We examine the correlation between globular cluster (GC) color and magnitude using HST/ACS imaging for a sample of 79 early-type galaxies (−21.7 \u3c MB \u3c −15.2 mag) with accurate surfacebrightness fluctuation distances from the ACS Virgo Cluster Survey. Using the KMM mixture modeling algorithm, we find a highly significant correlation, z ≡ d(g−z) dz = −0.037 ± 0.004, between color and magnitude for the subpopulation of blue GCs in the co-added GC color-magnitude diagram of the three brightest Virgo cluster galaxies (M49, M87 and M60). The sense of the correlation is such that brighter GCs are redder than their fainter counterparts. For the single GC systems of M87 and M60, we find similar correlations; M49 does not appear to show a significant trend. There is no correlation between (g − z) and Mz for GCs belonging to the red subpopulation. The correlation g ≡ d(g−z) dg for the blue subpopulation is much weaker than z. Using Monte Carlo simulations, we attribute this finding to the fact that the blue subpopulation in Mg extends to higher luminosities than does the red subpopulation, which biases the KMM fit results. The highly significant correlation between color and Mz, however, is a real effect: this conclusion is supported by biweight fits to the same color distributions. We identify two environmental dependencies which influence the derived color-magnitude relation: (1) the slope of the color-magnitude relation decreases in significance with decreasing galaxy luminosity, although it remains detectable over the full luminosity range of our sample; and (2) the slope is stronger for GC populations located at smaller galactocentric distances. These characteristics suggest that the observed trend is, at least partially, shaped by external agents. We examine several physical mechanisms that might give rise to the observed color-magnitude relation including: (1) presence of contaminants like super-clusters, stripped galactic nuclei, or ultra-compact dwarfs; (2) accretion of GCs from low-mass galaxies; (3) stochastic effects; (4) the capture of field stars by individual GCs; and (5) GC self-enrichment. Although none of these scenarios offers a fully satisfactory explanation of the observations, we conclude that self-enrichment and field-star capture, or a combination of these processes, offer the most promising means of explaining our observations
