Results of cladistic analysis of HCF Triceratops . ( A ) Strict consensus tree produced by analysis of HCF specimens using a heuristic search and multistate coding once the most fragmentary specimens were removed (See SI Text and Fig. S5 for additional results). Bootstrap support values below nodes. Bremer support values greater than 1 above nodes. Torosaurus specimens are recovered as basal to a stratigraphic succession of specimens. MOR 3011 does not preserve characters of the parietal-squamosal frill. ( SI Text ). ( B ) Analysis (multistate coding, branch-and-bound search) excluding specimens that could not be coded for at least 10 cranial characters or characters of the frill. ( C ) Analysis (multistate coding, branch-and-bound search) after removal of MOR 2924 ( SI Text ). 

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... retention index (RI) 0.8400] produced a polytomy of all HCF specimens (Fig. S5 A ). The holotype of Eotriceratops [Royal Tyrrell Museum (RTMP) 2002.57.7] was recovered as being basal to the HCF dataset, consistent with the initial hypothesis proposed by Wu et al. (41). The 50% majority tree revealed a succession of specimens that were consistent with stratigraphic position, aside from some specimens that were missing a large portion of codeable characters (e.g., MOR 2552 and MOR 3010). Specimens exhibiting the Torosaurus morphology clustered together as basal to the rest of the HCF dataset as these specimens exhibit several features (including a fenestrated parietal) that are observed in more basal taxa. MOR 3011, which preserves relatively thick sections of parietal-squamosal frill but is too fragmentary to be coded for features of these elements, was not distinguished from the Torosaurus group. Rerunning the analysis using multistate rather than binary characters produced a polytomy in the strict consensus tree (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8469), and the 50% majority-rule tree similarly produced a sequence of specimens consistent with stratigraphic position aside from the most fragmentary specimens (Fig. S5 B ). The analysis was next rerun after removing the most incomplete specimens (individuals that did not exhibit at least seven codeable features). This analysis resulted in a strict consensus (MPT 250,000, 55 steps, CI 0.7091, HI 0.4000, RI 0.8161) in which specimens were largely recovered in stratigraphic succession (except for MOR 3011, which, as noted above, grouped with Torosaurus specimens). MOR 1120 from L3 was found to be the most basal non- Torosaurus HCF specimen, and MOR 2982 from the lower M3 was recovered as the next most basal. Above MOR 2982 is a large polytomy consisting of specimens from the upper half of the formation. The identical topology was recovered when the multistate matrix was analyzed (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8214) (Fig. 3); however, a bremer decay value of 2 was recovered for the upper M3 – U3 polytomy when the binary matrix was used (as opposed to a value of 1 when the multistate matrix was used). The analysis was next run after removing specimens that could not be coded for features of the parietal-squamosal frill. A branch-and-bound search was used with the furthest addition sequence implemented. The strict consensus tree produced using the binary matrix (MPT 218,972, 55 steps, CI 0.7091, HI 0.4000, RI 0.8000) (Fig. S5 C ) recovered a polytomy of Torosaurus specimens as basal to other specimens. MOR 1120 and MOR 2982 from the lower half of the formation were recovered together as basal to a large polytomy of specimens from the upper half of the formation. The multistate analysis (MPT 189,820, 54 steps, CI 0.7222, HI 0.3889, RI 0.8077) (Fig. S5 D ) resulted in greater resolution; MOR 1120 was recovered as basal to the stratigraphically higher MOR 2982. MOR 1122 and MOR 981 clustered together. These specimens both exhibit a nasal boss and do not exhibit an epiossification or crenulation spanning the parietal-squamosal margin whereas the third Torosaurus specimen (MOR 3081) possesses a narrow dorsal surface of the epinasal and a parietal- squamosal crenulation. As these features appear