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.

Development of a genetic evaluation for body condition score for Canadian Holsteins.

Valacta (Sainte-Anne-de-Bellevue, Québec, Canada) is the Canadian Dairy Herd Improvement organization responsible for milk recording in Québec and Atlantic provinces. Up to 14 first-lactation body condition score (BCS) records were collected per cow (average of 2.5 records per cow), allowing the trait to be described by a random regression animal model so that animals could be ranked by the shape of their BCS curve. However, Valacta's BCS are available from Québec herds only and the long-term objective of this research is to develop a nationwide genetic evaluation of sires and cows for BCS. Alternatively, Holstein Canada (Brantford, Ontario, Canada) collects type trait records nationwide, primarily for first-lactation cows. Holstein Canada typically collects a single record per trait, so that selection for Holstein Canada BCS would be based on overall BCS level rather than the shape of the BCS curve. Several different methods of genetically evaluating Valacta's BCS were investigated, including consideration of average BCS level across lactation, the amount of fluctuation in the BCS curve during lactation, and combinations of BCS level and BCS fluctuation. Sires with ≥ 25 daughters were compared (as opposed to comparing cows) because their BCS estimated breeding values (EBV) are based on more information, and so should be more reliable. Of the different methods of calculating Valacta BCS EBV, ranking bulls based on overall BCS level gave the best results in that their daughter phenotypic BCS curves showed limited loss in early lactation BCS and replenished condition by the end of lactation. Whereas Valacta's BCS were analyzed using a random regression animal model, Holstein Canada only needs to collect 1 BCS record per cow at classification and the resulting BCS EBV was strongly correlated with Valacta's BCS EBV. Furthermore, because Holstein Canada's BCS are collected nationally and Valacta's BCS are not, a national genetic evaluation for Holstein Canada's BCS is more convenient. The results of this study do not eliminate the possibility of a genetic evaluation of BCS as a longitudinal trait, but indicate that other methods of calculating Valacta BCS EBV should be explored. Until that time, genetically evaluating Holstein Canada's BCS is simple, easily implemented, and may be effective in altering the level and shape of the genetic BCS curve.

Relationship between body condition score and health traits in first-lactation Canadian Holsteins.

The objective of this research was to estimate daily genetic correlations between longitudinal body condition score (BCS) and health traits by using a random regression animal model in first-lactation Holsteins. The use of indicator traits may increase the rate of genetic progress for functional traits relative to direct selection for functional traits. Indicator traits of interest are those that are easier to record, can be measured early in life, and are strongly genetically correlated with the functional trait of interest. Several BCS records were available per cow, and only 1 record per health trait (1=affected; 0=not affected) was permitted per cow over the lactation. Two bivariate analyses were performed, the first between BCS and mastitis and the second between BCS and metabolic disease (displaced abomasum, milk fever, and ketosis). For the first analysis, 217 complete herds were analyzed, which included 28,394 BCS records for 10,715 cows and 6,816 mastitis records for 6,816 cows. For the second analysis, 350 complete herds were analyzed, which included 42,167 BCS records for 16,534 cows and 13,455 metabolic disease records for 13,455 cows. Estimation of variance components by a Bayesian approach via Gibbs sampling was performed using 400,000 samples after a burn-in of 150,000 samples. The average daily heritability (posterior standard deviation) of BCS was 0.260 (0.026) and the heritabilities of mastitis and metabolic disease were 0.020 (0.007) and 0.041 (0.012), respectively. Heritability estimates were similar to literature values. The average daily genetic correlation between BCS and mastitis was -0.730 (0.110). Cows with a low BCS during the lactation are more susceptible to mastitis, and mastitic cows are likely to have low BCS. Daily estimates of genetic correlations between BCS and mastitis were moderate to strong throughout the lactation, becoming stronger as the lactation progressed. The average daily genetic correlation between BCS and metabolic disease was -0.438 (0.125), and was consistent throughout the lactation. A lower BCS during the lactation is genetically associated with the occurrence of mastitis and metabolic disease.

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.

