The aim of this paper is to set constraints of the epochs of early-type galaxy formation through the 'archaeology' of the stellar populations in local galaxies. Using our models of absorption line indices that account for variable abundance ratios, we derive the stellar population parameters of 124 early-type galaxies in high and low density environments. We find that all three parameters age, metallicity, and alpha/Fe ratio are correlated with velocity dispersion. We further find evidence for an influence of the environment on the stellar population properties. Massive early-type galaxies in low-density environments appear on average ~2 Gyrs younger and slightly more metal-rich than their counterparts in high density environments. No offsets in the alpha/Fe ratios, instead, are detected. We translate the derived ages and alpha/Fe ratios into star formation histories. We show that most star formation activity in early-type galaxies is expected to have happened between redshifts 3 and 5 in high density and between redshifts 1 and 2 in low density environments. We conclude that at least 50 per cent of the total stellar mass density must have already formed at z 1, in good agreement with observational estimates of the total stellar mass density as a function of redshift. Our results suggest that significant mass growth in the early-type galaxy population below z 1 must be restricted to less massive objects, and a significant increase of the stellar mass density between redshifts 1 and 2 should be present caused mainly by the field galaxy population. The results of this paper further imply vigorous star formation episodes in massive objects at z 2-5 and the presence of evolved ellipticals around z 1, both observationally identified as SCUBA galaxies and EROs.
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