Spectral line index data for a sample of 290 E and S0 galaxies are used to investigate the stellar populations of these galaxies. 250 of the galaxies are members of 11 nearby clusters (cz(CMB) < 11500 km s(-1)). We study how the stellar populations of the galaxies are related to the velocity dispersions, the masses of the galaxies, and the cluster environment. This is done by establishing relations between these parameters and the line indices Mg-2, [Fe] and H beta(G). The difference between the slope of the Mg-2-sigma relation and the slope of the [Fe]-sigma relation indicates that the abundance ratio [Mg/Fe] is 0.3-0.4 dex higher for galaxies with velocity dispersions of 250 km s(-1) compared to galaxies with velocity dispersions of 100 km s(-1). This is in agreement with previous estimates by Worthey et al. The [Fe] index is more strongly correlated with the projected cluster surface density, rho(cluster), than with the galactic mass or the velocity dispersion. Earlier we found that the residuals for the Mg-2-sigma relation depend on the cluster environment. Here we determine how both the Mg-2 index and the [Fe] index depend on the velocity dispersion and rho(cluster). Alternative explanations that could create a spurious environment dependence are discussed. No obvious alternatives are found. The environment dependence of the Mg-2-sigma relation is supported by data from Faber et al. The dependence on the environment implies that [Mg/Fe] decreases with increasing density, rho(cluster). The decrease in [Mg/Fe] is 0.1 dex over 2.5 dex in rho(cluster). We have also studied the extent to which the mass-to-light (M/L) ratios of the galaxies-are determined by the stellar populations. The M/L ratios are strongly correlated with the indices Mg-2 and H beta(G), while the [Fe] index is only weakly correlated with the M/L ratio. Based on current stellar population models, we find that it is not yet possible to derive unique physical parameters (mean age, mean abundances, mean IMF, and fraction of dark matter) from the observables (line indices, velocity dispersion, mass, M/L ratio).