Genetic parameters for producer-recorded health data in Canadian Holstein cattle.

Health traits are of paramount importance for economic dairy production. Improvement in liability to diseases has been made with better management practices, but genetic aspects of health traits have received less attention. Dairy producers in Canada have been recording eight health traits (mastitis (MAST), lameness (LAME), cystic ovarian disease (COD), left displaced abomasum (LDA), ketosis (KET), metritis (MET), milk fever (MF) and retained placenta (RP)) since April 2007. Genetic analyses of these traits were carried out in this study for the Holstein breed. Edits on herd distributions of recorded diseases were applied to the data to ensure a sufficient quality of recording. Traits were analysed either individually (MAST, LAME, COD) or were grouped according to biological similarities (LDA and KET, and MET, MF and RP) and analysed with multiple-trait models. Data included 46 104 cases of any of the above diseases. Incidence ranged from 2.3% for MF to 9.7% for MAST. MET and KET also had an incidence below 4.0%. Variance components were estimated using four different sire threshold models. The differences between models resulted from the inclusion of days at risk (DAR) and a cow effect, in addition to herd, parity and sire effects. Models were compared using mean squared error statistic. Mean squared error favoured, in general, the sire and cow within sire model with regression on DAR included. Heritabilities on the liability scale were between 0.02 (MET) and 0.21 (LDA). There was a moderate, positive genetic correlation between LDA and KET (0.58), and between MET and RP (0.79).

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.

Genetic and environmental relationships between body condition score and milk production traits in Canadian Holsteins.

The objective of this research was to estimate genetic parameters of first-lactation body condition score (BCS), milk yield, fat percentage (Fat%), protein percentage (Prot%), somatic cell score (SCS), milk urea nitrogen (MUN), lactose percentage (Lact%), and fat to protein ratio (F:P) using multiple-trait random regression animal models. Changes in covariances between BCS and milk production traits on a daily basis have not been investigated before and could be useful for determining which BCS estimated breeding values (EBV) might be practical for selection in the future. Field staff from Valacta milk recording agency (Sainte-Anne-de-Bellevue, QC, Canada) collected BCS from Québec herds several times per cow throughout the lactation. Average daily heritabilities and genetic correlations among the various traits were similar to literature values. On an average daily basis, BCS was genetically unfavorably correlated with milk yield (i.e., increased milk yield was associated with lower body condition). The unfavorable genetic correlation between BCS and milk yield became stronger as lactation progressed, but was equivalent to zero for the first month of lactation. Favorable genetic correlations were found between BCS with Prot%, SCS, and Lact% (i.e., greater BCS was associated with greater Prot%, lower SCS, and greater Lact%). These correlations were strongest in early lactation. On an average daily basis, BCS was not genetically correlated with Fat% or MUN, but was negatively correlated with F:P. Furthermore, BCS at 5 and 50 d in milk (DIM) had the most favorable genetic correlations with milk production traits over the lactation (at 5, 50, 150, and 250 DIM). Thus, early lactation BCS EBV shows potential for selection. Regardless, this study showed that the level of association BCS has with milk production traits is not constant over the lactation. Simultaneous selection for both BCS and milk production traits should be considered, mainly due to the unfavorable genetic correlation between BCS with milk yield.

Alternative parameterizations of the multiple-trait random regression model for milk yield and somatic cell score via recursive links between phenotypes.

