Appendix I: Character List
Characters used for phylogenetic analysis of Tyrannosauridae.  Multistate characters are listed as “O” for ordered and “UO” for unordered.  Scoring: 0 = primitive state; 1, 2, or 3 = derived character states.
Synapomorphies of Tyrannosauridae
1) Ventral ramus of the premaxilla: 0, as long or longer rostrocaudally than tall dorsoventrally; 1, taller dorsoventrally than long rostrocaudally.
2) Premaxillary tooth row arcade: 0, more rostrocaudally than mediolaterally oriented; 1, more mediolaterally than rostrocaudally oriented.
3) Nasals: 0, unfused; 1, fused.
4) Squamosal-quadratojugal flange constricting infratemporal fenestra: 0, absent; 1 present.
5) Prefrontals: 0, large; 1, reduced; 2, absent O
6) Well-formed sagittal crest on dorsal surface of parietals: 0, absent; 1, present.
7) Lateral nuchal crest formed by parietals: 0, absent or small; 1, present (at least twice as tall as foramen magnum vertical height).
8) Pair of tab-like processes on supraoccipital wedge: 0, absent; 1, present.
9) Basisphenoid sphenoidal sinus: 0, shallow, foramina small or absent; 1, deep, foramina large.
10) Prominent muscular fossae on dorsal surface of palatines: 0, present; 1, absent.
11) Rostral portion of the fused vomers: 0, small expansion (less than twice shaft width); 1 expanded to greater than twice shaft width to form a rhomboid- or diamond-shape.
12) Caudal surangular foramen: 0, small or absent; 1, very large.
13) Retroarticular process of articular: 0, present; 1, absent.
14) Premaxillary teeth cross section: 0, asymmetrical ovals with a rostral and a caudal carina; 1, D-shaped or U-shaped, with both carinae placed along the same plane perpendicular to the skull axis.
15) Premaxillary tooth size: 0, subequal to lateral teeth; 1, much smaller than lateral teeth.
16) Distal caudal neural spines: 0, axially short or absent; 1, axially elongate.
17) Acromial expansion: 0, small, less than twice scapula midshaft width; 1, well developed, more than twice scapula midshaft width.
18) Scapula contribution to glenoid: 0, half; 1, greater than half.
19) Femur-humerus ratio: 0, less than 2.5; 1, between 2.8 and 3.5; 2, greater than 3.5. O
20) Scapula-humerus ratio: 0, less than 2.1; 1, between 2.2 and 2.5; 2, greater than 2.5. O
21) Distal carpals of adults; 0, well formed with transverse trochlea; 1, poorly formed and lack trochlear surfaces.
22) Metacarpal III: 0, bears a digit; 1, very reduced and bears no digit.
23) Ilium length: 0, clearly shorter than femur; 1, slightly shorter than femur; 2, longer than femur.  O
24) Horizontal medial shelf from preacetabular blade to sacral ribs: 0, absent; 1, present;
25) Broad, ventral hook-like projection from preacetabular blade of ilium: 0, absent; 1, present.
26) Notch on cranial surface of preacetabular blade of ilium: 0, absent; 1, present.
27) Dorsal surfaces of iliac blades: 0, well separated in dorsal view; 1, converge closely along midline.
28) Pronounced midline crest on ilium: 0, absent; 1, present. 
29) Supracetabular crest on ilium: 0, prominent; 1, reduced.
30) Pubic boot length: 0, one-third or less pubis length (or femur length), 1, approximately one-half pubis length (or femur length); 2, approximately two-thirds or more pubis length (or femur length). O
31) Pronounced semicircular scar on caudolateral surface of ischium, just ventral to the iliac process: 0, absent; 1, present.
32) Shaft of ischium: 0, almost as long and thick as pubis; 1, long but more slender and shorter than pubis; 2, very short (66% or less pubis length).  UO
33) Ischium termination: 0, small expansion; 1, pointed tip.
34) Lesser trochanter height: 0, less than dorsalmost point of femoral head; 1, as tall or taller than dorsalmost point of femoral head.
35) Tibia proportions: 0, moderate (falls along main allometric trend of non-avian theropods); 1, elongate relative to comparable sized theropods (other than ornithomimosaurs).
36) Fibular cranial tubercle distal to cranial expansion: 0, absent or composed of single bulge; 1, composed of two longitudinal ridges.
37) Arctometatarsus: 0, absent; 1, present.
38) Metatarsal proportions: 0, moderate (falls along main allometric trend of non-avian theropods); 1, elongate and slender relative to comparable sized theropods (other than ornithomimosaurs).
39) Dorsal surface of metatarsal III: 0, oval or hourglass-shaped; 1, crescentic and limited to the caudal portion of the metatarsus dorsal surface.

