Recent studies of the near-infrared (NIR) properties of dwarf irregular galaxies (dIs) and blue compact dwarfs (BCDs) have provided improved estimates for the NIR luminosity of old stellar populations in these galaxies. These can be used to derive gas fractions, and thereby to evaluate how BCDs have evolved with respect to dIs. Oxygen abundances have been derived for four BCDs in the Virgo Cluster from a run at Gemini-North in 2003. Combining these new abundances with published values, we study the correlations among the metallicity, Ks luminosity, gas mass, baryonic mass, and gas fraction. Within errors, the two types of dwarfs appear to share a common relation between the oxygen abundance and the luminosity in Ks. The correlation between metallicity and the gas fraction is the same for BCDs as for dIs, indicating that BCD evolution has been similar to that of dIs. Since dIs appear to have evolved as isolated systems, the BCD bursts are unlikely to be a consequence of gas infall or merging.