  Environment plays a critical role in shaping the assembly of low-mass
galaxies. Here, we use the UniverseMachine (UM) galaxy-halo connection
framework and the Data Release 3 of the Satellites Around Galactic Analogs
(SAGA) Survey to place dwarf galaxy star formation and quenching into a
cosmological context. UM is a data-driven forward model that flexibly
parameterizes galaxy star formation rates (SFR) using only halo mass and
assembly history. We add a new quenching model to UM, tailored for galaxies
with stellar masses $\lesssim 10^9$ solar masses, and constrain the model down
to a stellar mass $\gtrsim 10^7$ solar masses using new SAGA observations of
101 satellite systems around Milky Way (MW)-mass hosts and a sample of isolated
field galaxies in a similar mass range from the Sloan Digital Sky Survey
(SDSS). The new best-fit model, 'UM-SAGA,' reproduces the satellite stellar
mass functions, average SFRs, and quenched fractions in SAGA satellites while
keeping isolated dwarfs mostly star forming. The enhanced quenching in
satellites relative to isolated field galaxies leads the model to maximally
rely on halo assembly to explain the observed environmental quenching.
Extrapolating the model down to a stellar mass $\sim 10^{6.5}$ solar masses
yields a quenched fraction of $\gtrsim$ 30% for isolated field galaxies and
$\gtrsim$ 80% for satellites of MW-mass hosts at this stellar mass. This
specific prediction can soon be tested by spectroscopic surveys to reveal the
relative importance of internal feedback, cessation of mass and gas accretion,
satellite-specific gas processes, and reionization for the evolution of faint
low-mass galaxies.
