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.