Achelousaurus was not descended from Einiosaurus, as it preceded both in age, and yet had a nasal boss. But he stressed that even if the lineages split off, its ancestor might have resembled Einiosaurus. Furthermore, it might still be possible that Einiosaurus was a direct descendant of Rubeosaurus. Also, the process of rapid displacements and extinctions of species could in his opinion still be elegantly explained by a westward expansion of the Bearpaw Sea. The process of anagenesis was affirmed by John Wilson and Jack Scannella in 2016, who studied the ontogenetic changes in horned dinosaurs. They compared a small Einiosaurus specimen, MOR 456 8-8-87-1, with Achelousaurus specimen MOR 591. Both proved to be quite similar, with the main differences being a longer face in MOR 456 8-8-87-1, and a sharper supraorbital horncore in MOR 591. They concluded that Achelousaurus was likely the direct descendant of Einiosaurus. The more adult Einiosaurus individuals approached the Achelousaurus morphology. The differences between the two taxa would have been caused by heterochrony – differential changes in the speed the various traits developed during the lifetime of an individual. Since Wilson and colleagues found in 2020 that Stellasaurus (Horner's "Taxon A") was intermediate between Styracosaurus and Einiosaurus in morphology and stratigraphy, they could not discount that it was a transitional taxon within an anagenetic lineage. Classification In 1995, Sampson formally placed Achelousaurus in the Ceratopsidae, more precisely the Centrosaurinae. In all analyses, Einiosaurus and Achelousaurus are part of the clade Pachyrhinosaurini. By definition, Achelousaurus is a member of the clade Pachyrostra (or "thick-snouts"), in which it is united with Pachyrhinosaurus. In 2010, Gregory S. Paul assigned A. horneri to the genus Centrosaurus, as C. horneri. This has found no acceptance among other researchers, with subsequent taxonomic assessments invariably keeping the generic name Achelousaurus. Phylogeny Sampson felt, in 1995, that there was not enough evidence to conclude that Achelousaurus was a direct descendant of Einiosaurus. Unlike Horner, he decided to perform a cladistic analysis to establish a phylogeny. This showed an evolutionary tree wherein Achelousaurus split off between Einiosaurus and Pachyrhinosaurus, as Horner had predicted. Contrary to Horner's claim, Styracosaurus albertensis could not have been a direct ancestor, as it was a sister species of Centrosaurus in Sampson's analysis. Subsequent studies have sought to determine the precise relationships within this part of the evolutionary tree, with conflicting results regarding the question whether Styracosaurus albertensis or Einiosaurus