Can the discrepancy between locally and globally derived neutral
  hydrogen mass functions be explained by a varying value of M*?
  I investigate whether it is possible to reconcile the recent ALFALFA
observation that the neutral hydrogen (HI) mass function (HIMF) across
different galactic densities has the same, non-flat, faint-end slope, with the
observations of isolated galaxies and many galaxy groups that show their HIMFs
to have flat faint-end slopes. I find that a fairly simple model in which the
position of the knee in the mass function of each individual group is allowed
to vary is able to account for both of these observations. If this model
reflects reality, the ALFALFA result points to an interesting `conspiracy'
whereby the differing group HIMFs always sum up to form global HIMFs with the
same faint-end slope in different environments. More generally, this result
implies that global environmental HIMFs do not necessarily reflect the HIMFs in
individual groups belonging to that environment, and cannot be used to directly
measure variations in group-specific HIMFs with environment.
