Editing Perissodactyla (section)

==Taxonomy==
{{See also|List of perissodactyls}}

===Outer taxonomy===
Traditionally, the odd-toed ungulates were classified with other mammals such as [[Even-toed ungulate|artiodactyls]], [[hyrax]]es, [[elephants]] and other "ungulates". A close family relationship with hyraxes was suspected based on similarities in the construction of the ear and the course of the [[carotid artery]].

Molecular genetic studies, however, have shown the ungulates to be [[Polyphyly|polyphyletic]], meaning that in some cases the similarities are the result of [[convergent evolution]] rather than [[common ancestor|common ancestry]]. Elephants and hyraxes are now considered to belong to [[Afrotheria]], so are not closely related to the perissodactyls. These in turn are in the [[Laurasiatheria]], a superorder that had its origin in the former supercontinent [[Laurasia]]. Molecular genetic findings suggest that the cloven [[Artiodactyla]] (containing the [[cetacea]]ns as a deeply nested subclade) are the sister taxon of the Perissodactyla; together, the two groups form the [[Ungulate|Euungulata]].<ref name="Graur et al. 1997">{{cite journal|author1=Dan Graur|author2=Manolo Gouy|author3=Laurent Duret|title=Evolutionary Affinities of the Order Perissodactyla and the Phylogenetic Status of the Superordinal taxa Ungulata and Altungulata Molecular Phylogenetics and Evolution|year= 1997|pages= 195–200|doi= 10.1006/mpev.1996.0391|volume= 7|issue=2|journal=Molecular Phylogenetics and Evolution|pmid=9126561}}</ref> More distant are the [[bat]]s (Chiroptera) and [[Ferae]] (a common taxon of carnivorans, [[Carnivora]], and pangolins, [[Pholidota]]).<ref name="Hu et al. 2012">{{cite journal|author1=Jingyang Hu|author2=Zhang Yaping|author3=Li Yu|title=Summary of Laurasiatheria (Mammalia) Phylogeny|journal=Zoological Research|year=2012|pages=65–74|doi=10.3724/sp.j.1141.2012.e05-06e65|pmid=23266984|volume=33|issue=6|s2cid=30067369 |doi-access=free|hdl=1807/64815|hdl-access=free}}</ref> In a discredited alternative scenario, a close relationship exists between perissodactyls, carnivorans, and bats, this assembly comprising the [[Pegasoferae]].<ref name="Nishihara et al. 2006">{{cite journal|author1=Hidenori Nishihara|author2=Masami Hasegawa|author3=Norihiro Okada|title=Pegasoferae, an unexpected mammalian clade revealed by tracking ancient retroposon insertions|journal=Proceedings of the National Academy of Sciences USA |volume=103 |issue=26|pages=9929–9934 |doi=10.1073/pnas.0603797103 |pmid=16785431|pmc=1479866|year=2006|bibcode=2006PNAS..103.9929N|doi-access=free}}</ref>

{| class="wikitable" style="float:right;"
|-
|+ Internal taxonomy of the Euungulata after Welker ''et al.'' 2015<ref name="Welker et al. 2015"/>
|-
|{{Clade|style=font-size:75%; line-height:100%
|label1=[[Euungulata]]
|1={{Clade
     |1=[[Artiodactyla]] (Even-toed ungulates and cetaceans)
     |label2=[[Panperissodactyla]]
     |2={{Clade
          |1='''Perissodactyla'''(Odd-toed ungulates)
          |2=[[extinct|†]] [[Meridiungulata]] (South American ungulates,<br />especially [[Notoungulata]] and [[Litopterna]])
          }}
     }}
}}
|}

