Appendix 4. D escription of characters used in the phylogenetic analyses. Characters are polarized with respect to Homogalax protapirinus, Isectolophus latidens, and I. annectens as outgroups. All characters are treated as unordered.

 (1) Distinct cuspules on cheekteeth shearing lophs: present (0); absent, lophs continuous (1).

(2) Upper canine length compared to upper incisors: canines shorter (0); canines longer (1); canines absent (2). Modified from character 18 of Colbert (1993), and character 10 of Hooker (1989).

(3) I3 size relative to I2-3: similar size (0); enlarged (1). Modified from character 29 of Colbert (1993) .

(4) I3 posterior cuspule: present (0); absent (1).

(5) i3 size relative to i1-3: similar size (0); reduced (1); i3 absent (2). Modified from character 30 of Colbert (1993) .

(6) Incisor shape: not spatulate (0); spatulate (1).

(7) Upper molar metacone enamel surface: wrinkled labially (0); not wrinkled (1).

(8) M1 metacone buccal surface: broadly rounded (0); ribbed buccally (1); flat to concave (2). Modified from character 4 of Dashzeveg and Hooker (1997), and from character 23 of Colbert (1993) . Similar to character 55 of Hooker (1989) .

(9) M2 metacone buccal surface: broadly rounded (0), ribbed buccally (1); flat to concave (2). Modified from character 4 of Dashzeveg and Hooker (1997), and from character 23 of Colbert (1993) . Similar to character 55 of Hooker (1989) .

(10) M3 metacone buccal surface: broadly rounded (0), ribbed buccally (1); flat to concave (2). Modified from character 4 of Dashzeveg and Hooker (1997), and from character 23 of Colbert (1993) . Similar to character 55 of Hooker (1989) .

(11) M1 parastyle separation from paracone: well separated (0); compressed against paracone, curving around the paracone labial face (1). Modified from character 7 of Dashzeveg and Hooker (1997), similar to character 26 of Colbert (1993) .

(12) M2 parastyle separation from paracone: well separated (0); compressed against paracone, curving around the paracone labial face (1). Modified from character 7 of Dashzeveg and Hooker (1997), similar to character 26 of Colbert (1993) .

(13) M3 parastyle separation from paracone: well separated (0); compressed against paracone, curving around the paracone labial face (1). Modified from character 7 of Dashzeveg and Hooker (1997), similar to character 26 of Colbert (1993).

(14) M1 ectoloph long axis: essentially straight, joining vertically implanted or slightly distally tilted paracone (0); buccally convex, making U-shaped loph together with protoloph and metaloph, and having a slightly mesially tilted paracone (1). Modified from character 8 of Dashzeveg and Hooker (1997).

(15) M2 ectoloph long axis: essentially straight, joining vertically implanted or slightly distally tilted paracone (0); buccally convex, making U-shaped loph together with protoloph and metaloph, and having a slightly mesially tilted paracone (1). Modified from character 8 of Dashzeveg and Hooker (1997).

(16) M3 ectoloph long axis: essentially straight, joining vertically implanted or slightly distally tilted paracone (0); buccally convex, making U-shaped loph together with protoloph and metaloph, and having a slightly mesially tilted paracone (1). Modified from character 8 of Dashzeveg and Hooker (1997).

(17) M2 ectoloph developed into high shearing blade by lengthening metacone: not developed (0); developed (1).

(18) Position where M1 metaloph joins ectoloph: near middle (0); slighly in front of metacone (1); at metacone (2). Modified from character 9 of Dashzeveg and Hooker (1997), similar to character 47 of Hooker (1989) .

(19) Position where M2 metaloph joins ectoloph: near middle (0); slighly in front of metacone (1); at metacone (2). Modified from character 9 of Dashzeveg and Hooker (1997), similar to character 47 of Hooker (1989) .

(20) Position where M3 metaloph joins ectoloph: near middle (0); slighly in front of metacone (1); at metacone (2). Modified from character 9 of Dashzeveg and Hooker (1997), similar to character 47 of Hooker (1989) .

(21) M3 metaloph axis relative to ectoloph axis: not directed distinctly posteriorly, forms obtuse angle with ectoloph (0); directed distinctly posteriorly , forms acute angle with ectoloph (1).

(22) M3 lingual cingulum: incomplete (0); complete (1). Modified from character 11 of Dashzeveg and Hooker (1997).

(23) M1-2 lingual cingulum: incomplete (0); complete (1). Modified from character 11 of Dashzeveg and Hooker (1997) and from character 25 of Colbert (1993) .

(24) Shape and position of M1-2 ectocingulum adjacent to metacone: forming ridge and marginal (0); bulbous and encroaching on stylar shelf (1); ectocingulum absent (2). Modified from character 12 of Dashzeveg and Hooker (1997).

(25) Upper molar postmetacrista and lower molar paracristid (paralophid): mesiodistally oriented (0); obliquely oriented (1). Character 13 of Dashzeveg and Hooker (1997).

