The Sloan Digital Sky Survey (SDSS) and photometric/spectroscopic surveys in the GOODS-South field (the Chandra Deep Field-South, CDFS) are used to construct volume-limited, stellar mass-selected samples of galaxies at redshifts 0<z<1. The CDFS sample at 0.6<z<1.0 contains 207 galaxies complete down to M=4x10^10 Msol (for a ``diet Salpeter IMF), corresponding to a luminosity limit for red galaxies of M_B=-20.1. The SDSS sample at 0.020<z<0.045 contains 2003 galaxies down to the same mass limit, which corresponds to M_B=-19.3 for red galaxies. Morphologies are determined with an automated method, using the Sersic parameter n and a measure of the residual from the model fits, called ``bumpiness, to distinguish different morphologies. These classifications are verified with visual classifications. In agreement with previous studies, 65-70% of the galaxies are located on the red sequence, both at z~0.03 and at z~0.8. Similarly, 65-70% of the galaxies have n>2.5. The fraction of E+S0 galaxies is 43+/-3%$ at z~0.03 and 48+/-7% at z~0.8, i.e., it has not changed significantly since z~0.8. When combined with recent results for cluster galaxies in the same redshift range, we find that the morphology-density relation for galaxies more massive than 0.5M* has remained constant since at least z~0.8. This implies that galaxies evolve in mass, morphology and density such that the morphology-density relation does not change. In particular, the decline of star formation activity and the accompanying increase in the stellar mass density of red galaxies since z~1 must happen without large changes in the early-type galaxy fraction in a given environment.
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