-This study aimed to estimate heritability, genetic, and residual correlations between reproductive traits such as age at first calving, calving interval, dry period, and first service period and linear type traits measured in Holstein cows born between the years 1990 and 2008 in Brazil. The (co)variance components were estimated by restricted maximum likelihood, using the MTDFREML software. The heritability for reproductive traits and linear-type traits ranged from 0.02 to 0.03 and from 0.07 to 0.40, respectively. Estimates of genetic correlations between reproductive and linear-type traits ranged from -0.23 (top line) to 0.28 (angularity) to age at first calving, from -0.54 (final score) to 0.34 (foot angle) to calving interval, from -0.23 (angularity) to 0.56 (stature) to dry period, and from -0.52 (final score) to 0.36 (height udder) to first service period. Direct selection for any of the reproductive traits implies low genetic gains by virtue of their low heritabilities. Among the linear-type traits, the final score, chest width, top line, angularity, teat length, udder attachment, rear teat placement were highlighted as good auxiliary traits to improve reproductive efficiency of Holstein cows in Brazil. The simultaneous selection for reproductive and linear-type traits can lead a higher genetic progress in the reproductive traits.Key Words: age at first calving, dairy cattle, genetic parameters, reproductive efficiency Revista Brasileira de Zootecnia

The objective of this study was to estimate genetic parameters for survival measures from birth to 60 and 72 months of age, as well as survival up to 48 and 54 months after first calving. The genetic association of these measures with 20 linear type traits and final score in Holstein cows, born between years 1990 to 2004, was also evaluated. The components of (co)variance were estimated by Bayesian methods, using the programme THRGIBBS1F 90 in bivariate analyses, considering animal threshold model for measures of survival, and animal linear model for linear type traits. The mean posterior heritability for the measures of survival ranged from 0.09 to 0.15, and for those of the linear type traits ranged from 0.07 to 0.36. The posterior genetic correlation between linear type traits and measures of survival varied from -0.37 to 0.50, respectively. Indirect genetic selection for udder depth, rear teat placement, udder texture, bone quality, fore udder attachment, body depth and chest width may lead to correlated gains in longevity in Holstein cows under tropical conditions.