Tyrannosaurid ingroup characters
40) Lateral flange of maxilla obscuring cranialmost portion of maxillary antorbital fossa in lateral view: 0, absent; 1, present as small crest; 2, large shelf.  O
41) Size of maxillary fenestra: 0, small, less than one-half area of eyeball-bearing portion of orbit; 1, expanded, approximately two-thirds area of eyeball-bearing portion of orbit.
42) Maxillary fenestra cranial margin: 0, terminates caudal to cranial margin of antorbital fossa, promaxillary fenestra present; 1, terminates along cranial margin of antorbital fossa, promaxillary fenestra lost (or absorbed).
43) Internal antorbital fenestra proportions: 0, longer than tall; 1, as tall or taller than long.
44) Ventral curvature of maxilla: 0, absent; 1, present; 2, pronounced. O
45) Maxillary tooth count in adults: 0, 18; 1, 13 or fewer.
46) Nasal rugosity: 0, absent; 1, present.
47) Nasal caudal width: 0, nearly as wide between lacrimal as rostral to lacrimals; 1, pinched between lacrimals, thinnest point approximately 1/2 mediolateral width of thickest point; 2, extremely pinched, thinnest point approximately 1/6 mediolateral width of thickest point.  O
48) Nasal caudal suture shape: 0, medial projection extends as far or further caudally than lateral projections; 1, lateral projections extend further caudally than medial projections.
49) Dorsal surface of antorbital fossa: 0, restricted to maxilla and lacrimal; 1, contacts the nasal margin.
50) Dorsal ramus of lacrimal: 0, slender; 1, inflated appearance.
51) Triangular hornlet on lacrimal: 0, absent; 1, present.
52) Lacrimal horn orientation: 0, absent; 1, dorsal; 2, rostrodorsal.  UO
53) Lacrimal horn position: 0, absent; 1, directly dorsal to descending ramus of lacrimal; 2, rostral to descending ramus of lacrimal. UO
54) Angle of the descending and dorsal rami contact of lacrimal: 0, right angle; 1, strongly acute angle.
55) Margin of external antorbital fenestra on craniolateral surface of descending ramus of lacrimal: 0, continued as clearly demarcated margin on lateral surface of jugal; 1, flattens out and is not continued on surface of jugal.
56) Postorbital dorsal surface in adults: 0, smooth; 1, enlarged bump; 2, large rugose boss. O
57) Suborbital prong of postorbital: 0, absent or very small; 1, prominent.
58) Contact between dorsal surface of lacrimal and postorbital in lateral view: 0, absent; 1, present, no intergrowth; 2, intergrowth of bone to form supraorbital torus. O
59) Convex tablike prominence on dorsolateral surface of postorbital: 0, absent; 1, present
60) Ventral termination of postorbital descending ramus: 0, nearly as ventral as ventralmost margin of orbit, and clearly ventral to the squamosal-quadratojugal contact; 1, well dorsal to ventralmost margin of orbit, and approximately the same level as the squamosal-quadratojugal contact.
61) Shape of frontals in adults: 0, triangular; 1, caudal end expanded laterally; 2, main body rectangular, only small triangular cranial prong remains. O
62) Supratemporal fossa on frontal: 0, absent; 1, occupies laterocaudal third; 2, occupies laterocaudal half; 3, occupies most of caudal frontal, meet along midline to form frontal sagittal crest. O
63) Nuchal crest mediolateral width: 0, less than twice height; 1, more than twice height.
64) Nuchal crest rostrocaudal thickness: 0, relatively thin, dorsal margin smooth; 1, much thicker, dorsal margin rugose.
65) Orientation of occipital region: 0, caudal; 1, caudoventral.
66) Supraoccipital contribution to foramen magnum: 0, present, 1, absent (exoccipitals form complete dorsal margin).
67) Basitubera size: 0, large (comparable to ventral ends of basipterygoid processes); 1, reduced.
68) Ventral pocket to ectopterygoid chambers: 0, present; 1, greatly reduced;
69) Ectopterygoid sinus: 0, moderate; 1, inflated.
70) Palatine shape: 0, triradiate; 1, inflated trapezoid.
71) Foramina on ventral surface of palatine: 0, 1; 1, 2 or more.
72) Vertical depth of caudal portion of dentary: 0, only half again as deep or less of vertical depth at symphysis; 1, twice or more as deep as depth at symphysis.
73) Caudal termination of angular: 0, caudal or ventral to caudal surangular foramen; 1, rostral to caudal surangular foramen.
74) Surangular shelf: 0, horizontal; 1, slightly pendant, overhangs dorsal margin of caudal surangular foramen.
75) Dentary tooth count in adults: 0, 16 or more; 1, 15 or fewer.
76) Premaxillary teeth serrations: 0, present; 1, absent.
77) Vertical ridge on caudal surface of premaxillary teeth: 0, weakly developed; 1, strongly developed.
78) Number of incisiform teeth in rostral end of maxilla: 0, none; 1, first maxillary tooth incisiform; 2, first 2 to 3 maxillary teeth incisiform.
79) Lateral teeth: 0, ziphodont; 1, incrassate (cross-section greater than 60% wide mediolaterally as long craniodistally).
80) Cervical centra: 0, longer than height of cranial face (neck length only slightly shorter than length of dorsal series); 1, less than one half as long as height of vertical face (neck much shorter than dorsal series).
81) Tallest cervical neural spines: 0, less than vertical diameter of centrum; 1, more than vertical diameter of centrum.
82) Distal end of scapula: 0, not expanded; 1, greatly expanded cranially and caudally to more than twice midshaft width.
83) Deltapectoral crest: 0, relatively large; 1, reduced.
84) Metacarpal II-metacarpal I ratio: 0, 200%; 1, 170%; 2, 160% or shorter. O
85) Phalanx 1 of manual digit I: 0, longer than metacarpal II; 1, subequal to metacarpal II; 2, shorter than metacarpal II.  O
86) Distal end of manual unguals: 0, tapers to point; 1, blunt.

