Biomedical subjects

R Rekaya

Publications and source records attributed to R Rekaya.

36 records · Page 2Linked to original sources

PubMed2003

Application of a multiple-trait herd cluster model for genetic evaluation of dairy sires from seventeen countries.

The multiple-trait across country evaluation method is currently used for international genetic evaluation of dairy sires. This method simultaneously combines national estimated breeding value (EBV) of sires in all countries and produces a separate breeding value to be used in each of the 24 countries that participate in the service. The major drawbacks to this method are the large number of genetic parameters that must be estimated and the large number of EBV produced for each sire. In the current method, each sire receives an EBV for each separate environment, and environments change at the country borders. It is unreasonable to assume that each country contains only one homogeneous environment and that every country has a distinctly different environment from all others. In the present study, an alternative method for international sire evaluation was utilized. Herds were grouped according to important management, climatic, and genetic factors rather than country borders. Data consisted of 16,403,413 first lactation cows in Australia, Austria, Belgium, Canada, Czech Republic, Estonia, Finland, Germany, Hungary, Ireland, Israel, Italy, The Netherlands, New Zealand, South Africa, Switzerland, and the United States. Herds were grouped according to 13 descriptive herd variables, including temperature, rainfall, peak yield, persistency, herd-size, age at calving, seasonality of calving, standard deviation of milk yield, culling percentage, fat-to-protein ratio, days to peak yield, percent of North American Holstein genes, and average PTA milk of sires. Variables were weighted by their relative importance in explaining genotype by environment interactions between herds. Herds were grouped into seven clusters; clusters ranged in size from 4805 to 59,272 herds and 1,414,966 to 3,966,431 cows. The proposed model predicts EBV for dairy sires based on the production environment in which their progeny wili perform, rather than the country where they will be located.

Animals↗

PubMed2003

Bivariate analysis of liability to clinical mastitis and to culling in first-lactation cows.

Records taken on 13,070 first-lactation daughters of 250 Norwegian Cattle sires were used to examine associations between susceptibility to clinical mastitis and to culling. Clinical mastitis was defined as a binary trait, whereas culling was treated as either binary (culled or not culled) or continuous (length of opportunity period) for two sampling periods (120 or 300 d of lactation). Two Bayesian models were employed; 1) a bivariate threshold model with both mastitis and culling as binary traits, and 2) a bivariate model with mastitis as a threshold binary variable and time to culling as Gaussian. The heritability of liability to clinical mastitis was not affected by either the length of sampling period (120 vs. 300 d) or by whether culling (binary) or length of opportunity period was the second trait in the bivariate analysis. The posterior mean (standard deviation) of heritability of liability to clinical mastitis was 0.06 to 0.07 (0.02) in all analyses. The heritability estimate of length of opportunity period was less than 0.001. Culling (threshold trait) in first lactation had a low heritability, but a high genetic correlation with clinical mastitis. The posterior means (standard deviation) for heritability of liability to culling were 0.01 (0.006) for 120 d and 0.02 (0.009) for 300 d, and the posterior means (standard deviation) of the genetic correlation between liability to clinical mastitis and to culling were 0.48 (0.24) and 0.53 (0.21) for 120 and 300 d, respectively.

Analysis of Variance↗

PubMed2003

Identification of factors that cause genotype by environment interaction between herds of Holstein cattle in seventeen countries.

Currently, the International Bull Evaluation Service calculates international dairy sire evaluations using the multiple-trait across country evaluation procedure. This method depends implicitly on political boundaries between countries, because the input data are national evaluations from each participating country. Therefore, different countries are treated as different production environments. The goal of this study was to identify factors that describe the production system on each farm. Such factors could be used to group herds across countries for borderless genetic evaluations. First lactation milk records of Holstein cows calving between January 1, 1990 and December 31, 1997 in Australia, Austria, Belgium, Canada, Czech Republic, Estonia, Finland, Germany, Hungary, Ireland, Israel, Italy, The Netherlands, New Zealand, South Africa, Switzerland, and the USA were used in this study. Thirteen genetic, management, and climatic variables were considered as potential indicators of production environments: peak milk yield, persistency, herd size, age at first calving, seasonality of calving, standard deviation of milk yield, culling rate, days to peak yield, fat to protein ratio, sire PTA milk, percentage of North American Holstein genes, maximum monthly temperature, and annual rainfall. Herds were grouped into quintiles based on herd averages for each of these variables. Genetic correlations for lactation milk yield between quintiles were significantly less than one for maximum monthly temperature, sire PTA milk, percent North American Holstein genes, herd size, and peak milk yield. The variables can be used to group herds into similar production environments, regardless of country borders, for the purpose of accounting for genotype by environment interaction in international dairy sire evaluation.

