We used a bivariate animal model to investigate the genetic correlations between yield traits or days open (DO) as characters measured in cows and semen production traits as characters measured in bulls. Lactation records of 305-day milk, fat, and protein yields, and DO, from 386 809 first-lactation Holstein cows in Hokkaido, Japan, that calved between 2008 and 2014 were used. Semen production records were collected between 2005 and 2014 and included volume per ejaculate (VOL), sperm concentration (CON), number of sperm per ejaculate (NUM), progressive motility index of sperm (MOT), and MOT after freeze-thawing (A-MOT). Number of sperm per ejaculate was log-transformed into a NUM score (NUMS). A total of 30 373 semen production records from 1196 bulls were obtained. The pedigree file used for analysing the records was involving 885 345 animals. Heritability was estimated for VOL (0.42), CON (0.12), NUMS (0.37), MOT (0.08), and A-MOT (0.11). Weak and negative genetic correlations were recorded between yield traits measured in cows and VOL, CON or NUMS measured in bulls. Moderate and negative genetic correlations were obtained between DO and MOT (–0.42) or A-MOT (–0.43). Selection focused on MOT or A-MOT measured in bulls may therefore improve DO measured in cows.

Pregnancy and calving are elements indispensable for dairy production, but the daily milk yield of cows decline as pregnancy progresses, especially during the late stages. Therefore, the effect of stage of pregnancy on daily milk yield must be clarified to accurately estimate the breeding values and lifetime productivity of cows. To improve the genetic evaluation model for daily milk yield and determine the effect of the timing of pregnancy on productivity, we used a test-day model to assess the effects of stage of pregnancy on variance component estimates, daily milk yields and 305-day milk yield during the first three lactations of Holstein cows. Data were 10 646 333 test-day records for the first lactation; 8 222 661 records for the second; and 5 513 039 records for the third. The data were analyzed within each lactation by using three single-trait random regression animal models: one model that did not account for the stage of pregnancy effect and two models that did. The effect of stage of pregnancy on test-day milk yield was included in the model by applying a regression on days pregnant or fitting a separate lactation curve for each days open (days from calving to pregnancy) class (eight levels). Stage of pregnancy did not affect the heritability estimates of daily milk yield, although the additive genetic and permanent environmental variances in late lactation were decreased by accounting for the stage of pregnancy effect. The effects of days pregnant on daily milk yield during late lactation were larger in the second and third lactations than in the first lactation. The rates of reduction of the 305-day milk yield of cows that conceived fewer than 90 days after the second or third calving were significantly (P<0.05) greater than that after the first calving. Therefore, we conclude that differences between the negative effects of early pregnancy in the first, compared with later, lactations should be included when determining the optimal number of days open to maximize lifetime productivity in dairy cows.