According to studies published in March 2015, odd-toed ungulates are in a close family relationship with at least some of the so-called [[South American native ungulates|Meridiungulata]], a very diverse group of mammals living from the Paleocene to the Pleistocene in South America, whose systematic unity is largely unexplained. Some of these were classified based on their paleogeographic distribution. However, a close relationship can be worked out to perissodactyls by [[protein sequencing]] and comparison with fossil collagen from remnants of phylogenetically young members of the Meridiungulata (specifically ''[[Macrauchenia]]'' from the [[Litopterna]] and ''[[Toxodon]]'' from the [[Notoungulata]]). Both kinship groups, the odd-toed ungulates and the Litopterna-Notoungulata, are now in the higher-level taxon of [[Panperissodactyla]]. This kinship group is included among the Euungulata, which also contains the even-toed ungulates (Artiodactyla). The separation of the Litopterna-Notoungulata group from the perissodactyls probably took place before the [[Cretaceous–Paleogene extinction event]]. "Condylarths" can probably be considered the starting point for the development of the two groups, as they represent a heterogeneous group of primitive ungulates that mainly inhabited the northern hemisphere in the [[Paleogene]].<ref name="Welker et al. 2015">{{cite journal|author1=Frido Welker|author2=Matthew J. Collins|author3=Jessica A. Thomas|author4=Marc Wadsley|author5=Selina Brace|author6=Enrico Cappellini|author7=Samuel T. Turvey|author8=Marcelo Reguero|author9=Javier N. Gelfo|author10=Alejandro Kramarz|author11=Joachim Burger|author12=Thomas Jane Oates|author13=David A. Ashford|author14=Peter D. Ashton|author15=Keri Rowsell|author16=Duncan M. Porter|author17=Benedikt Kessler|author18=Roman Fischer|author19=Carsten Baessmann|author20=Stephanie Kaspar|author21=Jesper V. Olsen|author22=Patrick Kiley|author23=James A. Elliott|author24=Christian D. Kelstrup|author25=Victoria Mullin|author26=Michael Hofreiter|author27=Eske Willerslev|author28=Jean-Jacques Hublin|author29=Ludovic Orlando|author30=Ian Barnes|author31=Ross DE MacPhee|title=Ancient protein resolve the evolutionary history of Darwin's South American ungulates|journal=Nature|doi=10.1038/nature14249|volume=522|issue=7554|pages=81–84|pmid=25799987|year=2015|bibcode=2015Natur.522...81W|s2cid=4467386|url=http://eprints.whiterose.ac.uk/91438/1/Welker_postprint.docx|hdl=11336/14769|hdl-access=free}}</ref><ref>{{cite journal|author1=Ross MacPhee|author2=Frido Welker|author3=Jessica Thomas|author4=Selina Brace|author5=Enrico Cappellini|author6=Samuel Turvey|author7=Ian Barnes|author8=Marcelo Reguero|author9=Javier Gelfo|author10=Alejandro Kramarz|title=Ancient protein sequencing Resolves litoptern and notoungulate superordinal affinities|journal=The History of Life: A View from the Southern Hemisphere|year=2014|page=186}}</ref>

===Modern members===
Odd-toed ungulates comprise three living families with around 17 species—in horses, however, the exact count is still controversial. Rhinos and tapirs are more closely related to each other than to horses. According to molecular genetic analysis, the separation of horses from other perissodactyls took place in the [[Paleocene]] some 56 million years ago, while the rhinos and tapirs split off in the lower-middle [[Eocene]], about 47 million years ago. 
{| class="wikitable" style="float:right;"
|-
|+ Internal relationships of extant Perissodactyla<ref>{{cite journal|author1= Christelle Tougard|author2=Thomas Delefosse|author3=Catherine Hänni|author4=Claudine Montgelard|title=Phylogenetic Relationships of the Five Extant Rhinoceros species (Rhinocerotidae, Perissodactyla) Based on Mitochondrial Cytochrome b and 12S rRNA gene|journal=Molecular Phylogenetics and Evolution|year=2001|pages=34–44|doi=10.1006/mpev.2000.0903|volume=19|issue=1|pmid=11286489|bibcode=2001MolPE..19...34T |url=http://doc.rero.ch/record/16553/files/PAL_E3210.pdf }}</ref><ref>{{cite journal|author1=Cynthia C. Steiner|author2=Oliver A. Ryder|title=Molecular phylogeny and evolution of the Perissodactyla|journal=Zoological Journal of the Linnean Society|year=2011|pages=1289–1303|doi=10.1111/j.1096-3642.2011.00752.x|volume=163|issue=4|doi-access=free}}</ref><ref>{{cite journal|author1=Mario A. Cozzuol|author2=Camila L. Clozato|author3=Elizete C. Holanda|author4=Flávio HG Rodrigues|author5=Samuel Nienow|author6=Benoit de Thoisy|author7=Rodrigo Redondo|author8=AF Fabrício R. Santos|title= A new species of tapir from the Amazon|journal=Journal of Mammalogy|volume=94|issue=6|page=1331 to 1345|doi=10.1644/12-MAMM-A-169.1
|year=2013|doi-access=free}}</ref>
|-
|{{Clade|style=font-size:75%; line-height:100%
|label1='''Perissodactyla'''
|1={{Clade
     |1={{Clade
             |label1=[[Equidae]]
             |1={{Clade
                    |1=''[[Equus ferus]]''
                    |2={{Clade
                          |1=''[[Equus asinus]]''
                          |2={{Clade
                                |1={{Clade
                                      |1=''[[Equus hemionus]]''
                                      |2=''[[Equus kiang]]''
                                      }}
                                |2={{Clade
                                      |1=''[[Equus zebra]]''
                                      |2={{Clade
                                            |1=''[[Equus grevyi]]''
                                            |2=''[[Equus quagga]]''
                                            }}
                                      }}
                                }}
                          }}
                    }}
             |2={{Clade
                    |label1=[[Tapiridae]]
                    |1={{Clade
                          |1=''[[Tapirus indicus]]''
                          |2={{Clade
                                |1=''[[Tapirus bairdii]]''
                                |2={{Clade
                                      |1=''[[Tapirus kabomani]]''
                                      |2={{Clade
                                            |1=''[[Tapirus pinchaque]]''
                                            |2=''[[Tapirus terrestris]]''
                                            }}
                                      }}
                                }}
                          }}
                    |label2=[[Rhinocerotidae]]
                    |2={{Clade
                          |1={{Clade
                                |1=''[[Ceratotherium simum]]''
                                |2=''[[Diceros bicornis]]''
                                }}
                          |2={{Clade
                                |1=''[[Dicerorhinus sumatrensis]]''
                                |2={{Clade
                                      |1=''[[Rhinoceros sondaicus]]''
                                      |2=''[[Rhinoceros unicornis]]''
                                      }}