to exhibit a large degree of variation within Triceratops (2), intraspecific variation appears more likely than these differences being taxonomic in nature. We note that, in this analysis, a midline epiparietal (character 32) was coded as absent in MOR 1122 as the element is not present and there does not appear to be a pronounced crenulation on the midline. Scannella and Horner (1) suggested the presence of a midline epiparietal in this specimen based on vascular patterns observed on the parietal. The 50% majority tree for both analyses (Fig. S5 E and F ) found MOR 3045 to be more derived than MOR 3027. UCMP 113697 clusters with MOR 2924 (U3) in the binary analysis, and with MOR 2924 and MOR 2999 in the multistate analysis. These topologies suggest that UCMP 113697 is more derived than other specimens from upper M3; however, we note that this result may be influenced by missing data. MOR 2924 (recovered from the sandstone at the base of U3) preserves a broader posterior surface of the epinasal than other specimens from U3 but does not preserve postorbital horn cores. The anteromedial processes of nasals of MOR 2924 are unobservable due to articulation with the premaxillae. The morphology of the anteromedial processes on the nasals of UCMP 113697 are currently obscured due to the mounting of the disarticulated skull elements for display. When specimens that did not preserve at least 10 codeable features (in the multistate matrix) were removed from the analysis, the strict consensus trees (binary coding: MPT 7036; 54 steps; CI 0.7222; HI 0.3889; RI 0.8000) (Fig. S5 G ) (multistate coding: MPT 7036, 53 steps, CI 0.7358, HI 0.3774, RI 0.8082) (Fig. 3 B ) exhibited an identical topology. Torosaurus specimens were recovered as basal to MOR 1120 and MOR 1982, and specimens from the upper half of the formation were again recovered in a large polytomy. When MOR 2924 was removed from the analysis, both analyses (binary coding: MPT 282; 53 steps; CI 0.7358; HI 0.3774; RI 0.8028) (Fig. S5 H ) (multistate coding: MPT 282; 52 steps; CI 0.7500; HI 0.3654; RI 0.8116) (Fig. 3 C ) recovered MOR 3045 as basal to U3 specimens and as more derived than UCMP 113697 and MOR 3027, which cluster together. Stratocladistic Analysis. Stratocladistics incorporates stratigraphic data into cladistic analyses (see, for example, refs. 43 – 48). A stratocladistic analysis was performed using the program StrataPhy, which produces trees that can indicate possible ancestor- descendant relationships (49). The multistate dataset was used for the analysis, with the specimens MOR 981, MOR 1604, and MOR 2978 removed from the analysis due to ambiguity over their precise stratigraphic position. Rather than coding specimens separately, specimens from the lower M3, upper M3, lower U3, and upper U3 were combined into operational units based on stratigraphic position. MOR 3081 and MOR 3005 were considered separately from other specimens from the same stratigraphic zones due to the distinct ontogenetic [(2) or, alternatively, taxonomic (4 – 6)] morphological differences between these specimens. MOR 3005 is a fragmentary specimen, but preserves thin sections of frill and thus may represent the Torosaurus morphology. A single stratigraphic character was added [stratigraphic position: (position 0) stratigraphically below the HCF; (position 1) lower L3; (position 2) upper L3; (position 3) lower M3; (position 4) upper M3; (position 5) lower U3; (position 6) upper U3]. Arrhinoceratops (ROM 796) was designated the outgroup. MAXTREES was set to 250,000, and all other pa- rameters were StrataPhy ’ s default settings (49). The initial analysis produced 61 trees with nine topologies (total debt = 64) (Fig. S6 A ). Aside from one tree that suggests all operational units arose via cladogenesis, specimens from the upper half of the formation were consistently found to represent an anagenetic succession. The position of operational units from the lower half of the formation varied and were not always consistent with stratigraphic position. This result is likely influenced by the fact that specimens from the lower half of M3 do not preserve features of the parietal-squamosal