Genetic relationships between yield and type traits were investigated using multiple-trait REML procedures with an animal model. Computing strategies were developed to deal with large populations and numbers of traits. Data consisted of records for 3 production and 15 type traits for 20,836 primiparous cows from 1982 to 1988. The model included 2358 herd management effects, 28,749 animal effects, and 23 groups for unknown parents. (Co)variance components were estimated using a canonical transformation with an accelerated expectation-maximization REML algorithm. Direct inversion of the coefficient matrix and solution to die transformed single-trait equations were by a sparse matrix solver. Heritabilities for milk, fat, and protein yield were .44, .42, and .40, respectively. Heritabilities for type traits ranged from .10 to .42; the largest was for stature. Dairy form had the largest genetic correlations with yield traits, which ranged from .59 with milk to .68 with fat. Genetic correlations between all yield and most type traits were positive (from .01 to .68); exceptions were fore udder attachment, udder depth, and front teat placement (-.01 to -.44). Selection solely for increased milk yield would cause some udder characteristics to deteriorate. Restricted selection for milk yield while holding udder traits constant would decrease response in milk yield by 15%.