Aublysodon molnari
87) Rostral end of dentary tooth row: 0, along same curve as rest of tooth row; 1, placed on a dorsally raised step.

Kirtland Shale aublysodontine
88) Medial margin of tibial facet for ascending processes of astragalus: 0, smooth curve; 1) small embayment.

Shanshanosaurus houyanshanensis
89) Cervical vertebrae centra: 0, amphicoelous or amphiplatyan; 1, slightly procoelous.

Alioramus remotus
90) Nasal surface: 0, no individual hornlets; 1, double row of five vertical blades.
91) Prootic rostral expansion: 0, absent; 1, present.
92) Trigeminal foramen: 0, in laterosphenoid; 1, in prootic.

Gorgosaurus libratus
93) Promaxillary fenestra: 0, rostral to maxillary fenestra (or absent); 1, rostrodorsal to maxillary fenestra in adults.
94) Postorbital-lacrimal ventral contact: 0, do not contact below orbit; 1, contact below orbit in adults, orbit more circular (dorsoventral axis not twice or more rostrocaudal axis) than in other large theropods.

Albertosaurus sarcophagus
95) Rostral margin of postorbital suborbital prong: 0, smooth (or prong absent); 1, jagged.
96) Basisphenoid foramina in sphenoidal sinus: 0, lies within same surface; 1, each foramen lies within a distinct fossa.

Daspletosaurus torosus
97) Premaxillary symphysis: 0, no intergrowth; 1, intergrowth.
98) Premaxilla-nasal contact: 0, premaxilla contacts nasal ventral to external nares (although not always visible in lateral view); 1, premaxilla does not contact nasal ventral to external nares.
99) Number of lacrimal apertures: 0, 1; 1, two or more.

Tyrannosaurus bataar
100) Ulnar-humeral ratio: 0, 60%; 1, 45%.
101) Metacarpal III: 0, longer than metacarpal  I; 1, shorter than metacarpal I.
102) Postacetabular blade of ilium: 0, squared end; 1, tapered end.