                                }}
                          }}
                    }}
              }}
      }}
}}
|}

* '''Order Perissodactyla'''
**'''Suborder Hippomorpha'''
***'''Family [[Equidae]]''': horses and allies, seven species in one genus
**** [[Wild horse]], ''Equus ferus''
*****[[Tarpan]], [[Extinction|†]]''Equus ferus ferus''
***** [[Przewalski's horse]], ''Equus ferus przewalskii''
***** Domestic [[horse]], ''Equus ferus caballus''
**** [[African wild ass]], ''Equus africanus''
*****[[Nubian wild ass]], ''Equus africanus africanus''
***** [[Somali wild ass]], ''Equus africanus somaliensis''
***** Domesticated ass ([[donkey]]), ''Equus africanus asinus''
***** [[Atlas wild ass]], [[Extinction|†]]''Equus africanus atlanticus''
**** [[Onager]] or Asiatic wild ass, ''Equus hemionus''
***** [[Mongolian wild ass]], ''Equus hemionus hemionus''
***** [[Turkmenian kulan]], ''Equus hemionus kulan''
***** [[Persian onager]], ''Equus hemionus onager''
***** [[Indian wild ass]], ''Equus hemionus khur''
***** [[Syrian wild ass]], [[Extinction|†]]''Equus hemionus hemippus''
**** [[Kiang]] or Tibetan wild ass, ''Equus kiang''
***** Western kiang, ''Equus kiang kiang''
***** Eastern kiang, ''Equus kiang holdereri''
***** Southern kiang, ''Equus kiang polyodon''
**** [[Plains zebra]], ''Equus quagga''
***** [[Quagga]], [[Extinction|†]]''Equus quagga quagga''
***** [[Burchell's zebra]], ''Equus quagga burchellii''
***** [[Grant's zebra]], ''Equus quagga boehmi''
***** [[Maneless zebra]], ''Equus quagga borensis''
***** [[Chapman's zebra]], ''Equus quagga chapmani''
***** [[Crawshay's zebra]], ''Equus quagga crawshayi''
***** [[Selous' zebra]], ''Equus quagga selousi''
**** [[Mountain zebra]], ''Equus zebra''
*****[[Cape mountain zebra]], ''Equus zebra zebra''
*****[[Hartmann's mountain zebra]], ''Equus zebra hartmannae''
****[[Grévy's zebra]], ''Equus grevyi''
** '''Suborder Ceratomorpha'''
***'''Family [[Tapir]]idae''': tapirs, five species in one genus
****[[South American tapir|Brazilian tapir]], ''Tapirus terrestris''
**** [[Mountain tapir]], ''Tapirus pinchaque''
**** [[Baird's tapir]], ''Tapirus bairdii''
**** [[Malayan tapir]], ''Tapirus indicus''
****[[Tapirus kabomani|Kabomani tapir]], ''Tapirus kabomani''
*** '''Family [[Rhinocerotidae]]''': rhinoceroses, five species in four genera
****[[Black rhinoceros]], ''Diceros bicornis''
***** [[Southern black rhinoceros]], [[Extinction|†]]''Diceros bicornis bicornis''
***** [[North-eastern black rhinoceros]], [[Extinction|†]]''Diceros bicornis brucii''
***** [[Chobe black rhinoceros]], ''Diceros bicornis chobiensis''
***** [[Uganda black rhinoceros]], ''Diceros bicornis ladoensis''
***** [[Western black rhinoceros]], [[Extinction|†]]''Diceros bicornis longipes''
***** [[Eastern black rhinoceros]], ''Diceros bicornis michaeli''
***** [[South-central black rhinoceros]], ''Diceros bicornis minor''
***** [[South-western black rhinoceros]], ''Diceros bicornis occidentalis''
**** [[White rhinoceros]], ''Ceratotherium simum''
***** [[Southern white rhinoceros]], ''Ceratotherium simum simum''
***** [[Northern white rhinoceros]], ''Ceratotherium simum cottoni''
**** [[Indian rhinoceros]], ''Rhinoceros unicornis''
**** [[Javan rhinoceros]], ''Rhinoceros sondaicus''
***** Indonesian Javan rhinoceros, ''Rhinoceros sondaicus sondaicus''
***** Vietnamese Javan rhinoceros, ''[[Rhinoceros sondaicus annamiticus]]''
***** [[Lesser Indian rhinoceros|Indian Javan rhinoceros]], [[Extinction|†]]''Rhinoceros sondaicus inermis''
**** [[Sumatran rhinoceros]], ''Dicerorhinus sumatrensis''
***** Western Sumatran rhinoceros, ''Dicerorhinus sumatrensis sumatrensis''
*****[[Bornean rhinoceros|Eastern Sumatran rhinoceros]], ''Dicerorhinus sumatrensis harrissoni''
***** [[Northern Sumatran rhinoceros]], [[Extinction|†]]''Dicerorhinus sumatrensis lasiotis''

===Prehistoric members===
[[File:Paleotherium magnum.jpg|thumb|Restoration of ''[[Palaeotherium]]'', a [[palaeothere]] genus first formally described in 1804]]
[[File:ChalicotheriumDB1.jpg|thumb|Live reconstruction of [[chalicothere]] ''[[Anisodon]] grande'' (formerly ''Chalicotherium grande'')]]
There are many perissodactyl fossils of multivariant form. The major lines of development include the following groups:

