Genetic analysis of somatic cell scores in US Holsteins with a Bayesian mixture model

The objective of this study was to apply finite mixture models to field data for somatic cell scores (SCS) for estimation of genetic parameters. Data were approximately 170,000 test-day records for SCS from first-parity Holstein cows in Wisconsin. Five different models of increasing level of complexity were fitted. Model 1 was the standard single-component model, and the others were 2-component Gaussian mixtures consisting of similar but distinct linear models. All mixture models (i.e., 2 to 5) included separate means for the 2 components. Model 2 assumed entirely homogeneous variances for both components. Models 3 and 4 assumed heterogeneous variances for either residual (model 3) or genetic and permanent environmental variances (model 4). Model 5 was the most complex, in which variances of all random effects were allowed to vary across components. A Bayesian approach was applied and Gibbs sampling was used to obtain posterior estimates. Five chains of 205,000 cycles were generated for each model. Estimates of variance components were based on posterior means. Models were compared by use of the deviance information criterion. Based on the deviance information criterion, all mixture models were superior to the linear model for analysis of SCS. The best model was one in which genetic and PE variances were heterogeneous, but residual variances were homogeneous. The genetic analysis suggested that SCS in healthy and infected cattle are different traits, because the genetic correlation between SCS in the 2 components of 0.13 was significantly different from unity.     

Use of test-day records beyond three hundred five days for estimation of three hundred five-day breeding values for production traits and somatic cell score of Canadian Holsteins

The Canadian Test-Day Model includes test-day (TD) records from 5 to 305 d in milk (DIM). Because 60% of Canadian Holstein cows have at least one lactation longer than 305 d, a significant number of TD records beyond 305 DIM could be included in the genetic evaluation. The aim of this study was to investigate whether TD records beyond 305 DIM could be useful for estimation of 305-d estimated breeding value (EBV) for milk, fat, and protein yields and somatic cell score. Data were 48,638,184 TD milk, fat, and protein yields and somatic cell scores from the first 3 lactations of 2,826,456 Canadian Holstein cows. All production traits were preadjusted for the effect of pregnancy. Subsets of data were created for variance-component estimation by random sampling of 50 herds. Variance components were estimated using Gibbs sampling. Full data sets were used for estimation of breeding values. Three multiple-trait, multiple-lactation random regression models with TD records up to 305 DIM (M305), 335 DIM (M335), and 365 DIM (M365) were fitted. Two additional models (M305a and M305b) used TD records up to 305 DIM and variance components previously estimated by M335 and M365, respectively. The effects common to all models were fixed effects of herd × test-date and DIM class, fixed regression on DIM nested within region × age × season class, and random regressions for additive genetic and permanent environmental effects. Legendre polynomials of order 6 and 4 were fitted for fixed and random regressions, respectively. Rapid increase of additive genetic and permanent environmental variances at extremes of lactations was observed with all 3 models. The increase of additive genetic and permanent environmental variances was at earlier DIM with M305, resulting in greater variances at 305 DIM with M305 than with M335 and M365. Model M305 had the best ability to predict TD yields from 5 through 305 DIM and less error of prediction of 305-d EBV than M335 and M365. Model M335 had smaller change of 305-d EBV of bulls over the period of 7 yr than did M305 and M365. Model M305a had the least error of prediction and change of 305-d EBV from all models. Therefore, the use of TD records of Holstein cows from 5 through 305 DIM and variance components estimated using records up to 335 DIM is recommended for the Canadian Test-Day Model.     

Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.     