(26) Molar transverse loph lateral profile: straight (0); curved occlusomesially in uppers and occlusodistally in lowers (1). Character 14 of Dashzeveg and Hooker (1997).

(27) Upper molar postmetacrista and lower molar trigonid: relatively long (0); slightly shortened (1); greatly shortened (2). Character 15 of Dashzeveg and Hooker (1997).

(28) P1 hypocone: absent (0); present (1). Character 17 of Dashzeveg and Hooker (1997).

(29) P2 lingual cingulum: complete (0); broken or absent (1).

(30) P3 lingual cingulum: complete (0); broken or absent (1).

(31) P4 lingual cingulum: complete (0); broken or absent (1).

(32) P3 hypocone presence, metaloph shape: P3 either absent or connects directly to metaloph (postprotocrista) (0); hypocone independent of metaloph (postprotocrista), which joins protocone (1). Character 19 of Dashzeveg and Hooker (1997).

(33) P3 loph posterior to the protoloph: absent (0); P3 with postprotocrista (1); P3 with metaloph (2). Modified from character 21 of Colbert (1993) .

(34) P3 with protocone and hypocone: not divided (0); divided (1). This character was used Dashzeveg and Hooker (1997) to characterize Colodon.

(35) P4 metaloph (postprotocrista): essentially complete (0); broken buccal of protocone (1). Character 20 of Dashzeveg and Hooker (1997).

(36) P4 loph development: P4 with postprotocrista (0); P4 with metaloph (1). Modified from character 20 of Colbert (1993) .

(37) P4 protocone and hypocone: not divided (0); divided (1). This character was used Dashzeveg and Hooker (1997) to characterize Colodon.

(38) P4 postprotocrista (metaloph): joins protocone rather than hypocone (0); joins hypocone (1). This character was used Dashzeveg and Hooker (1997) to characterize Colodon.

(39) P4 ectoloph concave, paracone and metacone displaced lingually relative to preparacrista/ parastyle, and postmetacrista/metastyle: no (0); yes (1).

(40) m3 hypoconulid lobe: large (0); small (1); in the form of a cuspate cingulum (2); absent (3). Character 16 of Dashzeveg and Hooker (1997). Similar to character 28 of Colbert (1993) , and to character 59 of Hooker (1989) . This is a continuous multistate character.

(41) Lower molar posthypocristid: cuspate (0); weakly present (1); absent (2). Character 26 of Dashzeveg and Hooker (1997). This is a continuous multistate character.

(42) Cristid-like structure on the lower molars: absent (0); present (1). Character discussed by Albright (1998). Modified from character 31 of Colbert (1993) .

(43) “Cingulum around the lingual end of the mesial arm of the lower molar paralophid, where the latter recurves slightly distally” Dashzeveg and Hooker (1997: 107): absent (0); present (1). This character was used by Dashzeveg and Hooker (1997) to distinguish Lophialetes from Schlosseria.

(44) m1 protolophid and hypolophid parallel: yes (0); no (1).

(45) m2 protolophid and hypolophid parallel: yes (0); no (1).

(46) m3 protolophid and hypolophid parallel: yes (0); no (1).

(47) Relative depth of the horizontal ramus of the dentary: ratio of M2 length to dentary depth of at level of M2 less than 45% (0); greater than 45% (1). Modified from character 15 of Colbert (1993) .

(48) Posterior extent of the fused symphysis of dentary: anterior to anterior edge of p2 (0); posterior to anterior edge of p2 (1). Modified from character 16 of Colbert (1993) . Note that in Breviodon, the posterior extent of the symphysis is approximately at the level of anterior p3.

(49) p1: present (0), absent (1).

(50) p3 paraconid: much lower than protoconid (0); p3 paraconid nearly as tall as protoconid with trenchant paracristid (1). Modified from character 23 of Dashzeveg and Hooker (1997).

(51) p3 metaconid: weak (0); strong (1). Character 22 of Dashzeveg and Hooker (1997).

(52) p3-4 talonids: no broader than trigonids (0); broader than trigonids (1). Character 24 of Dashzeveg and Hooker (1997); character 22 of Colbert (1993) .

(53) Metastylids on dp2: absent (0), present (1). Modified character 22 of Hulbert (1995).

(54) Metastylids on dp3: absent (0), present (1). Modified character 22 of Hulbert (1995).

(55) Metastylids on dp4. Absent (0), present (1). Modified character 22 of Hulbert (1995).

(56) Posterior extent of nasoincisive incisure: P1 (0); P2 (1); P3 (2) P4 (3), M1 (4), M2 (5) M3 (6). Modified from character 1 of Dashzeveg and Hooker (1997); character 4 of Hooker (1989) , and character 5 of Colbert (1993) . This is a continuous multistate character.