*[[File:Paraceratherium-Scale-Diagram-SVG-Steveoc86.svg|thumb|Scale diagram of the [[paraceratheriid]] ''[[Paraceratherium]],'' one of the largest land mammals to have ever existed]]Brontotherioidea were among the earliest known large mammals, consisting of the families of [[Brontotheriidae]] (synonym Titanotheriidae), the most well-known representative being ''[[Megacerops]]'' and the more basal family [[Lambdotheriidae]]. They were generally characterized in their late phase by a bony horn at the transition from the nose to the frontal bone and flat molars suitable for chewing soft plant food. The Brontotheroidea, which were almost exclusively confined to North America and Asia, died out at the beginning of the Upper [[Eocene]].
*[[Equoidea]] also developed in the Eocene. [[Palaeotheriidae]] are known mainly from Europe. In contrast, the horse family ([[Equidae]]) flourished and spread. Over time this group saw a reduction in toe number, extension of the limbs, and the progressive adjustment of the teeth for eating hard grasses.
*[[Chalicotherioidea]] represented another characteristic group, consisting of the families [[Chalicothere|Chalicotheriidae]] and [[Lophiodontidae]]. The Chalicotheriidae developed claws instead of hooves and considerable extension of the forelegs. The best-known genera include ''[[Chalicotherium]]'' and ''[[Moropus]]''. Chalicotherioidea died out in the [[Pleistocene]].
*Rhinocerotoidea (rhino relatives) included a large variety of forms from the Eocene up to the Oligocene, including dog-size leaf feeders, semiaquatic animals, and also huge long-necked animals. Only a few had horns on the nose. The [[Amynodontidae]] were hippo-like, aquatic animals. [[Hyracodontidae]] developed long limbs and long necks that were most pronounced in the ''[[Paraceratherium]]'' (formerly known as ''Baluchitherium'' or ''Indricotherium''), the second largest known land mammal ever to have lived (after ''[[Palaeoloxodon namadicus]]''<ref>{{cite journal | author = Larramendi A | year = 2016 | title = Withers height, body mass and shape of proboscideans | url = http://www.app.pan.pl/article/item/article/item/app001362014.html?pdf=39| journal = Acta Palaeontologica Polonica | volume = 61 | doi = 10.4202/app.00136.2014 | doi-access = free }}</ref>). The rhinos (Rhinocerotidae) emerged in the Middle Eocene; five species survive to the present day.
*[[Tapiroidea]] reached their greatest diversity in the Eocene, when several families lived in Eurasia and North America. They retained a primitive physique and were noted for developing a trunk. The extinct families within this group include the [[Helaletidae]].{{citation needed|date=August 2020}}
*Several mammal groups traditionally classified as [[condylarth]]s, long-understood to be a [[wastebasket taxon]], such as [[Hyopsodontidae|hyopsodontids]] and [[Phenacodontidae|phenacodontids]], are now understood to be part of the odd-toed ungulate assemblage. Phenacodontids seem to be stem-perissodactyls, while hyopsodontids are closely related to horses and brontotheres, despite their more primitive overall appearance.
*[[Desmostylia]]<ref>{{cite journal |author1=Cooper L. N. |author2=Seiffert E. R. |author3=Clementz M. |author4=Madar S. I. |author5=Bajpai S. |author6=Hussain S. T. |author7=Thewissen J. G. M. |display-authors= 3| year = 2014 | title = Anthracobunids from the Middle Eocene of India and Pakistan Are Stem Perissodactyls | journal = PLOS ONE| volume = 9 | issue = 10| page = e109232 | doi = 10.1371/journal.pone.0109232 | pmid = 25295875 | pmc=4189980|bibcode=2014PLoSO...9j9232C |doi-access=free }}</ref> and [[Anthracobunidae]] have traditionally been placed among the [[Afrotheria|afrotheres]], but they may actually represent stem-perissodactyls. They are an early lineage of mammals that took to the water, spreading across semi-aquatic to fully marine niches in the [[Tethys Ocean]] and the northern [[Pacific Ocean|Pacific]]. However, later studies have shown that, while anthracobunids are definite perissodactyls, desmostylians have enough mixed characters to suggest that a position among the Afrotheria is not out of the question.