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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., (© 2011 Blackwell Verlag GmbH.)

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., (© 2011 Blackwell Verlag GmbH.)

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., (Copyright © 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Cow evaluations for production derived from an intraherd model for six dairy breeds were studied. Cow evaluations calculated within each of two herds were correlated and agreed closely with correlations expected from selection index. Another study compared genetic trends from sires, dams, and cows and found that trends from sire usage were more than twice as large as trends from dams. Comparison of sire evaluations with average evaluations of mates showed that nonrandom mating of sires with dams occurred infrequently and likely had no influence on sire evaluations. Other possible uses of cow evaluations were for differences between herds, genetic trends within herds, pedigree indexes for future offspring, and relation of pedigree indexes to Estimated Transmitting Abilities.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]