frill that would allow them to be distinguished from the Torosaurus morphology. MOR 2982 preserves an anterolateral projection of the squamosal, which is consistent with the morphology expressed in several other HCF specimens, including the Torosaurus specimen MOR 3081. Incorporation of Torosaurus specimens into Triceratops operational units (total debt = 67, nine trees, three topologies) (Fig. S6 B ) produced a single tree suggesting that all operational units arose via cladogenesis and two additional topologies that include ancestor-descendant relationships. In four trees, all operational units were recovered within an anagenetic lineage except the lower M3 group. This operational unit was recovered as basal to the upper L3 operational unit, suggesting a cladogenetic event. The remaining four trees exhibited a bifurcation event in L3 giving rise to two lineages. Given the lack of frill characters for the lower M3 operational unit, the influence of Torosaurus specimens on the results was examined by pruning all Torosaurus from the analysis. This pruning resulted in reduced total debt (57) and 12 trees (Fig. S6 C ). Four trees indicate that all HCF operational units represent a single anagenetic lineage with specimens exhibiting the T. horridus morphology evolving into T. prorsus (Fig. 4 A ). Eight trees recovered two lineages suggested to diverge at some point in L3 or before the deposition of the HCF. One lineage gave rise to lower M3 specimens and the other to U3 specimens. This result suggests that two anagenetic lineages, one comprising specimens referable to T. horridus and the other giving rise to T. prorsus , coexisted in the HCF (for at least some time) (Fig. 4 B ). Characters Incorporated in Cladistic Analysis. The first use in a cladistic study is cited. 1 ) Postorbital horn-core length: (code 0) long (postorbital horn-core/basal-skull length ratio: ≥ 0.64); (code 1) short (postorbital horn-core/basal-skull length ratio: < 0.64). [(50) character 58 modified; (12) character 2 modified]. 2 ) Cross-section of postorbital horn core: (code 0) circular to subcircular; (code 1) narrow. The postorbital horn cores of some specimens of Triceratops (e.g., MOR 2702 and MOR 2923) exhibit a markedly narrow morphology that does not appear to be a product of taphonomic distortion. MOR 2923 exhibits no evidence of lateral compression, and yet the postorbital horn cores of this specimen have a pronounced ventral keel. Specimens for which ...

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... in HCF Triceratops initially used the heuristic search strategy of the program PAUP* 4.0b10 (35). Nexus files are available on MorphoBank (36) as project 1099. Analyses used the random addition sequence with tree-bisection-reconnection (TBR) branch swap- ping and 1,000 replicates; all most parsimonious trees were saved. Characters were unordered and unweighted. Maxtrees was set to 250,000. Analyses were initially performed using binary coding for morphological characters (37, 38). Additional analyses were performed using multistate coding that combined binary characters 10 and 11 (development of the epinasal-nasal protuberance), 25 and 26 (development of the anterolateral projection of the squamosal), and 29 and 30 (number of epiparietals). Support for clades was determined using nonparametric bootstrap resampling (39) in PAUP* 4.0b10; 10,000 bootstrap replicates were analyzed, with one tree retained per replicate. Application of bootstrap resampling to data in which multistate characters have been dis- tilled to binary characters is problematic (39) but was performed for comparative purposes. In addition, Bremer support indices were calculated using TreeRot.v3 (40) and PAUP* 4.0b10 (34). This analysis focused on features found to vary within the HCF Triceratops dataset. Eotriceratops was included in the analysis to test the hypothesis that it represents a taxon distinct from Triceratops . As such, characters found to distinguish Eotriceratops by Sampson et al. (24) and characters describing the relative height of the narial process and the morphology of the epijugal (41) were examined. Forster (12) noted five