(57) Anterior extent of orbit: posterior to anterior M1 (0), posterior to anterior M2 (1), posterior to anterior M3 (2), posterior to P4 (3). This is a continuous multistate character.

(58) Posterior process of premaxilla: long, terminates in acute point (0), short, bluntly terminated (1). Modified character 13 of Hulbert (1995).

(59) Anteromedial process of maxilla: absent to very slender, little or no lateral exposure (0); moderate lateral exposure (1); broad, well-exposed laterally (2). Modified character 14 of Hulbert (1995).

(60) Premaxillary–nasal contact: present (0); absent(1). Modified from character 9 of Colbert (1993), and from character 2 of Dashzeveg and Hooker (1997).

(61) Shape of nasals not contacting premaxillae: have splint-like anterior process (0); lack splint-like anterior extension (1). Modified from character 9 of Colbert (1993), and from character 2 of Dashzeveg and Hooker (1997).

(62) Oblique lateral ridge on nasals: absent (0); present located posteriorly (1); present located anteriorly (2). Modified from character 10 of Colbert (1993) .

(63) Premaxillary-maxillary suture: descends anterior to canine in lateral view (0), descends to middle of canine (1). Modified character 15 of Hulbert (1995).

(64) Dorsal maxillary flange: does not embrace mesethmoid (0); embraces mesethmoid to limited extent (1), broadly embraces mesethmoid (2). Modified character 16 of Hulbert (1995). This is a continuous multistate character.

(65) Maxillary fossa: absent (0); present (1). Modified from character 7 of Colbert 1993 .

(66) Lateral groove, anterior portion: absent (0); present (1). Modified from character 32 of Colbert (1993).

(67) Infraorbital foramen position: anterior to anterior edge of P3 (0); posterior to anterior edge of P3, and anterior to anterior edge of P4 (1); posterior to anterior edge of P4 (2). Modified from character 8 of Colbert (1993) . This is a continuous multistate character.

(68) Anterior extent of the masseteric muscle scar: posterior to anterior edge of M2 (0); anterior to anterior edge of M2 (1). Modified from character 12 of Colbert (1993).

(69) Anterior lacrimal tubercle/ process: weak or absent (0); well developed (1). Modified character 16 of Hulbert (1995).

(70) Palatine fissures: paired (0); single confluent median fissure (1). Modified from character 6 of Colbert (1993) .

(71) Anteromedial process of frontals: extends between nasals (0); does not extend between nasals (1). Modified character 6 of Hulbert (1995).

(72) Sagittal crest anterior to frontal crests: absent (0); present (1). Character 1 of Colbert (1993) .

(73) Narrow grooves on posterolateral nasals and frontals at the posterior terminus of the narial incision: absent (0); present, short, largely restricted to posterolateral nasals (1); present, long and straight, extending well onto frontals (2). Modified from character 2 of Colbert (1993) .

(74) Lateral groove, posterior portion: absent (0); present, continues posteriorly to frontal crests (1); present, curled or compressed onto postero-dorsal nasal (2). Modified from character 3 of Colbert (1993) .

(75) Medial grooves on dorsal surface of frontals: absent (0); present (1). Modified from character 4 of Colbert (1993) .

(76) Lateral supraorbital process: broad (0); reduced to small rugosity (1). Modified from character 11 of Colbert (1993) .

(77) Adult width of sagittal crest: relatively narrow (0); broad (1). Modified character 2 of Hulbert (1995).

(78) Frontal inflation: none or slight (0); moderate to great (1). Modified character 4 of Hulbert (1995).

(79) Dorsal contour of skull: relatively straight (0); nasals notably stepped down from frontals (1). Modified character 12 of Hulbert (1995).

(80) Interparietal: present (0); absent (1). Hulbert’s (1995) character 5 coded the interparietal either fused early or later in ontogeny. However, based on observation of early postnatal (possibly neonatal material) it is clear that the interparietal is lacking in most T. terrestris.

(81) Postglenoid foramen on posteromedial portion of postglenoid process: present (0); absent (1). Modified from character 13 of Colbert (1993) .

(82) Foramen ovale: distinct (0); confluent with the middle lacerate foramen (1). Modified from character 33 of Colbert (1993) . This character is also discussed in MacFadden (1976), and Edinger and Kitts (1954).

(83) Relative width of paroccipital process: narrow and slender (0); broad and massive (1). Modified character 17 of Hulbert (1995).

(84) Manus digit V: present (0); absent (1). Character 31 of Dashzeveg and Hooker (1997).

(85) Lower canines: present (0); absent (1).

(86) Postglenoid process axis less than 45 degree angle to long axis of skull: no (0); yes (1).

(87) Postglenoid process shape: low and rounded (0); tall and post-like (1); tall and compressed (2)

(88) Astragalus sustentacular and posterior calcaneal facets confluent:no (0); yes (1).

(89) m2 metalophids reduced: no(0); yes (1).