Genetic analysis of male and female fertility using longitudinal binary data

A longitudinal Bayesian threshold analysis of insemination events during the first 250 d after calving of first-parity Holsteins was carried out. The outcome of an insemination event was treated as a binary response of either a success (1) or a failure (0). Thus, all breeding information for a cow, including all service sires, was included, thereby allowing for a joint evaluation of male and female fertility. An edited data set of 297,823 insemination records from 151,758 first lactation cows was used. On the liability scale, the model included the systematic effects of herd-year of insemination, technician, month of insemination, and regressions on age of service sire, 3 test days in the first 100 d of lactation (early milk yield), and days in milk at insemination. The random effects in the model were the additive breeding value, the permanent effect of the cow, and the service sire effect. Posterior mean (standard deviation) of the dispersion parameters in the model were 0.034 (0.006), 0.009 (0.001), and 0.171 (0.013) for the additive, service sire, and permanent environmental variances, respectively. The residual variance was fixed at 1, as a result of the nonidentifiability of the threshold model. The posterior mean (standard deviation) of heritability was 0.028 (0.005). This point estimate of heritability is well within the range of available estimates for the trait. Thus, these estimates suggest that some genetic variation exists that can potentially be used to improve reproductive performance or at least avoid its further deterioration. The estimate of the regression coefficient on age of service sire was 0.001, indicating better fertility among older bulls. However, this result has to be interpreted with caution given the preferential use of proven bulls on well-managed cows (as opposed to problem breeders). The estimate of the regression coefficient was negative (-0.005) for early milk yield, as expected, and positive (0.003) for days in milk at insemination. This suggests that high-producing cows are less likely to conceive at the beginning of lactation.