We study the effects of galaxy environment on the evolution of the stellar–mass function ( SMF ) over 0.2 < z < 2.0 using the FourStar Galaxy Evolution ( ZFOURGE ) survey and NEWFIRM Medium–Band Survey ( NMBS ) down to the stellar–mass completeness limit , \log M _ { \ast } / M _ { \odot } > 9.0 ( 9.5 ) at z = 1.0 ( 2.0 ) . We compare the SMFs for quiescent and star–forming galaxies in the highest and lowest environments using a density estimator based on the distance to the galaxies ’ third–nearest neighbors . For star–forming galaxies , at all redshifts there are only minor differences with environment in the shape of the SMF . For quiescent galaxies , the SMF in the lowest densities shows no evolution with redshift , other than an overall increase in number density ( \phi ^ { \ast } ) with time . This suggests that the stellar–mass dependence of quenching in relatively isolated galaxies is both universal and does not evolve strongly . While at z \gtrsim 1.5 the SMF of quiescent galaxies is indistinguishable in the highest and lowest densities , at lower redshifts it shows a rapidly increasing number density of lower–mass galaxies , \log M _ { \ast } / M _ { \odot } \simeq 9 - 10 . We argue this evolution can account for all the redshift evolution in the shape of the total quiescent–galaxy SMF . This evolution in the quiescent–galaxy SMF at higher redshift ( z > 1 ) requires an environmental–quenching efficiency that decreases with decreasing stellar mass at 0.5 < z < 1.5 or it would overproduce the number of lower–mass quiescent galaxies in denser environments . This requires a dominant environment process such as starvation combined with rapid gas depletion and ejection at z > 0.5 - 1.0 for galaxies in our mass range . The efficiency of this process decreases with redshift allowing other processes ( such as galaxy interactions and ram–pressure stripping ) to become more important at later times , z < 0.5 .