Tyrannosaurus rex
103) Mediolateral width of rostrum at caudal end of maxillary tooth row: 0, twice or less width of nasals; 1, approximately three times width of nasals.
104) Maximum postorbital skull width: 0, less than one half premaxilla-occipital condyle length; 1, more than two-thirds premaxilla-occipital condyle length.
105) Orbits: 0, directed mostly laterally; 1, directed more rostrally.
106) Nasal processes of premaxilla: 0, slightly divergent at dorsal end; 1, tightly appressed throughout entirely length, terminate as single tip.
107) Premaxillary dental arcade: 0, teeth closely appressed; 1, teeth less closely appressed (although teeth retain U-shaped cross-section).
108) Maxillary palatal shelves: 0, contact vomer for length one half or less length of tooth row; 1. contact vomer for length greater than three quarters the length of tooth row.
109) Jugal contribution to margin of internal antorbital fenestra: 0, extensive; 1, restricted between maxilla and lacrimal to very small surface.
110) Shape of vomer cranial end: 0, lanceolate (lateral margins parallel sided); 1, diamond.
111) Iliac antitrochanter just dorsal to iliac-ischial articulation: 0, absent; 1, present.

Appendix II: Data Matrix
Character states 0-3 as above.  ? = uncertainty, numbers in paranetheses indicate more than one character state observed in that taxon.
Outgroup	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	0
Aublysodon molnari	??1??	?????	???11	?????	?????	?????	?????	????0	???1?	0????	?????	?????	01???	?????	?????	1100?	?????	?1??0	??0??	?????	??0??	?????	?
Alectrosaurus olseni	1?11?	?????	?1111	???1?	?????	?????	????1	11110	00010	0??0?	?????	00?0?	????0	?????	?0??0	1120?	?????	000?0	??000	?????	?????	???0?	?
Kirtland Shale aublysodontine	?????	1????	???11	?????	?????	????1	???1?	?11??	?????	?????	?????	1??1?	01???	?????	?????	11???	?????	??1??	????0	?????	?????	?????	?
Alioramus remotus	??11?	1111?	?11??	?????	?????	?????	?????	?11??	??010	1???0	000??	00100	12101	01???	?0000	???0?	?????	????1	11?00	0????	???00	?????	?
Gorgosaurus libratus	11111	11111	11111	11111	11111	11111	11111	11111	00011	10100	12200	10000	12000	10100	01001	00110	00101	00000	00110	00000	00000	00000	0
Albertosaurus sarcophagus	11111	11111	?1111	11111	11111	11111	11111	11111	00011	10000	11200	11000	12001	11100	11001	00010	01000	00000	00001	10000	00000	00000	0
Daspletosaurus torosus	11111	11111	11111	11111	11211	11112	11111	11111	10121	11000	11101	10011	12000	10010	01011	00011	10100	00000	00000	01110	00000	0000?	0
Two Medicine tyrannosaurine	1111?	11???	?1111	?????	?????	?????	?????	????1	10111	1??00	11101	20001	????0	?????	?1111	??01?	?????	?0??0	??000	???0?	?????	?0?0?	?
Tyrannosaurus bataar	11111	11111	?0111	11122	11211	11112	11111	11112	11021	11011	00011	21001	23111	11011	11111	00011	10120	10000	00000	00001	11000	0000?	0
Tyrannosaurus rex	11111	11111	11111	11111	11211	11112	11111	11112	11121	12011	00011	21(02)00	23111	11011	(01)1011	00011	11012	10000	00000	00000	?0111	11111	1
Shanshanosaurus houyanshanensis	1????	?????	?1011	?1?11	?????	????1	???11	????0	?0?11	???0?	?????	?????	?????	?????	?0??1	??00?	?01??	?001?	?????	??0??	??0??	?????	?
"Maleevosaurus novojilovi"	1?1??	?????	???11	11???	??211	11112	11111	11110	00021	1???0	0001?	0010?	?????	?????	????1	??010	1??1?	?000?	??000	???0?	?1000	?????	0
"Nanotyrannus lancensis"	11111	1111?	?1111	?????	?????	?????	?????	????0	00020	1?110	00011	00000	13101	?1010	?101?	0010?	?????	????0	??000	0000?	??111	1011?	?
Siamotyrannus isanensis	?????	?????	?????	?????	???11	?1100	10???	?????	?????	?????	?????	?????	?????	?????	?????	?????	?????	?????	?????	?????	?0???	?????	0
Ornithomimosauria	00000	00000	00010	00000	10000	11000	10011	01100	00000	00000	00000	00000	00001	00000	00000	00000	00000	00000	00000	00000	00000	00000	0
Maniraptora	00001	00000	00000	00000	00000	00000	02110	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	00000	01000	0