Perissodactyla
Higher classification of perissodactyls

Relationships within the large group of odd-toed ungulates are not fully understood. Initially, after the establishment of "Perissodactyla" by Richard Owen in 1848, the present-day representatives were considered equal in rank. In the first half of the 20th century, a more systematic differentiation of odd-toed ungulates began, based on a consideration of fossil forms, and they were placed in two major suborders: Hippomorpha and Ceratomorpha. The Hippomorpha comprises today's horses and their extinct members (Equoidea); the Ceratomorpha consist of tapirs and rhinos plus their extinct members (Tapiroidea and Rhinocerotoidea). The names Hippomorpha and Ceratomorpha were introduced in 1937 by Horace Elmer Wood, in response to criticism of the name "Solidungula" that he proposed three years previously. It had been based on the grouping of horses and Tridactyla and on the rhinoceros/tapir complex. The extinct brontotheriidae were also classified under Hippomorpha and therefore possess a close relationship to horses. Some researchers accept this assignment because of similar dental features, but there is also the view that a very basal position within the odd-toed ungulates places them rather in the group of Titanotheriomorpha.

Originally, the Chalicotheriidae were seen as members of Hippomorpha, and presented as such in 1941. William Berryman Scott thought that, as claw-bearing perissodactyls, they belong in the new suborder Ancylopoda (where Ceratomorpha and Hippomorpha as odd-toed ungulates were combined in the group of Chelopoda). The term Ancylopoda, coined by Edward Drinker Cope in 1889, had been established for chalicotheres. However, further morphological studies from the 1960s showed a middle position of Ancylopoda between Hippomorpha and Ceratomorpha. Leonard Burton Radinsky saw all three major groups of odd-toed ungulates as peers, based on the extremely long and independent phylogenetic development of the three lines. In the 1980s, Jeremy J. Hooker saw a general similarity between Ancylopoda and Ceratomorpha based on dentition, especially in the earliest members, leading to the unification in 1984 of the two submissions in the interim order, Tapiromorpha. At the same time, he expanded the Ancylopoda to include the Lophiodontidae. The name "Tapiromorpha" goes back to Ernst Haeckel, who coined it in 1873, but it was long considered synonymous to Ceratomorpha because Wood had not considered it in 1937 when Ceratomorpha were named, since the term had been used quite differently in the past. Also in 1984, Robert M. Schoch used the conceptually similar term Moropomorpha, which today applies synonymously to Tapiromorpha. Included within the Tapiromorpha are the now extinct Isectolophidae, a sister group of the Ancylopoda-Ceratomorpha group and thus the most primitive members of this relationship complex.
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