Variance of Interaction Effects of Sire and Herd for Yield Traits of Holsteins in California, New York, and Pennsylvania with an Animal Model

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Abstract
An animal model with a REML algorithm was used to estimate variances of additive genetic effects and interaction effects of sire and herd. Milk and fat yields were analyzed for first, second, and third lactations of Holsteins from California, New York, and Pennsylvania. Twenty samples of data were used in the study: 10 from California, 4 from New York, and 6 from Pennsylvania. Mean number of lactations per sample was 36,820 from 18,189 cows in 156 herds. Mean fractions of phenotypic variance of interaction effects of sire and herd for milk and fat yields were .015 and .019 for first lactation and .019 and .021 for all (up to three) lactations rather than the .14 used for national genetic evaluations in the US. Mean heritability estimates for milk and fat yields were .26 and .24 for first lactation and .21 and .21 for all lactations in California and .34 and .35 for first lactations and .28 and .29 for all lactations in New York. Sums of variances of permanent environmental and interaction effects of sire and herd were similar to those used for national genetic evaluations in the US. Analysis of another 10 samples from California and 10 samples from New York showed only slightly different fractions of phenotypic variance for milk yield for interaction effects of sire by herd, sire by herd by year, and sire by herd by year by season: .023, .027, and .037 for California and .023, .017, and .023 for New York, respectively.