between countries as well as the advantages and disadvantages of the multiple-country approach to international comparisons were discussed. The proposed method appears to be better theoretically than methods in which the genetic correlations among countries are assumed to be 1. The relationships of estimated transmitting abilities of sires from the multiple-country analysis with international conversion formulas were discussed.