  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 / Msun > 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*) 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 >~
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 / Msun ~= 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.
