Effect of Relationships on Estimation of Variance Components with an Animal Model and Restricted Maximum Likelihood

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Abstract
Milk, fat, and protein yields in first lactation of two samples of 12 herds consisting of 4020 and 4024 Holstein cows in New York were used to estimate genetic and phenotypic covariances with an animal model by REML. Relationships were calculated within herd in three ways to provide inverses of relationship matrices. Full relationships consisted of tracing relationships to parents (base animals) of animals with milk and fat records between 1970 and 1980. Full relationships less base animals consisted of tracing relationships only one generation back from when protein records became available in 1981. Sire-only relationships were compiled using only relationships through sires. Fractions of nonzero elements in inverses of within-herd relationship matrices were 0.72 for full, 0.62 for full-less-base, and 0.04 for sire-only relationships. Heritability estimates averaged over milk, fat, and protein were 0.35 with full, 0.33 with full-less-base, and 0.25 with sire-only relationship matrices. Estimates of genetic and phenotypic correlations were not affected by how relationships were computed. Comparable analyses of milk and fat yields from other sets of California, New York, and Wisconsin herds resulted in estimates of heritability that were slightly greater when only daughter and dam records were used than when all records in a herd were used.