I believe in the 4 species system for Lophophora, mostly because of breeding experiments I have done. A species should be able to reproduce with other individuals of the same species, these 4 species do not readily cross.
The results of my own test breeding found that L. diffusa does not readily cross with any other Lophophora, nor does L. williamsii (except one questionable time i have one plant from a possible L. frici x L. williamsii breeding).
Lophophora fricii pollen does seem readily accepted by L. koehresii, but not the other way around, which would be hard to put them in the same species, if not also for all the morphological differences.
There is a current model put out for the 4 species system, which uses sections. This is published in "Kaktusy Special 2, 2005: The Genus Lophophora Coulter" ISSN: 0862-4372.
The sections used were Lophophora which contains Lophophora wiliamsii, and section Diffusae which contains L. diffusa, L. fricii and L. koehresii.
All have more or less isolated locations in the wild
all can have up to 21 ribs
main alkaloid is pellotine, rather than mescaline in L. williamsii
areole wool easy to pull off.
ribs often uneven/wavy
Wide spread in nature
Up to 13 ribs
main alkaloid is mescaline, rather than pellotine in other species
rounded flowers (though there are populations with pointed tips)
areole wool not so easy to pull off.
ribs generally straight/spiral
The most important thing i find that makes a 4 species system clear cut, is none of these will *readily* cross with any other species of the same genus, something that would not be an issue if they were in fact of the same species (at least according to the current definition of a species).
Because a key concept to defining a species in my opinion is reproduction, there can be no less than 4 species in the genus Lophophora. All other morphological differences just back up this assumption.