cranial characters that vary within Triceratops . Four of these characters were included in this analysis (Forster ’ s character 4, which describes rostrum shape, was modified in this analysis to reflect the influence of NPP orientation) (5). Forster ’ s character 1 (describing the postorbital, jugal, squamosal suture pattern) was not found to vary in the HCF dataset. Either all coded specimens exhibited the “ primitive ” state of the jugal contributing to the dorsal margin of the lateral temporal fenestra, or sutural relationships of this region were unpreserved or were obscured by fusion. Initially, specimens that were collected or stratigraphically relocated during the Hell Creek Project and that were largely complete or exhibited morphologies not otherwise found within their respective stratigraphic units (e.g., MOR 2552 and UCMP 128561) were included in the cladistic analysis. Only post-juvenile stage specimens were included in the analyses (42). MOR 981 exhibits the Torosaurus morphology and was collected from a mudstone above the basal sand of the formation; however, detailed stratigraphic data are unavailable for this specimen. The initial strict consensus tree produced using binary coding [most parsimonious trees (MPT) 250,000, 55 steps, consistency index (CI) 0.7091, homoplasy index (HI) 0.4000, retention index (RI) 0.8400] produced a polytomy of all HCF specimens (Fig. S5 A ). The holotype of Eotriceratops [Royal Tyrrell Museum (RTMP) 2002.57.7] was recovered as being basal to the HCF dataset, consistent with the initial hypothesis proposed by Wu et al. (41). The 50% majority tree revealed a succession of specimens that were consistent with stratigraphic position, aside from some specimens that were missing a large portion of codeable characters (e.g., MOR 2552 and MOR 3010). Specimens exhibiting the Torosaurus morphology clustered together as basal to the rest of the HCF dataset as these specimens exhibit several features (including a fenestrated parietal) that are observed in more basal taxa. MOR 3011, which preserves relatively thick sections of parietal-squamosal frill but is too fragmentary to be coded for features of these elements, was not distinguished from the Torosaurus group. Rerunning the analysis using multistate rather than binary characters produced a polytomy in the strict consensus tree (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8469), and the 50% majority-rule tree similarly produced a sequence of specimens consistent with stratigraphic position aside from the most fragmentary specimens (Fig. S5 B ). The analysis was next rerun after removing the most incomplete specimens (individuals that did not exhibit at least seven codeable features). This analysis resulted in a strict consensus (MPT 250,000, 55 steps, CI 0.7091, HI 0.4000, RI 0.8161) in which specimens were largely recovered in stratigraphic succession (except for MOR 3011, which, as noted above, grouped with Torosaurus specimens). MOR 1120 from L3 was found to be the most basal non- Torosaurus HCF specimen, and MOR 2982 from the lower M3 was recovered as the next most basal. Above MOR 2982 is a large polytomy consisting of specimens from the upper half of the formation. The identical topology was recovered when the multistate matrix was analyzed (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8214) (Fig. 3); however, a bremer decay value of 2 was recovered for the upper M3 – U3 polytomy when the binary matrix was used (as opposed to a value of 1 when the multistate matrix was used). The analysis was next run after removing specimens that could not be coded for features of the parietal-squamosal frill. A branch-and-bound search was used with the furthest addition sequence implemented. The strict consensus tree produced using the binary matrix (MPT 218,972, 55 steps, CI 0.7091, HI 0.4000, RI 0.8000) (Fig. S5 C ) recovered a polytomy of Torosaurus specimens as basal to other specimens. MOR 1120 and MOR 2982 from the lower half of the formation were recovered together as basal to a large polytomy of specimens from the upper half of the formation. The multistate analysis (MPT 189,820, 54 steps, CI 0.7222, HI 