Application of a finite mixture model to somatic cell scores of Italian goats

The objectives of this study were to apply a finite mixture model (FMM) to data for somatic cell count in goats and to compare the fit of the FMM with that of a standard linear mixed effects model. Bacteriological information was used to assess the ability of the model to classify records from healthy or infected goats. Data were 4518 observations of somatic cell score (SCS) and bacterial infection from both udder halves of 310 goats from 5 herds in Northern Italy. The records were from a complete production season, and were taken monthly from February to November 2000. Explanatory factors in both models included a 3-parameter regression on days in milk (DIM); fixed class effects of herd-test-day, parity group, and udder side (left or right); and random effects of goat and udder half within goat. In addition, the 2-component FMM included a fixed mean for the second component of the model (theoretically corresponding to infected udder halves), as well as an unknown probability of membership to a given putative infection status. A Bayesian statistical approach was used for the analysis with Gibbs sampling used to obtain draws from posterior distributions of parameters of interest. Two sampling chains of 200,000 cycles each were generated for each model. The FMM yielded a much lower estimate of residual variance than the standard model (1.28 vs. 3.02 SCS²), and a slightly higher estimate for the between-goat variance (1.79 vs. 1.48). The deviance information criterion (DIC) was used to compare the fit of the 2 models. The DIC was much lower for the FMM, indicating a better fit to the data. The FMM was able to classify correctly 60 and 48% of the healthy and infected observations, respectively. This was slightly higher than what would be expected from random classification, but not high enough for useful mastitis diagnosis. Nevertheless, increased precision of genetic evaluation is the goal of applying the FMM, rather than timely and accurate mastitis diagnosis. The results suggest that more research on FMM for SCS is merited and necessary for proper application.     

Components of genetic variance and covariance for linear type traits in Jersey cattle

First available appraisals for 67,644 Jersey cows were used to estimate relative magnitudes of additive and selected sources of nonadditive genetic variance and covariance for 13 type traits scored linearly from 50 to 99 points. Covariances among four types of relatives were used to estimate components of genetic variance and covariance for each of the 13 traits. Direct additive, direct dominance, and additive maternal genetic variances and the direct-maternal additive genetic covariance were estimated using covariances among paternal half-sibs, full-sibs, daughters and dams, and maternal half-sibs. Estimates of additive genetic variance were 11 to 36% of variance within herd-appraiser subclasses with largest values for stature, strength, rump angle, rump width, and udder depth. Dominance components were two to four times the magnitude of additive components for dairy character, rump width, fore udder, rear udder height, rear udder width, and suspensory ligament but much smaller for other traits. Maternal effects and the direct-maternal additive genetic covariance appeared small for all linear type traits.     

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

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

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

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

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.     

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.     

Within-herd effects of age at test day and lactation stage on test-day yields

Variance ratios were estimated for random within-herd effects of age at test day and lactation stage, on test-day yield and somatic cell score to determine whether including these effects would improve the accuracy of estimation. Test-day data starting with 1990 calvings for the entire US Jersey population and Holsteins from California, Pennsylvania, Wisconsin, and Texas were analyzed. Test-day yields were adjusted for across-herd effects using solutions from a regional analysis. Estimates of the relative variance (fraction of total variance) due to within-herd age effects were small, indicating that regional adjustments for age were adequate. The relative variances for within-herd lactation stage were large enough to indicate that accuracy of genetic evaluations could be improved by including herd stage effects in the model for milk, fat, and protein, but not for somatic cell score. Because the within-herd lactation stage effect is assumed to be random, the effect is regressed toward the regional effects for small herds, but in large herds, lactation curves become herd specific. Model comparisons demonstrated the greater explanatory power of the model with a within-herd-stage effect as prediction error standard deviations were greater for the model without this effect. The benefit of the within-herd-stage effects was confirmed in a random regression model by comparing variance components from models with and without random within-herd regressions and through log-likelihood ratio tests.     

Variance components for test-day milk, fat, and protein yield, and somatic cell score for analyzing management information

Test-day (TD) models are used in most countries to perform national genetic evaluations for dairy cattle. The TD models estimate lactation curves and their changes as well as variation in populations. Although potentially useful, little attention has been given to the application of TD models for management purposes. The potential of the TD model for management use depends on its ability to describe within- or between-herd variation that can be linked to specific management practices. The aim of this study was to estimate variance components for milk yield, milk component yields, and somatic cell score (SCS) of dairy cows in the Ragusa and Vicenza areas of Italy, such that the most relevant sources of variation can be identified for the development of management parameters. The available data set contained 1,080,637 TD records of 42,817 cows in 471 herds. Variance components were estimated with a multilactation, random-regression, TD animal model by using the software adopted by NRS for the Dutch national genetic evaluation. The model comprised 5 fixed effects [region × parity × days in milk (DIM), parity × year of calving × season of calving × DIM, parity × age at calving × year of calving, parity × calving interval × stage of pregnancy, and year of test × calendar week of test] and random herd × test date, regressions for herd lactation curve (HCUR), the animal additive genetic effect, and the permanent environmental effect by using fourth-order Legendre polynomials. The HCUR variances for milk and protein yields were highest around the time of peak yield (DIM 50 to 150), whereas for fat yield the HCUR variance was relatively constant throughout first lactation and decreased following the peak around 40 to 90 DIM for lactations 2 and 3. For SCS, the HCUR variances were relatively small compared with the genetic, permanent environmental, and residual variances. For all the traits except SCS, the variance explained by random herd × test date was much smaller than the HCUR variance, which indicates that the development of management parameters should focus on between-herd parameters during peak lactation for milk and milk components. For SCS, the within-herd variance was greater than the between-herd variance, suggesting that the focus should be on management parameters explaining variances at the cow level. The present study showed clear evidence for the benefits of using a random regression TD model for management decisions.     