Aging↗

PubMed2003

Genotype x environment interaction for milk production in Guernsey cattle.

International genetic evaluations that use national genetic evaluation results as input need to acknowledge country boundaries. The current model for international evaluation treats each country as a genetically separate trait, i.e., assumes milk production to be similar within country, but different between countries. The use of cow performance records does not require such restriction, and allows for other statistical models to consider genotype x environment interaction. First-lactation records from 40,000 Guernsey cows in four countries (Australia, Canada, United States, and South Africa) were used to detect and describe genotype x environment interaction for milk production traits. Five statistical models were considered: single-trait across-county (ST), single-trait across-country with heterogeneous residual variance (SThet), multiple-trait across-country (MT), multiple-trait herd cluster model (HC), and reaction norm model (RR). For the herd cluster model, herds were clustered into groups based on information on herd management, genetic composition, and climate. Reaction norms describe the phenotype expressed by a genotype as a function of the environment, and was modeled by random regression on the herd average for peak milk yield as the descriptor of production environment. Gibbs sampling was used to make inferences about the parameters of interest, and models were compared based on goodness of fit and deviance information criterion. Posterior mode of the heritability for the single-trait model was 0.32, and ranged from 0.15 to 0.53 for models SThet and MT. Posterior mode of the genetic correlations between countries estimated with model MT were generally high (0.78 to 0.90). However, posterior SD were high (up to 0.15 for Australia-South Africa), and values near unity for the genetic correlations were not unlikely. Model HC gave more precise inferences but lower goodness of fit compared with model MT. Results from model RR provided evidence for heterogeneity of genetic variances. This model was least supported by the data, probably because heterogeneity of residual variances was not considered. Among the models in this study, the one with homogeneous genetic and heterogeneous residual variances across countries fitted best to the data, and we expect a model for which the assumption of homogeneous genetic variance is relaxed to show an even better fit to the data.

Animals↗

PubMed2003

Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States.

Inference about genetic covariance matrices using multiple-trait models is often hindered by lack of information. This leads to imprecise estimates of genetic parameters and of breeding values. Patterns in a genetic covariance matrix can be exploited to reduce the number of parameters and to increase quality of inferences. A structural model for genetic covariances was developed and fitted to milk yield data in five regions of the United States. This was compared with a standard multiple-trait analysis using a deviance information criterion, a measure of quality of fit. Data consisted of 3,465,334 Holstein first-lactation records from daughters of 43,755 sires in five regions of the United States (Midwest, Northeast, Northwest, Southeast, Southwest). Parameters of the structural model included an intercept and effects of measures of genetic and of management similarity on genetic covariances. Genetic similarity depended on the number of records contributed by sires that were common to a pair of regions. Management similarity was a function of the quantity of concentrate used to produce 1000 kg of milk in each pair of regions. The structural and the multiple-trait models gave similar estimates of genetic covariances, but the number of parameters was 8 in the former vs. 15 in the latter. Hence, estimates of genetic covariances were more precise with the structural model. A deviance information criterion suggested a slight superiority of the multiple-trait model, although probably within sampling error. For both models, genetic correlations between milk yield in five regions of the United States were larger than 0.93.

Analysis of Variance↗

PubMed2003

Bayesian estimates of covariance components between lactation curve parameters and disease liability in Danish Holstein cows.

