Available data on the magnesium-velocity dispersion (Mg-σ) relation for ～2000 early-type galaxies is analyzed. As noted previously, the Mg residuals from a fitted line are roughly Gaussian near the median but have an asymmetric blue tail, probably from subpopulations of relatively young stars. We define statistics for scatter and asymmetry of scatter in the Mg dimension and find impressive uniformity among data sets. We construct models of galaxy formation built to be as unbiased as possible toward the question of the importance of mergers in the formation of early-type galaxies. The observational constraints (Mg-σ-width, asymmetry, and mean Mg strength, plus mean age and width of abundance distribution) are severe enough to eliminate almost all models. Eliminated are models with merger rates proportional to (1 + z)" with n > 0, models that assume early formation followed by recent drizzling of new stars, merger-only models in which the number of mergers exceeds ≈80, merger-only models with less than ≈20 mergers, and models with a cold dark matter power spectrum (at least within our approximations). The most successful models were those with merger probability constant or mildly declining with time, with the number of mergers needed to form the galaxy around 50 and gas fractions of ～0.2-0.35. These models are characterized by mean light-weighted ages of 8-9 Gyr (consistent with spectroscopic studies), an abundance distribution that does not exceed local constraints, and a look-back time behavior nearly indistinguishable from passive evolution of old stellar populations. Our simulations suggest that the evolution of median Mg index strength is not a good discriminator between mergers and passive evolution and that better discriminators such as Mg-σ scatter and asymmetry require N > 1000 sample sizes with accuracies similar to today's local measurements.
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