Recent work suggests that galaxy evolution, and the build-up of stellar mass (M * ) over cosmic time, is characterized by changes with redshift of star formation rate (SFR) and oxygen abundance (O/H). In a companion paper, we have compiled a large dataset to study Metallicity Evolution and Galaxy Assembly (MEGA), consisting of ∼1000 galaxies to z 3.7 with a common O/H calibration. Here we interpret the MEGA scaling relations of M * , SFR, and O/H with an updated version of the model presented by Dayal et al. (2013). This model successfully reproduces the observed O/H ratio of ∼80 000 galaxies selected from the Sloan Digital Sky Survey to within 0.05−0.06 dex. By extending the model to the higher redshift MEGA sample, we find that although the specific mass loading of outflows does not change measurably during the evolution, the accretion rate and gas content of galaxies increase significantly with redshift. These two effects can explain, either separately or possibly in tandem, the observed lower metal abundance of high-z galaxies.