In the present work, covariance components for milk yield and disease liability were estimated with bivariate random regression test-day sire models using a Bayesian approach and implemented via the Gibbs sampler. The data consist of 8075 first-parity Danish Holstein (DH) cows, from 1259 sires, performing in 57 herds from 1992 to 1997. Treatments associated with five different type of diseases were pooled into a single general disease liability for each cow. Two models were fitted to the data. First, using a bivariate model, milk yield is modeled via a random regression, and disease liability via a repeatablility model. Second, using a bivariate model, both milk yield and disease liability are modeled using random regressions. A comparison based on a Bayes factor provides very strong support for the bivariate random regression model. Posterior means of heritabilities for each of the traits were estimated for five different points in time throughout lactation. Across models, heritabilities for milk yield are lowest in the beginning of the lactation (0.19) and highest at the end of the lactation (0.35). Posterior means of heritabilities of disease liability range from 0.04 to 0.10 for test days, and is equal to 0.20 for the whole lactation. Heritability of persistency measures estimated from the two models are 0.20 and 0.21. Estimates of posterior means of genetic correlations between single test-day milk yield and single test-day disease liability are in the range of 0.31 to 0.57. The estimates of posterior mean and of the 95% posterior interval of the genetic correlation between persistency and (total) disease liability using the model with the highest posterior probability are -0.12 and (-0.44; 0.20), respectively. Even though the largest proportion of the posterior probability mass is spread along negative values of the correlation (indicating that individuals with a flatter lactation curve tend to have lower disease liability), a value of zero of the genetic correlation falls comfortably within the 95% posterior interval. Thus the prospects of reducing incidence of disease by manipulating persistency as defined in this work remain inconclusive.

Animals↗

PubMed2003

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.

Analysis of Variance↗

PubMed2003

Seasonality of days open in US Holsteins.

The objectives of this study were to establish a pattern for the seasonality of days open (DO) by state and region within the United States and to present statistics on regional trends for DO. Data included 8,676,915 records on DO for Holsteins from 1997 to 2002 covering all regions of the United States. Fixed effects in the model included herd, parity, milk-class, state x month of calving (MOC), year of calving x MOC, and parity x MOC. Least squares means of DO were highest for calvings in March and lowest for calvings in September. The highest mean DO of 155 d was recorded in the Southeast, while the mean DO for the Midwest, Northeast, Northwest, and Southwest were 142, 141, 140, and 137 d, respectively. Variation in monthly averages of DO was highest in Southeast with a range of 51 d, and less than 25 d in all the other regions. Seasonality of calving was defined as the ratio of the fewest to the most calvings in months. The SOC was > or = 60% in Southeast and < or = 23% in the other regions. Selected states: Texas, Oklahoma, and Arizona in the Southwest and Missouri, Kansas, and Kentucky in the Midwest showed patterns of variation in monthly averages and seasonality of calving similar to those of Southeast. Distributions of DO were bimodal for some months of calving due to postponed breeding during the hot season or depressed fertility as a result of thermal stress; the second mode at > 200 d was highest in the Southeast but also could be observed in Texas, Wisconsin, and California. High level of heat stress for DO exists in the Southeast and in selected states of the Midwest and the Southwest; these regions contribute less than 10% of national records. A methodology for analyzing DO especially under heat stress needs to consider effects of intentionally delayed breeding--by using a model that accounts for bimodality, for example.

Animals↗

PubMed2001

Threshold model for misclassified binary responses with applications to animal breeding.

A Bayesian procedure for misclassified binary data was developed. An animal breeding simulation indicated that, when error of classification was ignored, the variance between clusters was inferred incorrectly. Data were reanalyzed assuming that the probability of misclassification was either known or unknown. In the first case, input parameter values were recovered in the analysis. When the probability was unknown, there was a slight bias; the true probability of misclassification and the true number of miscoded observations appeared within high credibility regions. An analysis of fertility in dairy cows is presented.

Animals↗

PubMed2001

Application of a structural model for genetic covariances in international dairy sire evaluations.

