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Additional file 1: Supplementary Material 1. Threshold for the approximate empirical null distribution of additive and dominance transmissionratio distortion (TRD) for different ranges of number of informative offspring.

In the dairy industry, mate allocation is dependent on the producer’s breeding goals and the parents’ breeding values. The probability of pregnancy differs among sire-dam combinations, and the compatibility of a pair may vary due to the combination of gametic haplotypes. Under the hypothesis that incomplete incompatibility would reduce the odds of fertilization, and complete incompatibility would lead to a non-fertilizing or lethal combination, deviation from Mendelian inheritance expectations would be observed for incompatible pairs. By adding an interaction to a transmission ratio distortion (TRD) model, which detects departure from the Mendelian expectations, genomic regions linked to gametic incompatibility can be identified. This study aimed to determine the genetic background of gametic incompatibility in Holstein cattle. A total of 283,817 genotyped Holstein trios were used in a TRD analysis, resulting in 422 significant regions, which contained 2075 positional genes further investigated for network, overrepresentation, and guilt-by-association analyses. The identified biological pathways were associated with immunology and cellular communication and a total of 16 functional candidate genes were identified. Further investigation of gametic incompatibility will provide opportunities to improve mate allocation for the dairy cattle industry.