We reinvestigate the dramatic rise in the S0 fraction, f_S0, within clusters since z ~ 0.5. In particular, we focus on the role of the global galaxy environment on f_S0 by compiling, either from our own observations or the literature, robust line-of-sight velocity dispersions, sigmas, for a sample of galaxy groups and clusters at 0.1 < z < 0.8 that have uniformly determined, published morphological fractions. We find that the trend of f_S0 with redshift is twice as strong for sigma < 750 km/s groups/poor clusters than for higher-sigma, rich clusters. From this result, we infer that over this redshift range galaxy-galaxy interactions, which are more effective in lower-sigma environments, are more responsible for transforming spiral galaxies into S0s than galaxy-environment processes, which are more effective in higher-sigma environments. The rapid, recent growth of the S0 population in groups and poor clusters implies that large numbers of progenitors exist in low-sigma systems at modest redshifts (~ 0.5), where morphologies and internal kinematics are within the measurement range of current technology.
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