A structural model for estimation of genetic covariances in international dairy sire evaluations was compared with a standard multiple-trait mixed model using milk yield data from 13 environments (Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, Israel, Switzerland and five regions of the United States). Data consisted of 2,885,117 first-lactation records from daughters of 17,867 Holstein sires. Parameters of the structural model for genetic covariances included an intercept and measures of genetic, management, and climate similarity. Genetic similarity was defined as the ratio between the number of daughters of common bulls used in a given pair of regions and the total number of daughters of all bulls. The measure of management similarity was the ratio between the absolute value of the difference in average milk yield between two regions and the sum of these averages. Climate similarity was a function of the difference in heat indices between pairs of regions. Results showed that the structural model for the genetic covariances gave more precise estimates of the latter than the standard multivariate analysis because the number of parameters to be estimated in the genetic covariance matrix was reduced from 91 to 16. A comparison of the two models using a deviance information criterion (a measure of quality of fit) showed a slight superiority for the structural model. For the latter, the posterior means of the genetic correlations between environments ranged between 0.63 and 0.98.

Analysis of Variance↗

PubMed2001

Bayesian analysis of liability of clinical mastitis in Norwegian cattle with a threshold model: effects of data sampling method and model specification.

First-lactation records of Norwegian Cattle were used to infer heritability of liability to clinical mastitis with a threshold sire model. Mastitis was defined as a binary response (presence or absence) in a defined period of first lactation (opportunity period). Length of opportunity period (from 30 d before calving up to 120 or 300 d of lactation) had less effect on heritability estimates than data sampling methods (include or exclude records of cows culled before the end of the opportunity period) whereas sire ranking was more affected by the former. Including all cows, whether culled before the end of the opportunity period or not, gave a sharper and more symmetric posterior distribution of heritability of liability to clinical mastitis. When we analyzed data for all cows, model specification had a small effect on heritability estimates, while sire ranking was affected markedly. Posterior means of heritability range from 0.058 to 0.074. A model regressing on the length of the opportunity period for culled cows without mastitis, was shown favorable for the two opportunity periods using Bayes factors and the deviance information criterion for model comparison. This model, in which liability of mastitis depends on time to culling, may allow utilizing information from all first lactations in genetic evaluation, irrespectively of duration and culling outcome.

Animals↗

PubMed2001

Characterization of dairy production systems in countries that participate in the International Bull Evaluation Service.

The International Bull Evaluation Service Centre has routinely calculated international dairy sire evaluations since 1994. Production systems vary between countries and between herds within a country, and these differences can cause significant genotype x environment interactions. First-lactation records of Holstein cows calving from January 1, 1990 through December 31, 1997, were used in this study. Countries that provided data for this study included Australia, Austria, Belgium, Canada, Czech Republic, Estonia, Finland, Germany, Hungary, Ireland, Israel, Italy, The Netherlands, New Zealand, South Africa, Switzerland, and the United States. Country means were calculated for 13 variables related to climate, herd management, and genetic background. These variables were considered as possible causes of genotype by environment interaction. Highest peak yields were found in Israel and the United States at 31.4 and 30.5 kg, respectively. New Zealand and Estonia had the lowest daily peak yields at 17.1 and 18.9 kg, respectively. This was consistent with genetic differences between these countries, because Israel had the highest average predicted transmitting abilities (PTA) milk among sires, while Estonia had the lowest PTA milk. Persistency of lactation, defined as milk yield at 240 d postpartum divided by milk yield at 60 d postpartum, was highest in the Czech Republic and Estonia at 1.34, and lowest in Israel at 1.05. Herd size also varied substantially between countries, ranging from 2.3 first-lactation cows per herd-year in Finland to 62 per herd-year in Hungary. In summary, tremendous variation exists between the leading dairy countries in management, genetic, and climatic factors.

Animal Husbandry↗

PubMed2001

International genetic evaluation of dairy sires using a multiple-trait model with individual animal performance records.

