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Random regression models for male and female fertility evaluation using longitudinal binary data.

A longitudinal Bayesian threshold analysis of insemination outcomes was carried out using 2 random regression models with 3 (Model 1) and 5 (Model 2) parameters to model the additive genetic values at the liability scale. All insemination events of first-parity Holstein cows were used. 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 369,353 insemination records from 210,373 first-lactation cows was used. On the liability scale, both models included the systematic effects of herd-year, month of insemination, technician, and regressions on age of service sire and milk yield during the first 100 d of lactation. The random effects in the model were the 3 or 5 random regression coefficients specific to each cow, the permanent effect of the cow, and the service sire effect. Using Model 1, the estimated heritability of an insemination outcome decreased from 0.035 at d 50 to 0.032 at d 140 and then increased continuously with DIM. The genetic correlations for insemination success at different time points ranged from 0.83 to 0.99, and their magnitude decreased with an increase in the interval between inseminations. A similar trend was observed for heritability and genetic correlations using Model 2. However, the average estimate of heritability was much higher (0.058) than those obtained using Model 1 or a repeatability model. In addition, the estimated genetic correlations followed the same trend as Model 1, but were lower and with a higher rate of decrease when the interval between inseminations increased. The posterior mean of service sire variance was 0.01 for both models, and permanent environmental variance was 0.05 and 0.02 for Models 1 and 2, respectively. Model comparison based on the Bayes factor indicated that Model 1 was more plausible, given the data.