Application of Genomic Random Regression Models for Genetic Parameter Estimations of Female Fertility Traits in Different Parities in German Holsteins

The aim of the present study was to infer genetic (co) variance components and to estimate parity-specific breeding values for the female fertility traits non-return rate after 56 days, the interval from calving to first service and days open by applying random regression models on a time-dependent parity scale. In this regard, we considered a female fertility dataset comprising 592,829 records on 190,269 German Holstein cows and heifers kept in 45 large-scale dairy contract herds. From a subset of 21,316 cattle with phenotypic records, (imputed) 50 K genotypes were available. The applied genomic random regression model considered Legendre polynomials of order 2 for the additive-genetic effects along the parity scale, and combined pedigree and genomic relationships through the H-matrix. Results were compared with genetic parameter estimates from a multiple-trait model, considering the same fertility trait in different parities as different traits. From both modelling approaches, we observed the trend of increasing genetic variances and heritabilities with increasing parity. Especially for the non-return rate, the genetic variance in heifers was substantially smaller than in all parities of cows. With regard to the random regression model, genetic correlations between the same fertility traits from adjacent parities were close to 1, but gradually declined with increasing parity distances. Small genetic correlations were also estimated between non-return rates in heifers with non-return rates in all cow parities, i.e., 0.50 with parity 1, 0.44 with parity 2, 0.41 with parity 3, 0.35 with parity 4, 0.33 with parity 5, and 0.25 with parity 6. A similar pattern for genetic correlations in the same traits across parities was confirmed from the multiple-trait model application. Estimated breeding values for all fertility traits in different parities of sires with at least 10 phenotyped daughters per trait (estimates from the random regression model) were correlated with their official breeding indexes from the national genetic evaluation. In this regard, moderate differences were observed when comparing breeding value correlations for non-return rates in heifers with respective correlations in all cow parities. From a practical breeding perspective, the most important results were the rather small genetic correlations for the same traits in different parities (e.g., 0.24 between calving to first service in parities 1 and 6), and differing breeding value correlations with other breeding indexes in different parities. These findings suggest the implementation of specific genetic evaluations for specific cow parities, as an extension to the existing separation between heifer and cow fertility traits. Parity-specific breeding value correlations from the random regression and the multiple-trait model considering the sires with at least 10 daughters were larger than 0.85, suggesting only minor re-rankings of sires from the two different modeling approaches.