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\section{Introduction}  Galaxies in denser environments are more likely to have suppressed (quiescent) star-formation rates (SFR) and little-to-no coldatomic/molecular  gas than galaxies of similar stellar mass, $\mstar$, in less dense environments. The observed environmental effects within in  the Local Group (LG) on the satellite dwarf galaxies within thehost  halos of the Milky Way (MW) and M31 Andromeda (M31)  \citep[for example,][]{Mateo1998, example,][]{LyndenBell1974, Mateo1998,  McConnachie2012, Phillips2014, SlaterBell2014, Spekkens2014} are particularly strong, even compared to the effects on (more massive) satellite galaxies within massive groups/clusters. Specifically, the galaxies around the Milky Way (MW) and Andromeda (M31) show a strikingly sharp transition in their properties within $\approx 300 \kpc$, corresponding to the virial radii, $\rvir$, of the halos of the MW and M31 for $\mvir \approx 10 ^ {12} \msun$ \citep[for example,][]{Deason2012, vanderMarel2012, BoylanKolchin2013}.  Within this distance, galaxies transition from (1) having irregular to elliptical/spheroidal morphologies, (2) having most of their baryonic mass in cold atomic/molecular gas to having little-to-no measured cold gas, and (3) being actively star-forming to quiescent \citep[][and references therein]{Einasto1974, McConnachie2012}.  This environmental transition of the population is almost complete, with just a few exceptions.