Estimating Effects of Permanent Environment, Lactation Stage, Age, and Pregnancy on Test-Day Yield

Test-day variances for permanent environmental effects within and across parities were estimated along with lactation stage, age, and pregnancy effects for use with a test-day model. Data were test-day records for calvings since 1990 for Jerseys and for Holsteins from California, Pennsylvania, Texas, and Wisconsin. Single-trait repeatability models were fitted for milk, fat, and protein test-day yields. Method R and a preconditioned conjugate gradient equation solver were used for variance component estimation because of large data sets. Test-day yields were adjusted for environmental effects of calving age, calving season, and milking frequency and for estimated breeding value (EBV) expressed on a daily basis. To assess the effect of adjustments, test-day yields also were analyzed without adjustment. For adjusted data, permanent environmental variances across parities relative to phenotypic variance ranged from 8.3 to 15.2% for milk, 4.4 to 8.3% for fat, and 6.9 to 11.0% for protein across regions and breeds; relative permanent environmental variances within parity ranged from 31.4 to 34.7% for milk, 18.2 to 22.3% for fat, and 28.3 to 29.1% for protein and were similar across regions and breeds. Adjustment for EBV reduced permanent environmental variance across parities and removed cow genetic variance. Relative permanent environmental variances within parity from unadjusted test-day yields were nearly identical to those from adjusted test-day yields. For unadjusted test-day yields, heritabilities ranged from 0.19 to 0.30 for milk, 0.13 to 0.15 for fat, and 0.17 to 0.23 for protein. Adjustments for lactation stage, age at milking, previous days open, and days pregnant were estimated from adjusted test-day yields using the same single-trait repeatability models and variance ratios estimated for permanent environment within and across parities. Those adjustments can be applied additively to test-day yields before evaluation analysis. Variance components and solutions for the various effects can be used to calculate test-day deviations in an analysis within herd that contributes to an analysis across herds.     

Method R estimates of additive genetic, dominance genetic, and permanent environmental fraction of variance for yield and health traits of Holsteins

Fractions of variance accounted for by additive genetic, dominance genetic, and permanent environmental effects for milk, fat, and protein yields; somatic cell score; and productive life were estimated from Holstein data used for national genetic evaluations. Contemporary group assignments were determined using the national procedure. Data included 1,973,317 milk and fat records for 812,659 cows, 1,019,421 protein records for 462,067 cows, 468,374 lactation average somatic cell score (SCS) records for 232,909 cows, and 735,256 cows with productive-life records. Variance components were estimated with the JAADOM program, which uses iteration on data and second-order Jacobi iteration for obtaining solutions to the mixed-model equations and Method R for estimation of variance components. Ten different random data subsets were used to estimate parameters for each trait. Estimated additive genetic, dominance genetic, and permanent environmental fractions of variance were 0.34, 0.05, and 0.10 for milk yield; 0.34, 0.05, and 0.11 for fat yield; 0.31, 0.05, and 0.10 for protein yield; and 0.17, 0.01, and 0.16 for lactation average SCS. Estimated additive genetic and dominance genetic fractions of variance were 0.12 and 0.06 for productive life. Mean empirical standard errors of additive genetic, dominance genetic, and permanent environmental variance fractions were 0.003, 0.006, and 0.006.     