Multiple-trait random regression models with recursive phenotypic link from somatic cell score (SCS) to milk yield on the same test day and with different restrictions on co-variances between these traits were fitted to the first-lactation Canadian Holstein data. Bayesian methods with Gibbs sampling were used to derive inferences about parameters for all models. Bayes factor indicated that the recursive model with uncorrelated environmental effects between traits was the most plausible specification in describing the data. Goodness of fit in terms of a within-trait weighted mean square error and correlation between observed and predicted data was the same for all parameterizations. All recursive models estimated similar negative causal effects from SCS to milk yield (up to -0.4 in 46-115 days in milk in lactation). Estimates of heritabilities, genetic and environmental correlations for the first two regression coefficients (overall level of a trait and lactation persistency) within both traits were similar among models. Genetic correlations between milk and SCS were dependent on the restrictions on genetic co-variances for these traits. Recursive model with uncorrelated system genetic effects between milk and SCS gave estimates of genetic correlations of the opposite sign compared with a regular multiple-trait model. Phenotypic recursion between milk and SCS seemed, however, to be the only source of environmental correlations between these two traits. Rankings of sires for total milk yield in lactation, average daily SCS and persistency for both traits were similar among models. Multiple-trait model with recursive links between milk and SCS and uncorrelated random environmental effects could be an attractive alternative for a regular multiple-trait model in terms of model parsimony and accuracy.

Short communication: estimates of genetic parameters of body condition score in the first 3 lactations using a random regression animal model.

The objective of this research was to estimate the genetic parameters of body condition score (BCS) in the first 3 lactations in Canadian Holstein dairy cattle using a multiple-lactation random regression animal model. Field staff from Valacta milk recording agency (Sainte-Anne-de-Bellevue, QC, Canada) collected BCS from Québec herds several times throughout each lactation. Approximately 32,000, 20,000, and 11,000 first-, second-, and third-parity BCS were analyzed, respectively, from a total of 75 herds. Body condition score was a moderately heritable trait over the lactation for parity 1, 2, and 3, with average daily heritabilities of 0.22, 0.26, and 0.30, respectively. Daily heritability ranged between 0.14 and 0.26, 0.19 and 0.28, and 0.24 and 0.33 for parity 1, 2, and 3, respectively. Genetic variance of BCS increased with days in milk within lactations. The low genetic variance in early lactation suggests that the evolution of the ability to mobilize tissue reserves in early lactation provided cattle with a major advantage, and is, therefore, somewhat conserved. The increasing genetic variance suggests that more genetic differences were related to how well cows recovered from the negative energy balance state. More specifically, increasing genetic variation as lactation progressed could be a reflection of genetic differences in the ability of cows to efficiently control the rate of mobilization of tissue reserves, which would not be crucial in early lactation. The shape of BCS curves was similar across parities. From first to third parity, differences included the progressively deeper nadir and faster rate of recovery of condition. Daily genetic correlations between parities were calculated from 5 to 305 DIM, and were summed and divided by 301 to obtain average daily genetic correlations. The average daily genetic correlations were 0.84 between parity 1 and 2, 0.83 between parity 1 and 3, and 0.86 between parity 2 and 3. Although not 1, these genetic correlations are still strong, so much of the variation observed in BCS was controlled by the same genes for each of the first 3 lactations. If a genetic evaluation for BCS is developed, regular collection of first-lactation BCS records should be sufficient for genetic evaluation.

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.

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.

Sheep breeding schemes utilising artificial insemination; large-scale simulation with a complex breeding goal.

Alternative Norwegian sheep breeding schemes were evaluated by stochastic simulation of a breeding population with about 120 000 ewes, considering the gain for an aggregate genotype including nine traits and also the rate of inbreeding. The schemes were: a scheme where both young unproven rams (test rams) and proven rams (elite rams) are used in artificial insemination (AI scheme), a scheme with test rams in natural mating in ram circles and elite rams (from one and a half years of age) in AI across all flocks in the country (NMAI2 scheme), a scheme where, in addition to testing rams, the youngest elite rams (one and a half years of age) are also used in natural mating in ram circles, while older elite rams are used in AI (NMAI1 scheme), and a scheme, acting as a control, where both test and elite rams are used in natural mating (NM scheme). Within the NMAI- and AI-schemes, experimentation was performed for percent ewes inseminated to elite rams v. test rams (EM%), numbers of ewes inseminated per elite ram (EAIn), and numbers of ewes mated per test ram by natural service (TNMn) or by AI (TAIn), respectively. With a restriction on the rate of inbreeding (⩽0.8% per generation), the AI scheme gave similar gain to the NMAI2 scheme (and about 40% more than did the NM scheme). Less gain was generated by the NMAI1 scheme, but it was still considerably more than for the NM scheme (about 25%). In the AI scheme, relatively few ewes (200/300) should be inseminated to each test/elite ram, and a low EM% should be chosen (10%). In the NMAI schemes, TNMn should be relatively high (40 to 50), combined with average and somewhat larger than average EAIn (NMAI2: 700 ewes, NMAI1: 900 ewes), and EM% medium (30%).

