Age at first insemination, days from calving to first insemination, number of services, first-service nonreturn rate to 56 d, days from first service to conception, calving ease, stillbirth, gestation length, and calf size of Canadian Holstein cows were jointly analyzed in a linear multiple-trait model. Traits covered a wide spectrum of aspects related to reproductive performance of dairy cows. Other frequently used fertility characteristics, like days open or calving intervals, could easily be derived from the analyzed traits. Data included 94,250 records in parities 1 to 6 on 53,158 cows from Ontario and Quebec, born in the years 1997 to 2002. Reproductive characteristics of heifers and cows were treated as different but genetically correlated traits that gave 16 total traits in the analysis. Repeated records for later parities were modeled with permanent environmental effects. Direct and maternal genetic effects were included in linear models for traits related to calving performance. Bayesian methods with Gibbs sampling were used to estimate covariance components of the model and respective genetic parameters. Estimates of heritabilities for fertility traits were low, from 3% for nonreturn rate in heifers to 13% for age at first service. Interval traits had higher heritabilities than binary or categorical traits. Service sire, sire of calf, and artificial insemination technician were important (relative to additive genetic) sources of variation for nonreturn rate and traits related to calving performance. Fertility traits in heifers and older cows were not the same genetically (genetic correlations in general were smaller than 0.9). Genetic correlations (both direct and maternal) among traits indicated that different traits measured different aspects of reproductive performance of a dairy cow. These traits could be used jointly in a fertility index to allow for selection for better fertility of dairy cattle.

A model that contains both fixed and random linear regressions is described for analyzing test day records of dairy cows. Estimation of the variances and covariances for this model was achieved by Bayesian methods utilizing the Gibbs sampler to generate samples from the marginal posterior distributions. A single-trait model was applied to yields of milk, fat, and protein of first lactation Holsteins. Heritabilities of 305-d lactation yields were 0.32, 0.28, and 0.28 for milk, fat, and protein, respectively. Heritabilities of daily yields were greater than for 305-d yields and varied from 0.40 to 0.59 for milk yield, 0.34 to 0.68 for fat yield, and 0.33 to 0.69 for protein yield. The highest heritabilities were within the first 10 d of lactation for all traits. Genetic correlations between daily yields were higher as the interval between tests decreased, and correlations of daily yields with 305-d yields were greatest during midlactation.

The objective of this research was to estimate heritabilities of milk urea nitrogen (MUN) and lactose in the first 3 parities and their genetic relationships with milk, fat, protein, and SCS in Canadian Holsteins. Data were a random sample of complete herds (60,645 test day records of 5,022 cows from 91 herds) extracted from the edited data set, which included 892,039 test-day records of 144,622 Holstein cows from 4,570 herds. A test-day animal model with multiple-trait random regression and the Gibbs sampling method were used for parameter estimation. Regression curves were modeled using Legendre polynomials of order 4. A total of 6 separate 4-trait analyses, which included MUN, lactose, or both (yield or percentage) with different combinations of production traits (milk, fat and protein yield, fat and protein percentages, and somatic cell score) were performed. Average daily heritabilities were moderately high for MUN (from 0.384 to 0.414), lactose kilograms (from 0.466 to 0.539), and lactose percentage (from 0.478 to 0.508). Lactose yield was highly correlated with milk yield (0.979). Lactose percentage and MUN were not genetically correlated with milk yield. However, lactose percentage was significantly correlated with somatic cell score (-0.202). The MUN was correlated with fat (0.425) and protein percentages (0.20). Genetic correlations among parities were high for MUN, lactose percentage, and yield. Estimated breeding values (EBV) of bulls for MUN were correlated with fat percentage EBV (0.287) and EBV of lactose percentage were correlated with lactation persistency EBV (0.329). Correlations between lactose percentage and MUN with fertility traits were close to zero, thus diminishing the potential of using those traits as possible indicators of fertility.

The Canadian Test-Day Model is a 12-trait random regression animal model in which traits are milk, fat, and protein test-day yields, and somatic cell scores on test days within each of first three lactations. Test-day records from later lactations are not used. Random regressions (genetic and permanent environmental) were based on Wilmink's three parameter function that includes an intercept, regression on days in milk, and regression on an exponential function to the power -0.05 times days in milk. The model was applied to over 22 million test-day records of over 1.4 million cows in seven dairy breeds for cows first calving since 1988. A theoretical comparison of test-day model to 305-d complete lactation animal model is given. Each animal in an analysis receives 36 additive genetic solutions (12 traits by three regression coefficients), and these are combined to give one estimated breeding value (EBV) for each of milk, fat, and protein yields, average daily somatic cell score and milk yield persistency (for bulls only). Correlation of yield EBV with previous 305-d lactation model EBV for bulls was 0.97 and for cows was 0.93 (Holsteins). A question is whether EBV for yield traits for each lactation should be combined into one overall EBV, and if so, what method to combine them. Implementation required development of new methods for approximation of reliabilities of EBV, inclusion of cows without test day records in analysis, but which were still alive and had progeny with test-day records, adjustments for heterogeneous herd-test date variances, and international comparisons. Efforts to inform the dairy industry about changes in EBV due to the model and recovering information needed to explain changes in specific animals' EBV are significant challenges. The Canadian dairy industry will require a year or more to become comfortable with the test-day model and to realize the impact it could have on selection decisions.

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.