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 (...) >suite
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 (...) >continue
From the chronology of the sites (probably outdated table), it appears that the Group A is very old: Thomson, Echo Quarry, Trinity River.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 (...) >continue
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. >continue
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 (...) >continue