Genetic analysis of somatic cell score in Norwegian cattle using random regression test-day models

The dataset used in this analysis contained a total of 341,736 test-day observations of somatic cell scores from 77,110 primiparous daughters of 1965 Norwegian Cattle sires. Initial analyses, using simple random regression models without genetic effects, indicated that use of homogeneous residual variance was appropriate. Further analyses were carried out by use of a repeatability model and 12 random regression sire models. Legendre polynomials of varying order were used to model both permanent environmental and sire effects, as did the Wilmink function, the Lidauer-M?ntysaari function, and the Ali-Schaeffer function. For all these models, heritability estimates were lowest at the beginning (0.05 to 0.07) and higher at the end (0.09 to 0.12) of lactation. Genetic correlations between somatic cell scores early and late in lactation were moderate to high (0.38 to 0.71), whereas genetic correlations for adjacent DIM were near unity. Models were compared based on likelihood ratio tests, Bayesian information criterion, Akaike information criterion, residual variance, and predictive ability. Based on prediction of randomly excluded observations, models with 4 coefficients for permanent environmental effect were preferred over simpler models. More highly parameterized models did not substantially increase predictive ability. Evaluation of the different model selection criteria indicated that a reduced order of fit for sire effects was desireable. Models with zeroth- or first-order of fit for sire effects and higher order of fit for permanent environmental effects probably underestimated sire variance. The chosen model had Legendre polynomials with 3 coefficients for sire, and 4 coefficients for permanent environmental effects. For this model, trajectories of sire variance and heritability were similar assuming either homogeneous or heterogeneous residual variance structure.     

Genetic analyses of protein yield in dairy cows applying random regression models with time-dependent and temperature x humidity-dependent covariates

Data used in the present study included 1,095,980 first-lactation test-day records for protein yield of 154,880 Holstein cows housed on 196 large-scale dairy farms in Germany. Data were recorded between 2002 and 2009 and merged with meteorological data from public weather stations. The maximum distance between each farm and its corresponding weather station was 50 km. Hourly temperature-humidity indexes (THI) were calculated using the mean of hourly measurements of dry bulb temperature and relative humidity. On the phenotypic scale, an increase in THI was generally associated with a decrease in daily protein yield. For genetic analyses, a random regression model was applied using time-dependent (d in milk, DIM) and THI-dependent covariates. Additive genetic and permanent environmental effects were fitted with this random regression model and Legendre polynomials of order 3 for DIM and THI. In addition, the fixed curve was modeled with Legendre polynomials of order 3. Heterogeneous residuals were fitted by dividing DIM into 5 classes, and by dividing THI into 4 classes, resulting in 20 different classes. Additive genetic variances for daily protein yield decreased with increasing degrees of heat stress and were lowest at the beginning of lactation and at extreme THI. Due to higher additive genetic variances, slightly higher permanent environment variances, and similar residual variances, heritabilities were highest for low THI in combination with DIM at the end of lactation. Genetic correlations among individual values for THI were generally >0.90. These trends from the complex random regression model were verified by applying relatively simple bivariate animal models for protein yield measured in 2 THI environments; that is, defining a THI value of 60 as a threshold. These high correlations indicate the absence of any substantial genotype × environment interaction for protein yield. However, heritabilities and additive genetic variances from the random regression model tended to be slightly higher in the THI range corresponding to cows’ comfort zone. Selecting such superior environments for progeny testing can contribute to an accurate genetic differentiation among selection candidates.     

Genetic association of clinical mastitis with test-day somatic cell score and milk yield during first lactation of Finnish Ayrshire cows

