J. Jamrozik

Approximate accuracies of prediction from random regression models.

Abstract A procedure for obtaining approximate reliabilities of estimated breeding values under a random regression model is presented. The method is based on a concept of an equivalent number of progeny, with subsequent selection index approximation of reliability utilising equivalent progeny information on the animal and its parents. The accuracy of the proposed approximation was tested using a multiple trait random regression test day model for dairy production traits applied to Canadian Jersey data. Gibbs sampling method was used to generate exact reliabilities of genetic evaluations for several traits derived from the genetic random regression coefficients. The approximation was shown to be relatively unbiased for both bulls and cows. The method has been implemented in the Canadian test day model for dairy production traits.

Relationships between milk yield and somatic cell score in Canadian Holsteins from simultaneous and recursive random regression models

Multiple-trait random regression animal models with simultaneous and recursive links between phenotypes for milk yield and somatic cell score (SCS) on the same test day were fitted to Canadian Holstein data. All models included fixed herd test-day effects and fixed regressions within region-age at calving-season of calving classes, and animal additive genetic and permanent environmental regressions with random coefficients. Regressions were Legendre polynomials of order 4 on a scale from 5 to 305 d in milk (DIM). Bayesian methods via Gibbs sampling were used for the estimation of model parameters. Heterogeneity of structural coefficients was modeled across (the first 3 lactations) and within (4 DIM intervals) lactation. Model comparisons in terms of Bayes factors indicated the superiority of simultaneous models over the standard multiple-trait model and recursive parameterizations. A moderate heterogeneous (both across- and within-lactation) negative effect of SCS on milk yield (from -0.36 for 116 to 265 DIM in lactation 1 to -0.81 for 5 to 45 DIM in lactation 3) and a smaller positive reciprocal effect of SCS on milk yield (from 0.007 for 5 to 45 DIM in lactation 2 to 0.023 for 46 to 115 DIM in lactation 3) were estimated in the most plausible specification. No noticeable differences among models were detected for genetic and environmental variances and genetic parameters for the first 2 regression coefficients. The curves of genetic and permanent environmental variances, heritabilities, and genetic and phenotypic correlations between milk yield and SCS on a daily basis were different for different models. Rankings of bulls and cows for 305-d milk yield, average daily SCS, and milk lactation persistency remained the same among models. No apparent benefits are expected from fitting causal phenotypic relationships between milk yield and SCS on the same test day in the random regression test-day model for genetic evaluation purposes.

Genetic Correlation Patterns Between Somatic Cell Score and Protein Yield in the Italian Holstein-Friesian Population

Genetic parameters for somatic cell score (SCS) in the Italian Holstein-Friesian population were estimated addressing the pattern of genetic correlation with protein yield in different parities (first, second, and third) and on different days in milk within each parity. Three approaches for parameter estimation were applied using random samples of herds from the national database of the Italian Holstein Association. Genetic correlations for lactation measures (305-d protein yield and lactation SCS) were positive in the first parity (0.31) and close to zero in the second (0.01) and third (0.09) parities. These results indicated that larger values of SCS were genetically associated with increased production. The second and third sets of estimates were based on random regression test-day models, modeling the shape of lactation curve with the Wilmink function and fourth-order Legendre polynomials, respectively. Genetic correlations from both random regression models showed a specific pattern associated with days in milk within and across parities. Estimates varied from positive to negative in the first and second parity, and from null to negative in the third parity. Patterns were similar for both random regression models. The average overall correlation between SCS and protein yield was zero or slightly positive in the first lactation and ranged from zero to negative in later lactations. Correlation estimates differed by parity and stage of lactation. They also demonstrated the dubiousness of applying a single genetic correlation measure between SCS and protein in setting selection strategies. Differences in magnitude and the sign of genetic correlations between SCS and yields across and within parities should be accounted for in selection schemes.

Bayesian estimation of genetic parameters for test day records in dairy cattle using linear hierarchical models

Abstract Hierarchical models were fitted to first lactation test day milk yields of Canadian Holstein cows. Models included Wilmink’s lactation curve and herd-test date effects in the first stage, and herd–year–season of calving, region–age–season of calving and animal genetic effects in the second stage of the hierarchy, using various combinations of these factors. Functions of Wilmink’s function trajectory parameters were analysed jointly with the original parameters in selected models. Genetic and environmental variances, and heritabilities for lactation curve coefficients, daily and 305-day yields, and persistency of lactation were inferred by Bayesian methodology via Gibbs sampling. Accounting for the between herd–year–season variation in trajectory parameters resulted in more stable estimates of genetic variances over lactation, more sensible heritabilities for extreme days in milk, larger genetic correlations between yields at distant days of lactation, but lower heritabilities of lactation curve coefficients. Joint modelling of lactation curve parameters and selected functions thereof allowed for estimation of heritabilities of time-dependent traits, and reduced seemingly anomalous estimates of genetic parameters obtained with current implementations of certain random regression models.

Comparison of two computing algorithms for solving mixed model equations for multiple trait random regression test day models

Abstract Two computing algorithms for solving mixed model equations for a multiple lactation, multiple trait random regression test day model were compared. The model for each trait (yields of milk, fat, and protein, and somatic cell scores in the first three lactations) included fixed contemporary groups, fixed regressions within levels of time–region–age–season parity subclasses at calving and two sets of random regressions: animal genetic and permanent environmental effects, giving a total of twelve traits and 36 equations for each animal genetic effect and each animal permanent environmental effect. Algorithm A utilized the iteration on data with blocking strategy (with contemporary group and animal blocks) in a Gauss–Seidel iteration scheme. Block sizes for animal genetic and permanent environmental effects were of order 36. Algorithm B utilized an alternative blocking strategy for animal effects with separate blocks for each lactation of order 12. This allowed for significant reduction in memory requirements, less time per iteration, but slightly slower convergence compared to Algorithm A. The algorithms were compared in an application of the test day model to the national Canadian Jersey test day data set. Memory and disk space requirements for the two algorithms as well as extensions of the model were discussed.

Estimating daily yields of cows from different milking schemes

Abstract A multiple regression model was used to derive equations for predicting 24 h milk, fat, and protein yields of dairy cows on either two-times or three-times-a-day milking under different testing schemes. New prediction equations were developed for 72 subclasses of days in milk, parity, and season of calving for each of 18 possible three-times-a-day testing schemes and for each of four possible two-times-a-day testing schemes. The prediction equations were compared to current official factors and found to be slightly better than the official factors. For two-times-a-day testing schemes the accuracies of 24 h fat yield predictions from one milk weight and one fat and protein determination were 0.88 for an evening milking and 0.89 for a morning milking. For three-times-a-day milkings the accuracies of 24 h fat and protein yields from two milk weights with fat and protein contents on each were 0.91–0.94 depending on which two of the three milkings were observed. If only one of three milkings were recorded, then accuracies of 24 h predicted fat and protein yields dropped to 0.80–0.82. More data from herds milking three-times-a-day are needed on all breeds.