We present new measurements of the evolution in the Lyman break galaxy (LBG) population between z~4 and z~6. By utilizing the extensive multiwavelength datasets available in the GOODS fields, we identify 2443 B, 506 V, and 137 i-band dropout galaxies likely to be at z~4, 5, and 6. With the goal of understanding the duration of typical star formation episodes in galaxies at z>4, we examine the distribution of stellar masses and ages as a function of cosmic time. We find that at a fixed rest-UV luminosity, the average stellar masses and ages of galaxies do not increase significantly between z~6 and 4. In order to maintain this near equilibrium in the average properties of high redshift LBGs, we argue that there must be a steady flux of young, newly-luminous objects at each successive redshift. When considered along with the short duty cycles inferred from clustering measurements, these results may suggest that galaxies are undergoing star formation episodes lasting only several hundred million years. In contrast to the unchanging relationship between the average stellar mass and rest-UV luminosity, we find that the number density of massive galaxies increases considerably with time over 4<z<6. Given this rapid increase of UV luminous massive galaxies, we explore the possibility that a significant fraction of massive (M*>1e11 Msun) z~2-3 distant red galaxies (DRGs) were in part assembled in an LBG phase at earlier times. Integrating the growth in the stellar mass function of actively forming LBGs over 4<z<6 down to z~2, we find that z>3 LBGs could have contributed significantly to the quiescent DRG population, indicating that the intense star-forming systems probed by current sub-millimeter observations are not the only route toward the assembly of DRGs at z~2.
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