In this study the genetic association during lactation of 2 clinical mastitis (CM) traits: CM1 (7 d before to 30 d after calving) and CM2 (31 to 300 d after calving) with test-day somatic cell score (SCS) and milk yield (MY) was assessed using multitrait random regression sire models. The data analyzed were from 27,557 first-lactation Finnish Ayrshire cows. Random regressions on second- and third-order Legendre polynomials were used to model the daily genetic and permanent environmental variances of test-day SCS and MY, respectively, while only the intercept term was fitted for CM. Results showed that genetic correlations between CM and the test-day traits varied during lactation. Genetic correlations between CM1 and CM2 and test-day SCS during lactation varied from 0.41 to 0.77 and from 0.34 to 0.71, respectively. Genetic correlations of test-day MY with CM1 and CM2 ranged from 0.13 to 0.51 and from 0.49 to 0.66, respectively. Correlations between CM1 and SCS were strongest during early lactation, whereas correlations between CM2 and SCS were strongest in late lactation. Genetic correlations lower than unity indicate that CM and SCS measure different aspects of the trait mastitis. Milk yield in early lactation was more strongly correlated with both CM1 and CM2 than milk yield in later lactation. This suggests that selection for higher lactation MY through selection on increased milk yield in early lactation will have a more deleterious effect on genetic resistance to mastitis than selection for higher yield in late lactation. The approach used in this study for the estimation of the genetic associations between test-day and CM traits could be used to combine information from traits with different data structures, such as test-day SCS and CM traits in a multitrait random regression model for the genetic evaluation of udder health.     

Genetic parameters of legendre polynomials for first parity lactation curves

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day records from cows registered between 1990 to 1996 and collected by regular milk recording were available. For the data set, 23,700 complete lactations were selected from 475 herds sired by 262 sires. Because the application of a random regression model is limited by computing capacity, we investigated the minimum order needed to fit the variance structure in the data sufficiently. Predictions of genetic and permanent environmental variance structures were compared with bivariate estimates on 30-d intervals. A third-order or higher polynomial modeled the shape of variance curves over DIM with sufficient accuracy for the genetic and permanent environment part. Also, the genetic correlation structure was fitted with sufficient accuracy by a third-order polynomial, but, for the permanent environmental component, a fourth order was needed. Because equal orders are suggested in the literature, a fourth-order Legendre polynomial is recommended in this study. However, a rank of three for the genetic covariance matrix and of four for permanent environment allows a simpler covariance function with a reduced number of parameters based on the eigenvalues and eigenvectors.     

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.     

Assessment of homogeneity vs. heterogeneity of residual variance in random regression test-day models in a Bayesian analysis

Test-day first-lactation milk yields from Holstein cows were analyzed with a set of random regression models based on Legendre polynomials of varying order on additive genetic and permanent environmental effects. Homogeneity and heterogeneity of residual variance, assuming three and 30 arbitrary measurement error classes of different length were considered. Unknown parameters were estimated within a Bayesian framework. Bayes factors and a checking function for the cross-validation predictive densities of the data were the tools chosen for selecting among competing models. Residual variances obtained from 30 arbitrary intervals were nearly constant between d 70 and 300 and tended to increase towards the extremes of the lactation, especially at the onset. In early lactation, the temporary measurement errors were found to be larger and highly variable. A high order of the regression submodels employed for modeling the permanent environmental deviations tended to strongly correct the heterogeneity of the residual variance. Accordingly, the assumption of homogeneity of residual variance was the most plausible specification under both comparison criteria when the number of random regression coefficients was set to five. Otherwise, the heterogeneity assumption, using three or 30 error classes, was better supported, depending on the criterion and on the order of the submodel fitted for the permanent environmental effect.     

白肋烟烟叶腺毛分泌物的遗传分析

应用ADMP遗传模型对6个白肋烟品种Ky14、Ky8959、B21、B37、建选3号、Bx2003的完全双列杂交组合的12、18叶位烟叶表皮腺毛分泌物含量进行了分析,采用MINQUE(1)法估算遗传参数分量的方差,应用AUP法预测遗传效应值,Jackknife法估算遗传方差和效应值的抽样方差.结果表明:(1)表皮腺毛分泌物以烟碱、茄酮、9-十八炔和西柏三烯二醇为主;(2)各参试组合12、18叶位各类型腺毛分泌物表型变异主要受遗传背景控制,广义遗传率范围为48%～80%,说明对腺毛分泌物的遗传改良能够收到明显作用;(3)品种B21、BX2003的基因型加性效应显示其作为亲本较适合;(4)Ky14与B37、Ky8959与Bx2003、B37与建选3号、建选3号与Bx2003之间的组合的显性效应在显著降低烟叶表皮烟碱含量的同时增加其它腺毛分泌物含量;(5)品种Ky14和B21较适合作为母本材料;(6)品种Ky8959、B21、Bx2003较适合作为父本材料.