The objectives of this study were to estimate variance components and predict sire breeding values for milk, fat, and protein yield by using a multiple-trait model in which lactation yield in each country was considered as a different trait. Data included first lactation records of 16,145,832 Holstein-sired cows that calved between January 1, 1990, and December 31, 1997, in 243,466 herds in Australia, Austria, Belgium, Canada, the Czech Republic, Estonia, Finland, Germany, Hungary, Ireland, Israel, Italy, The Netherlands, New Zealand, South Africa, Switzerland, and the USA. Milk, fat, and protein were analyzed separately by using a 17-trait sire model; in this case, "traits" refer to measurements of the same biological parameter in different production systems. Our genetic model included the systematic effects of herd-year-season of calving, age at calving, milking frequency, and heterosis class (i.e., breed composition). Heritability estimates ranged from 0.24 in Australia (protein) to 0.34 in Israel (milk) and The Netherlands (fat). Genetic correlations between countries ranged from 0.77 for Austria-Czech Republic (protein), Estonia-Finland (fat), Estonia-Ireland (milk), Estonia-Israel (milk), and Hungary-New Zealand (fat), to 0.96 for Australia-Ireland (milk), Australia-New Zealand (milk), Belgium-Netherlands (milk), and Belgium-USA (fat). Correlations differed markedly from parameters used currently in international sire evaluations. In particular, genetic correlations were 0.91 to 0.96 between Australia, Ireland, and New Zealand; all of these countries rely heavily on rotational grazing. Correlations were also 0.91 to 0.96 between Belgium, Canada, Italy, The Netherlands, and the USA; all of these countries use intensive management systems. Correlations between these two groups of countries were 0.80 to 0.90. The percentage of elite bulls (top 1% for milk yield) selected in common by each pair of countries ranged from 0.42 for Germany-Estonia and Germany-Israel to 0.78 for Belgium-Netherlands.

Animals↗

PubMed2000

A multiple-trait herd cluster model for international dairy sire evaluation.

International dairy sire evaluations have traditionally been calculated using a two-step process. Lactation records within each country are used to predict national estimated breeding values, then these national breeding values are transformed to the genetic base, scale, and units of measurement of other countries by using conversion formulae or the multiple-trait, across-country evaluation method. A major limitation of this approach is the need to define environments (traits) according to country borders. Herds located in small, neighboring countries may be much more similar in management, climate, and genetic background than herds located far apart within a single large country. In the present study, international genetic evaluation with herd clusters is proposed. Data consisted of 4.6 million lactation records from 46,000 herds in Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, Israel, Switzerland, and five regions of the US (Midwest, Northeast, Northwest, Southeast, and Southwest). Herds were grouped into clusters based on data of 13 descriptive variables: herd size, calving interval, milking frequency, age at first calving, milk yield, month of calving, predicted transmitting ability of sire for milk, percentage North American genes of sire, latitude, altitude, temperature, rainfall, and percentage of arable land used for pasture. Five clusters were formed; each cluster contained herds from 5 to 11 countries or regions. Genetic correlations between herd clusters ranged from 0.81 to 0.97. The herd cluster model is intuitively appealing, because genetic merit of an animal is predicted for each unique environment or management system, regardless of country borders. This model is parsimonious (the number of traits was reduced from 13 to 5) and is computationally feasible for large data sets.

Animals↗

PubMed2000

Genetic parameters for reproductive traits of Holstein cattle in California and Minnesota.

