Despite the large amount of observational data available for Local Group dEs, there is currently no explanation for the diversity of star formation histories, only hints. For example, among the Galaxy's companions there is a tendency for the systems with stronger intermediate-age components to lie at larger Galactocentric distances. This also appears to be the case for M31's companions where, at least among the lower luminosity dE companions, it is the more distant system And II that has a definite intermediate-age population; systems closer to M31 lack such stars. These results suggest that proximity to a "parent galaxy" influences the evolution of dwarf galaxies. Indeed, recent theoretical simulations have shown how a dwarf irregular on an initial "plunging" orbit in the Milky Way halo can be converted into a dE satellite. At the same time it is notable that, with one exception, all the isolated dwarfs in the Local Group are not dEs; they show either recent or on-going star formation. The one local exception to this hypothesis that "parent galaxies" nurture initial gas-rich dwarf companions into dE galaxies, is the isolated dE Tucana. Despite its lack of association with any large galaxy, it nevertheless possesses a dominant old stellar population and there are no signs of any intermediate-age component. The existence of this system demonstrates that proximity to a large galaxy cannot be the only factor governing the evolution of dwarf galaxies.

To make progress in understanding the processes that govern dwarf galaxy evolution, we need to study systems beyond the Local Group. Such studies can be targeted at dEs that occupy a variety of environments, thereby allowing us to more readily distinguish between intrinsic properties and "parent galaxy" influence. In particular, we need to target a sizeable fraction of the dEs within our "Local Volume", the sphere of radius ~10 Mpc centered on the Local Group, seeking to establish what fraction of these systems show intermediate-age populations. This volume includes the relatively loose Sculptor Group, the more compact Cen A group, and a variety of other galaxy aggregations such as the loose association of galaxies that contain the Circinus galaxy at a distance of 6-7 Mpc. The observational signature of an intermediate-age population is the presence of upper-AGB stars, i.e., stars with sufficient mass to evolve on the AGB to luminosities above that of the red giant branch tip. For such stars there is a good correlation between the luminosity of the brightest upper-AGB star and the age of the intermediate-age component. The observations are best done at near-infrared wavelengths since these pass bands cover the wavelengths where the majority of the flux is emitted. Bolometric corrections are therefore small and well defined and the amplitude of variability is much reduced relative to the optical. Single epoch J and K band measurements then suffice for a determination of the bolometric magnitudes (two pass bands are required as the bolometric correction to the K magnitude is a function of J-K color). Although current near-infrared imagers can reach upper-AGB stars in the nearer of the dEs within the Local Volume using relatively long integration times, given the likelihood of a diversity of star formation histories, a sizeable sample of dwarfs in a variety of environments needs to be studied if underlying trends are to be revealed. GSAOI is the ideal instrument with which to carry out this program.