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\subsection{Observations}  To examine the observed properties of dwarf galaxies in the LG, we use the compilation from \citet{McConnachie2012}, which includes all galaxies known at that time within $3 \mpc$ of the Sun.  We select ``dwarf'' galaxies as $\mstar \lesssim 10^9 \msun$,thus  including the LMC ($\mstar = 1.5 \times 10^9 \msun$). %but not M33 ($\mstar = 5 \times 10^{10} \msun$).  The catalog includes the distance of each dwarf from both the MW and M31, and we define ``satellites'' as those within $300 \kpc$ of either host, motivated by the sharp transition in star formation, gas, and morphological properties within this distance.  $300 \kpc$ also coincides with the median virial radius, $\rvir$, for our simulated MW/M31 halos (see below).