Recursive relationships between milk yield and somatic cell score of Canadian Holsteins from finite mixture random regression models.

Finite mixture, multiple-trait, random regression animal models with recursive links between phenotypes for milk yield and somatic cell score (SCS) on the same test-day were applied to first lactation Canadian Holstein data. All models included fixed herd-test-day effects and fixed regressions within region-age at calving-season of calving classes, and animal additive genetic and permanent environmental regressions with random coefficients. Causal links between phenotypes for milk yield and SCS were fitted separately for records from healthy cows and cows with a putative, subclinical form of mastitis. Bayesian methods via Gibbs sampling were used for the estimation of model parameters. Bayes factors indicated superiority of the model with recursive link from milk to SCS over the reciprocal recursive model and the standard multiple-trait model. Differences between models measured by other, single-trait model comparison criteria (i.e., weighted mean squared error, squared bias, and correlation between observed and expected data) were negligible. Approximately 20% of test-day records were classified as originating from cows with mastitis in recursive mixture models. The proportion of records from cows infected with mastitis was largest at the beginning of lactation. Recursive mixture models exhibited different distributions of data from healthy and infected cows in different parts of lactation. A negative effect of milk to SCS (up to -0.15 score points for every kilogram of milk for healthy cows from 5 to 45 d in milk) was estimated for both mixture components (healthy and infected) in all stages of lactation for the most plausible model. The magnitude of this effect was stronger for healthy cows than for cows infected with mastitis. Different patterns of genetic and environmental correlations between milk and SCS for healthy and infected records were revealed, due to heterogeneity of structural coefficients between mixture components. Estimated breeding values for SCS from the best fitting model for sires of infected daughters were more related to estimated breeding values for the same trait from the regular multiple-trait model than evaluations for sires of mastitis-free cows.

Application of multiple-trait finite mixture model to test-day records of milk yield and somatic cell score of Canadian Holsteins.

Multiple-trait (MT) finite mixture random regression (MIX) model was applied using Bayesian methods to first lactation test-day (TD) milk yield and somatic cell score (SCS) of Canadian Holsteins, allowing for heterogeneity of distributions with respect to days in milk (DIM) in lactation. The assumption was that the associations between patterns of variation in these traits and mastitis would allow revealing the hidden structure in the data distribution because of unknown health status of cows. The MIX model assumed separate means and residual co-variance structures for two components in four intervals of lactation, in addition to fitting the fixed effect of herd-test-day, and fixed and random regressions with Legendre polynomials. Results indicated that the mixture model was superior to standard MT model, as supported by the Bayes factor. Approximately 20% of TD records were classified as originated from cows with a putative, sub-clinical form of mastitis. The proportion of records from mastitic cows was the largest at the beginning of lactation. The MIX model exhibited different distributions of data from healthy and infected cows in different parts of lactation. Records from sick cows were characterized by larger (smaller) means for SCS (milk) and larger variances. Residual, and daily genetic and environmental correlations between milk and SCS were smaller from the MIX model when compared with MT estimates. Heritabilities of both traits differed significantly among records from healthy, sick and MT model estimates. Both models fitted milk records from healthy cows relatively well. The ability of the MT model in handling SCS records, measured by model residuals, was low, but improved substantially, however, where the data were allowed to be separated into two components in the MIX parameterization. Correlations between estimated breeding values (EBV) for sires from both models were very high for cumulative milk yield (>0.99) and slightly lower (0.95 in the interval from 5 to 45 DIM) for daily SCS. EBV for SCS from MT and MIX models were weakly correlated with posterior probability of sub-clinical mastitis on the phenotypic scale.

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.