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This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$ \emph{all} known galaxies that are sufficiently isolated ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}. \textbf{XXX Not sure I agree with this claim -- as I show in Weisz et al. 2015, if you look at the Karachentsev catalog of nearby galaxies (Karachentsev et al. 2013), there are more dSphs in the field than this XXX -- I would say that *most* dSphs that we know of are located near a massive host -- but there are probably significant selection effects here}.   Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is the most compelling laboratory for studying environmental processes on galaxies.  Several environmental processes within a host halo can  regulate the gas content, star formation, morphology, and eventualtidal  disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy interactions \citep[e.g.,][]{FaroukiShapiro1981} and mergers \citep[e.g.,][]{Deason2014a},tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},  ram-pressure stripping of extended gasaround the satellite  \citep[e.g.,][]{Larson1980,McCarthy2008} or  ofthe  cold inter-stellar medium \citep[e.g.,][]{GunnGott1972,Tonnesen2009}, many some  of which can may  be assisted by stellar  feedbackfrom stars and/or black holes  within the satellites satellite  \citep[e.g.,][]{BaheMcCarthy2015}. %tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},  The key astrophysical challenge is understanding the relative importance of these processes, including which (if any) dominate, and how they might vary across both satellite and host mass scales.  One strong constraint for understanding their relative effects is in determining the timescale of environmental quenching, including its dependence on the mass of both the satellites and the host, as previous works have explored at higher masses \citep[e.g.,][]{Balogh2000,Wetzel2013,Hirschmann2014,Wheeler2014}.