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\subsection{Inferred Environmental Quenching Timescales}  We only examine satellites in the simulation out to the maximum distance that they are observed from the MW or M31 in \emph{each} $\mstar$ bin.  The timescale from \citet{Wheeler2014} is based on combining the the galaxy catalog from \citet{Geha2012} with satellite virial-infall times in the Millennium II simulation.  In particular, \citet{Wheeler2014} used a subset of satellites from \citet{Geha2012} at $8.25 < log(\mstar/\msun) < 8.75$ and $9.25 < log(\mstar/\msun) < 9.65$.  The \citet{Geha2012} sample includes all such satellites around hosts with $\mstar > 2.5 \times 10 ^ {10} \msun$, and as \citet{Wheeler2014} examined using mock catalogs in Millennium II, these satellites span a range of host halo masses $\mvir ~ 10 ^ {12.5 - 14} \msun$.