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The objective of this study was to estimate genetic and phenotypic parameters for linear type traits, as well as milk yield (MY), fat yield (FY) and protein yield (PY) in 18,831 Holstein cows reared in 495 herds in Brazil. Restricted maximum likelihood with a bivariate model was used for estimation genetic parameters, including fixed effects of herd-year of classification, period of classification, classifier and stage of lactation for linear type traits and herd-year of calving, season of calving and lactation order effects for production traits. The age of cow at calving was fitted as a covariate (with linear and quadratic terms), common to both models. Heritability estimates varied from 0.09 to 0.38 for linear type traits and from 0.17 to 0.24 for production traits, indicating sufficient genetic variability to achieve genetic gain through selection. In general, estimates of genetic correlations between type and production traits were low, except for udder texture and angularity that showed positive genetic correlations (>0.29) with MY, FY, and PY. Udder depth had the highest negative genetic correlation (-0.30) with production traits. Selection for final score, commonly used by farmers as a practical selection tool to improve type traits, does not lead to significant improvements in production traits, thus the use of selection indices that consider both sets of traits (production and type) seems to be the most adequate to carry out genetic selection of animals in the Brazilian herd.

In this study we aimed to evaluate the reduction in dimensionality of 20 linear type traits and more final score in 14,943 Holstein cows in Brazil using factor analysis, and indicate their relationship with longevity and 305 d first lactation milk production. Low partial correlations (-0.19 to 0.38), the medium to high Kaiser sampling mean (0.79) and the significance of the Bartlett sphericity test (p<0.001), indicated correlations between type traits and the suitability of these data for a factor analysis, after the elimination of seven traits. Two factors had autovalues greater than one. The first included width and height of posterior udder, udder texture, udder cleft, loin strength, bone quality and final score. The second included stature, top line, chest width, body depth, fore udder attachment, angularity and final score. The linear regression of the factors on several measures of longevity and 305 d milk production showed that selection considering only the first factor should lead to improvements in longevity and 305 milk production.