<ref name= "Gheerbrant 2016 e0157556">{{cite journal |last1= Gheerbrant| first1= Emmanuel| last2= Filippo| first2= Andrea | last3= Schmitt|first3= Arnaud | year = 2016 | title = Convergence of Afrotherian and Laurasiatherian Ungulate-Like Mammals: First Morphological Evidence from the Paleocene of Morocco | journal = PLOS ONE| volume = 11 | issue = 7| page = e0157556 | doi = 10.1371/journal.pone.0157556 | pmid=27384169 | pmc=4934866|bibcode=2016PLoSO..1157556G | doi-access= free}}</ref>
* '''Order Perissodactyla'''<ref name="Prothero 2009"/>
**'''Superfamily Brontotherioidea'''
*** †[[Brontotheriidae]]
**'''Suborder Hippomorpha'''
*** †[[Hyopsodontidae]]<ref>{{cite journal |last1= Ravel| first1= Anthony | last2= Orliac| first2= Maeva | year = 2014 | title = The inner ear morphology of the 'condylarthran' Hyopsodus lepidus | journal = Historical Biology | volume = 27 | issue = 8| page = 8 | doi = 10.1080/08912963.2014.915823 |s2cid=84391276 }}</ref>
*** †[[Pachynolophidae]]<ref name="Badiola2003">{{cite journal |last1= Badiola |first1= A. |last2= Pareda-Suberbiola |first2= X. |last3= Cuesta |first3= M. |date= 2003 |title= A new species of ''Pachynolophus'' (Mammalia, Perissodactyla) from Zambrana (Álava, Basque-Cantabrian Region). Phylogenetic analysis of ''Pachynolophus'' and first mention in the Late Eocene of the Iberian Peninsula |journal= Geobios |volume= 38 |issue= 1 |pages= 1–16 |doi= 10.1016/j.geobios.2003.07.005}}</ref>
*** '''Superfamily Equoidea'''
**** †[[Indolophidae]]<ref name="Tsubamoto2003">{{cite journal |last1= Tsubamoto |first1= T. |last2= Tun |first2= S.T. |display-authors = etal |date= 2003 |title= Reevaluation of some ungulate mammals from the Eocene Pondaung Formation, Myanmar |journal= Paleontological Research |volume= 7 |issue= 3 |pages= 219–43 |doi= 10.2517/prpsj.7.219|s2cid= 84061253 |doi-access= free |bibcode= 2003PalRe...7..219T }}</ref>
**** †[[Palaeotheriidae]] (might be a basal perissodactyl grade instead)
** '''Clade Tapiromorpha'''
*** †[[Isectolophidae]]<ref name="Holbrook 2001"/> (a basal family of Tapiromorpha; from the Eocene epoch)
*** †'''Suborder [[Ancylopoda]]'''
**** †[[Lophiodontidae]]
**** '''Superfamily [[Chalicotherioidea]]'''
***** †[[Eomoropidae]] (basal grade of chalicotheroids)
***** †[[Chalicothere|Chalicotheriidae]]
*** '''Suborder Ceratomorpha'''
**** '''Superfamily [[Rhinocerotoidea]]'''
***** †[[Amynodontidae]]
***** †[[Hyracodontidae]]
**** '''Superfamily [[Tapiroidea]]'''
***** †[[Deperetellidae]]
***** †[[Rhodopagidae]] (sometimes recognized as a subfamily of deperetellids)
***** †[[Lophialetidae]]<ref name=Gong2019>{{cite journal |last1= Gong |first1= Y. |last2= Wang |first2= Y. |display-authors = etal |date= December 2019 |title= Dietary adaptations and palaeoecology of Lophialetidae (Mammalia, Tapiroidea) from the Eocene of the Erlian Basin, China: combined evidence from mesowear and stable isotope analyses |journal= Palaeontology |volume= 63 |issue= 4 |pages= 547–564 |doi= 10.1111/pala.12471|s2cid= 214053761 }}</ref>
***** †[[Eoletidae]] (sometimes recognized as a subfamily of lophialetids)
** †[[Anthracobunidae]]<ref name="Cooper2014">{{Cite journal | doi = 10.1371/journal.pone.0109232| pmid = 25295875| title = Anthracobunids from the Middle Eocene of India and Pakistan Are Stem Perissodactyls| journal = PLOS ONE| volume = 9| issue = 10| pages = e109232| date = 2014-10-08| last1 = Cooper | first1 = L. N. | last2 = Seiffert | first2 = E. R. | last3 = Clementz | first3 = M. | last4 = Madar | first4 = S. I. | last5 = Bajpai | first5 = S. | last6 = Hussain | first6 = S. T. | last7 = Thewissen | first7 = J. G. M.| pmc=4189980| bibcode = 2014PLoSO...9j9232C| doi-access = free}}</ref> (a family of stem-perissodactyls; from the Early to Middle Eocene epoch)
** †[[Phenacodontidae]]<ref name="Cooper2014"/> (a clade of stem-perissodactyls; from the Early Palaeocene to the Middle Eocene epoch)