0.3889, RI 0.8077) (Fig. S5 D ) resulted in greater resolution; MOR 1120 was recovered as basal to the stratigraphically higher MOR 2982. MOR 1122 and MOR 981 clustered together. These specimens both exhibit a nasal boss and do not exhibit an epiossification or crenulation spanning the parietal-squamosal margin whereas the third Torosaurus specimen (MOR 3081) possesses a narrow dorsal surface of the epinasal and a parietal- squamosal crenulation. As these features appear to exhibit a large degree of variation within Triceratops (2), intraspecific variation appears more likely than these differences being taxonomic in nature. We note that, in this analysis, a midline epiparietal (character 32) was coded as absent in MOR 1122 as the element is not present and there does not appear to be a pronounced crenulation on the midline. Scannella and Horner (1) suggested the presence of a midline epiparietal in this specimen based on vascular patterns observed on the parietal. The 50% majority tree for both analyses (Fig. S5 E and F ) found MOR 3045 to be more derived than MOR 3027. UCMP 113697 clusters with MOR 2924 (U3) in the binary analysis, and with MOR 2924 and MOR 2999 in the multistate analysis. These topologies suggest that UCMP 113697 is more derived than other specimens from upper M3; however, we note that this result may be influenced by missing data. MOR 2924 (recovered from the sandstone at the base of U3) preserves a broader posterior surface of the epinasal than other specimens from U3 but does not preserve postorbital horn cores. The anteromedial processes of nasals of MOR 2924 are unobservable due to articulation with the premaxillae. The morphology of the anteromedial processes on the nasals of UCMP 113697 are currently obscured due to the mounting of the disarticulated skull elements for display. When specimens that did not preserve at least 10 codeable features (in the multistate matrix) were removed from the analysis, the strict consensus trees (binary coding: MPT 7036; 54 steps; CI 0.7222; HI 0.3889; RI 0.8000) (Fig. S5 G ) (multistate coding: MPT 7036, 53 steps, CI 0.7358, HI 0.3774, RI 0.8082) (Fig. 3 B ) exhibited an identical topology. Torosaurus specimens were recovered as basal to MOR 1120 and MOR 1982, and specimens from the upper half of the formation were again recovered in a large polytomy. When MOR 2924 was removed from the analysis, both analyses (binary coding: MPT 282; 53 steps; CI 0.7358; HI 0.3774; RI 0.8028) (Fig. S5 H ) (multistate coding: MPT 282; 52 steps; CI 0.7500; HI 0.3654; RI 0.8116) (Fig. 3 C ) recovered MOR 3045 as basal to U3 specimens and as more derived than UCMP 113697 and MOR 3027, which cluster together. Stratocladistic Analysis. Stratocladistics incorporates stratigraphic data into cladistic analyses (see, for example, refs. 43 – 48). A stratocladistic analysis was performed using the program StrataPhy, which produces trees that can indicate possible ancestor- descendant relationships (49). The multistate dataset was used for the analysis, with the specimens MOR 981, MOR 1604, and MOR 2978 removed from the analysis due to ambiguity over their precise stratigraphic position. Rather than coding specimens separately, specimens from the lower M3, upper M3, lower U3, and upper U3 were combined into operational units based on stratigraphic position. MOR 3081 and MOR 3005 were considered separately from other specimens from the same stratigraphic zones due to the distinct ontogenetic [(2) or, alternatively, taxonomic (4 – 6)] morphological differences between these specimens. MOR 3005 is a fragmentary specimen, but preserves thin sections of frill and thus may represent the Torosaurus morphology. A single stratigraphic character was added [stratigraphic position: (position 0) stratigraphically below the HCF; (position 1) lower L3; (position 2) upper L3; (position 3) lower M3; (position 4) upper M3; (position 5) lower U3; (position 6) upper U3]. Arrhinoceratops (ROM 796) was designated the outgroup. MAXTREES was set to 250,000, and all other pa- rameters were StrataPhy ’ s default settings (49). The initial analysis produced 61 trees with nine topologies (total ...

