Dairy sire mating recommendations to limit extremes and target intermediate optima.

Traditional genetic selection using total merit indexes operates under the simple assumption that higher is better. Some traits, however, are subject to preferred upper or lower thresholds and some may have intermediate optima. Therefore, mating recommender systems should consider these herd-specific breeding goals. Mating recommendations in this study were performed at a herd level for dairy cattle using a constrained optimization approach based on simulated estimates of genetic merit for 9 traits or subindexes. A total of 10,000 herds, each with 200 females, were simulated. The top 100 sires from a simulated population were chosen to represent the pool of candidate sires. Within each herd separately, candidate female-male pairings were evaluated on a mate utility function that combined parental average genetic merit for the 9 traits or subindexes. The utility function penalized matings expected to generate progeny exceeding predefined thresholds (milk yield was used as an example trait) or deviating from an intermediate optimum (cow liveweight was used as an example trait), thereby reflecting both avoidance of genetic extremes and targeting of biologically and system-relevant optima. Imposing a linear penalty on the parental average genetic merit for a trait exceeding a given threshold reduced, considerably, the number of recommended matings that had a parental average genetic merit exceeding that threshold. For the vast majority of herds, no mating that exceeded that parental average genetic merit threshold was recommended but it was unavoidable in some herds because of the presence of females with extreme genetic merit for the trait and the absence of sires capable of delivering the desired parental average genetic merit. Including the threshold penalty had minimal effect on the mean total merit index of the recommended matings. Preselection of candidate dams before mating recommendations, although slightly reducing the proportion of progeny exceeding the threshold, resulted in a lower mean total merit index of the recommended matings. Penalizing matings that generated parental averages deviating from an intermediate optimum resulted in recommended matings that, although lower in genetic merit for the total merit index, were more homogeneous in parental average for the trait in question. Although preselecting dams for mating consideration did not alter the proportion of matings deviating from the optimum, it resulted in a lower mean total merit of the matings. Although the specific conclusions of the present study are dependent on the simulated population, the overarching finding is that developing a utility function that penalizes matings exceeding defined thresholds or deviating from desired optima can support mating recommendations aligned with herd-specific breeding goals that are nonlinear in nature.