===Higher classification of perissodactyls===
{| class="wikitable" style="float:right;"
|-
|+ Internal classification of Perissodactyla<ref name="Holbrook et al. 2011"/>
|-
|{{Clade|style=white-space:nowrap;font-size:75%;line-height:100%
|label1='''Perissodactyla'''
|1={{Clade
  |label1=[[Hippomorpha]]
  |1={{Clade
     |label1=[[Equoidea]]
     |1={{Clade
        |1=[[Palaeotheriidae]] (†)
        |2=[[Equidae]]
        }}
     |label2=[[Brontotherioidea]]
     |2={{Clade
        |1=[[Lambdotheriidae]] (†)
        |2=[[Brontotheriidae]] (†)
        }}
     }}
   |label2=[[Tapiromorpha]]
   |2={{Clade
      |1=[[Isectolophidae]] (†)
      |2={{Clade
         |label1=[[Ancylopoda]]
         |1={{Clade
            |1=[[Lophiodontidae]] (†)
            |2=[[Chalicotheriidae]] (†)
            }}
         |label2=[[Ceratomorpha]]
         |2={{Clade
            |label1=[[Tapiroidea]]
            |1={{Clade
                |1=[[Helaletidae]] (†)
                |2=[[Tapiridae]]
                }}
            |label2=[[Rhinocerotoidea]]
            |2={{Clade
               |1=[[Amynodontidae]] (†)
               |2={{Clade
                  |1=[[Hyracodontidae]] (†)
                  |2=[[Rhinocerotidae]]
                  }}
               }}
            }}
        }}
     }}

