  With targeted imaging of groups in the local volume, the regions of collapse
around bright galaxies can be clearly identified by the distribution of dwarfs
and luminosity functions can be established to very faint levels. In the case
of the M81 Group there is completion to M_R ~ -9. In all well studied cases,
the faint end slopes are in the range -1.35 < alpha < -1.2, much flatter than
the slope for the bottom end of the halo mass spectrum anticipated by LambdaCDM
hierarchical clustering theory. Small but significant variations are found with
environment. Interestingly, the populations of dwarf galaxies are roughly
constant per unit halo mass. With the numbers of dwarfs as an anchor point,
evolved environments (dominated by early morphological types) have relatively
fewer intermediate luminosity systems and at least one relatively more
important galaxy at the core. The variations with environment are consistent
with a scenario of galaxy merging. However it is questionable if the universal
dearth of visible dwarf systems is a consequence of an astrophysical process
like reionization.