Genetic parameters for five reproductive traits were estimated using data from 51,528 Holstein cows that were inseminated from April to September 1998 in 1717 herds in California and Minnesota. Nonreturn rate and veterinary-confirmed pregnancy rate at 60 and 90 d after insemination were evaluated using linear and threshold models, including an additive genetic effect for the cow being inseminated and a random environmental effect for the service bull. Interval from calving to first insemination was evaluated using a linear model, including an additive genetic effect for the cow being inseminated. Linear model heritability estimates for 60-d (90-d) nonreturn rate were 1.4% (1.5%) in California and 4.1% (2.7%) in Minnesota. Corresponding estimates for 60-d (90-d) confirmed pregnancy rate were 1.4% (2.3%) in California and 1.0% (2.0%) in Minnesota; the proportion of cows with veterinary data available 60 d after breeding was 86% in California and 55% in Minnesota. Threshold model heritability estimates were slightly higher than linear model estimates in California but were lower in Minnesota, presumably because 25% of the herd-season classes in Minnesota contained either all successes or all failures. Linear model repeatability estimates for the service bull effect on 60-d (90-d) nonreturn rate were 0.5% (0.4%) in California and 0.3% (0.3%) in Minnesota. Corresponding estimates for 60-d (90-d) confirmed pregnancy rates were 0.6% (0.2%) in California and 0.1% (0.4%) in Minnesota. Threshold model estimates were slightly higher than linear model estimates in both states. Heritability estimates for the interval from calving to first insemination were 5.8% in California and 6.1% in Minnesota. Despite the low parameter estimates, variation was present among animals, and it should be possible to identify sires that possess superior or inferior reproductive characteristics.

Animals↗

PubMed2000

Bayesian analysis of lactation curves of Holstein-Friesian cattle using a nonlinear model.

A Bayesian procedure was developed for fitting Wood's incomplete Gamma function to test-day milk records of Spanish Holstein Friesian cattle. Each parameter of Wood's function was considered as a dependent variable in a submodel that accounted for systematic effects and genetic relationships among animals. Marginal posterior distributions of model parameters were obtained using Gibbs sampling. Variables of economic interest, such as 305-d yield, persistency, peak yield, and days in milk at peak day were predicted as functions of Wood's function curve parameters. Heritability estimates were 0.26, 0.32, and 0.19 for parameters of Wood's function and 0.26, 0.14, 0.26, and 0.05 for 305-d yield, persistency, peak yield, and days in milk at peak yield. These estimates indicate that it is possible to modify the shape of the lactation curve through genetic selection. Genetic correlations between parameters of Wood's curve and the aforementioned functions of these parameters suggest that selection for 305-d milk yield would result in higher and later peak yield, but only a slight improvement in persistency is expected.

Animals↗

PubMed1998

Impact of bovine somatotropin on genetic evaluation of dairy sires and cows.

Data for milk yield and bovine somatotropin (bST) injections were obtained for 92,463 lactations of 51,986 Holstein cows in 222 commercial dairy herds that had used bST during the previous 3 yr. The overall rate of bST usage in these herds was 29%, and little difference occurred across lactations. A slightly higher percentage of cows with a low pretreatment phenotypic milk yield received bST, but there was no relationship between bST usage rate and the genetic potential of the cows, as measured by the PTA for milk of the sire. The mean starting date of bST administration was 147 d of lactation. Breeding values were estimated using three different animal models. In the first model, all data regarding bST injection were ignored. The second model included a fixed effect of bST injection (0 or 1 for each lactation). In the third model, data for bST injection were used to define management groups such that cows within a particular herd, year, and season of calving that received bST during the lactation were in a different management group from their contemporaries that did not receive bST. Correlations for EBV between sire and cow either ignoring bST or treating bST as a fixed effect were > 0.999, and approximately 98% of selected individuals were chosen under both models. Use of bST information to define the management groups resulted in correlations > 0.99; the EBV from models that either ignored bST or treated bST as a fixed effect had 92 to 95% of the selected individuals chosen by the other two models. The genetic correlation between lactation milk yield with and without bST treatment, which was estimated using a multiple-trait model, was 0.98, which indicated minimal interaction of genotype and bST. In general, bST treatment had little impact on the genetic selection decisions in this study.

Animals↗

PubMedDate not supplied

Assessment of heterogeneity of residual variances using changepoint techniques.

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100,744 test-day records of 10,869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T1 and T2, (0<T1<T2<tmax), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t (sigma2(et)) in the lactation phase i was modeled as: sigma2(et) = t(lambda)(i)sigma2(ei) for (i =1,2,3), where lambda(i) is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20,000 iterations, 40,000 samples were drawn to estimate posterior features. The posterior modes of T1, T2, lambda1, lambda2, lambda3, sigma2(e1), sigma2(e2), sigma2(e3) were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg2, respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg2 at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.

Journal Article↗