  }}
}}
|}
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 ([[Equus (genus)|Equoidea]]); the Ceratomorpha consist of tapirs and rhinos plus their extinct members ([[Tapiroidea]] and [[Rhinocerotoidea]]).<ref name="Simpson 1945">{{cite journal|author=George Gaylord|title=The Principles of Classification and a Classification of Mammals|journal=Bulletin of the American Museum of Natural History |year=1945|pages=252–258}}</ref> 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.<ref>{{cite journal|author=Horace Elmer Wood|title=Revision of the Hyrachyidae|journal=Bulletin of the American Museum of Natural History|year=1934|pages=181–295}}</ref><ref>{{cite journal|author=Horace Elmer Wood|title=Perissodactyl suborders|journal=Journal of Mammalogy|year=1937|page=106|doi=10.1093/jmammal/18.1.106|volume=18|issue=1 }}</ref> 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''.<ref name="Holbrook et al. 2011">{{cite journal|author1=Luke T. Holbrook|author2=Joshua Lapergola|title= A new genus of perissodactyl (Mammalia) from the Bridgerian of Wyoming, with comments on basal perissodactyl phylogeny|journal=Journal of Vertebrate Paleontology|year=2011|volume=31|issue=4|pages=895–901|doi=10.1080/02724634.2011.579669|bibcode=2011JVPal..31..895H |s2cid=84351811}}</ref><ref name="Schoch 1989">{{cite book|author=Robert M. Schoch|chapter=A brief historical review of perissodactyl classification |title=The Evolution of Perissodactyls |publisher=Oxford University Press|year=1989|pages=13–23}}</ref>

Originally, the [[Chalicothere|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).<ref>{{cite journal|author=William Berryman Scott|title=Part V: Perissodactyla|journal=The Mammalian Fauna of the White River Oligocene Transactions of the American Philosophical Society |series=New Series|volume=28|issue=5|year=1941|pages=747–964|doi=10.2307/1005518|jstor=1005518}}</ref> 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 Radinsky|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.<ref>{{cite journal|author=Leonard B. Radinsky|title=''Paleomoropus'', a new early Eocene chalicothere (Mammalia, Perissodactyla), and a revision of Eocene chalicotheres|journal=American Museum Novitates|year=1964|pages=1–28}}</ref> 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.<ref>{{cite journal|author=JJ Hooker|title=A primitive ceratomorph (Perissodactyla, Mammalia) from the Early Tertiary of Europe|journal=Zoological Journal of the Linnean Society|year=1984|pages=229–244|doi=10.1111/j.1096-3642.1984.tb00545.x|volume=82|issue=1–2}}</ref> Also in 1984, Robert M. Schoch used the conceptually similar term Moropomorpha, which today applies synonymously to Tapiromorpha.<ref>{{cite journal|author=Robert Milton Schoch|title=Two unusual specimens of the Yale Peabody Museum Helaletes in collections, and some comments on the ancestry of the Tapiridae (Perissodactyla, Mammalia)|publisher=Peabody Museum, Yale University|year=1984|pages=1–20}}</ref> 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.<ref name="Schoch 1989"/><ref name="Holbrook 2001">{{cite journal|author=Luke T. Holbrook|title=Comparative osteology of early Tertiary tapiromorphs (Mammalia, Perissodactyla)|journal=Zoological Journal of the Linnean Society|year=2001|pages=1–54|doi=10.1111/j.1096-3642.2001.tb02270.x|volume=132|issue=1 |doi-access=free}}</ref>