  On dwarf galaxy scales, the different shapes of the galaxy stellar mass
function and the dark halo mass function require a star-formation efficiency
(SFE) in these systems that is currently more than 1 dex lower than that of
Milky Way-size halos. Here, we argue that this trend may actually be reversed
at high redshift. Specifically, by combining the resolved star-formation
histories of nearby isolated dwarfs with the simulated mass-growth rates of
dark matter halos, we show that the assembly of these systems occurs in two
phases: (1) an early, fast halo accretion phase with a rapidly deepening
potential well, characterized by a high SFE; and (2) a late slow halo accretion
phase where, perhaps as a consequence of reionization, the SFE is low. Nearby
dwarfs have more old stars than predicted by assuming a constant or decreasing
SFE with redshift, a behavior that appears to deviate qualitatively from the
trends seen amongst more massive systems. Taken at face value, the data suggest
that, at sufficiently early epochs, dwarf galaxy halos above the atomic cooling
mass limit can be among the most efficient sites of star formation in the
universe.
