Many explanations have been proposed for the function(s) of the POFs.
In Equus at least, one possible cause (not "function") is the "caveing-in" of the malar region when it is no more "sustained" by cheek teeth because they are too worn.
As example, here is the skull of an E. caballus found (...)
The scatter diagram SD-6 shows that (as far as I know) all Old World Hipparion skulls belong to Group B except H. prostylum (Lubéron LY 592) which has the same proportions as Group A-8 ( Ratio diagram A-8 and H. prostylum).
H. hendeyi (Langebaanweg E 22187), although larger, resembles (...)
From the chronology of the sites (probably outdated table), it appears that the Group A is very old: Thomson, Echo Quarry, Trinity River. Even the brachyodont Mesohippus, Miohippus (Meso-Mio), Hypohippus, Megahippus and Parahippus (Hypo-Mega-Para) have the same shortness of the naso-incisival (...)
The correlation between length of the cheek teeth P2-M3 and preorbital bar length (Scatter diagram 5) does not follow the same regression line for Cormohipparion (all morphs) and other archaic Northamerican equids.
It seems that the main axial proportions of the skull are independent from the existence and/or type of POF.
For instance, on the ratio diagram of Cormohipparion A (A-1), the skull 42449 from Kepler looks like a typical Cormohipparion A although it has no POF.
The ratio diagram A-2 shows (...)