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... a large portion of codeable characters (e.g., MOR 2552 and MOR 3010). Specimens exhibiting the Torosaurus morphology clustered together as basal to the rest of the HCF dataset as these specimens exhibit several features (including a fenestrated parietal) that are observed in more basal taxa. MOR 3011, which preserves relatively thick sections of parietal-squamosal frill but is too fragmentary to be coded for features of these elements, was not distinguished from the Torosaurus group. Rerunning the analysis using multistate rather than binary characters produced a polytomy in the strict consensus tree (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8469), and the 50% majority-rule tree similarly produced a sequence of specimens consistent with stratigraphic position aside from the most fragmentary specimens (Fig. S5 B ). The analysis was next rerun after removing the most incomplete specimens (individuals that did not exhibit at least seven codeable features). This analysis resulted in a strict consensus (MPT 250,000, 55 steps, CI 0.7091, HI 0.4000, RI 0.8161) in which specimens were largely recovered in stratigraphic succession (except for MOR 3011, which, as noted above, grouped with Torosaurus specimens). MOR 1120 from L3 was found to be the most basal non- Torosaurus HCF specimen, and MOR 2982 from the lower M3 was recovered as the next most basal. Above MOR 2982 is a large polytomy consisting of specimens from the upper half of the formation. The identical topology was recovered when the multistate matrix was analyzed (MPT 250,000, 54 steps, CI 0.7222, HI 0.3889, RI 0.8214) (Fig. 3); however, a bremer decay value of 2 was recovered for the upper M3 – U3 polytomy when the binary matrix was used (as opposed to a value of 1 when the multistate matrix was used). The analysis was next run after removing specimens that could not be coded for features of the parietal-squamosal frill. A branch-and-bound search was used with the furthest addition sequence implemented. The strict consensus tree produced using the binary matrix (MPT 218,972, 55 steps, CI 0.7091, HI 0.4000, RI 0.8000) (Fig. S5 C ) recovered a polytomy of Torosaurus specimens as basal to other specimens. MOR 1120 and MOR 2982 from the lower half of the formation were recovered together as basal to a large polytomy of specimens from the upper half of the formation. The multistate analysis (MPT 189,820, 54 steps, CI 0.7222, HI 0.3889, RI 0.8077) (Fig. S5 D ) resulted in greater resolution; MOR 1120 was recovered as basal to the stratigraphically higher MOR 2982. MOR 1122 and MOR 981 clustered together. These specimens both exhibit a nasal boss and do not exhibit an epiossification or crenulation spanning the parietal-squamosal margin whereas the third Torosaurus specimen (MOR 3081) possesses a narrow dorsal surface of the epinasal and a parietal- squamosal crenulation. As these features appear to exhibit a large degree of variation within Triceratops (2), intraspecific variation appears more likely than these differences being taxonomic in nature. We note that, in this analysis, a midline epiparietal (character 32) was coded as absent in MOR 1122 as the element is not present and there does not appear to be a pronounced crenulation on the midline. Scannella and Horner (1) suggested the presence of a midline epiparietal in this specimen based on vascular patterns observed on the parietal. The 50% majority tree for both analyses (Fig. S5 E and F ) found MOR 3045 to be more derived than MOR 3027. UCMP 113697 clusters with MOR 2924 (U3) in the binary analysis, and with MOR 2924 and MOR 2999 in the multistate analysis. These topologies suggest that UCMP 113697 is more derived than other specimens from upper M3; however, we note that this result may be influenced by missing data. MOR 2924 (recovered from the sandstone at the base of U3) preserves a broader posterior surface of the epinasal than other specimens from U3 but does not preserve postorbital horn cores. The anteromedial processes of nasals of MOR 2924 are unobservable due to articulation with the premaxillae. The morphology of the anteromedial processes on the nasals of UCMP 113697 are currently obscured due to the mounting of the disarticulated skull elements for display. When specimens that did not preserve at least 10 codeable features (in the multistate matrix) were removed from the analysis, the strict consensus trees (binary coding: MPT 7036; 54 steps; CI 0.7222; HI 0.3889; RI 0.8000) (Fig. S5 G ) (multistate coding: MPT 7036, 53 steps, CI 0.7358, HI 0.3774, RI 0.8082) (Fig. 3 B ) exhibited an identical topology. Torosaurus specimens were recovered as basal to MOR 1120 and MOR 1982, and specimens from the upper half of the formation were again recovered in a large polytomy. When MOR 2924 was removed from the analysis, both analyses (binary coding: MPT 282; 53 steps; CI 0.7358; HI 0.3774; RI 0.8028) (Fig. S5 H ) (multistate coding: MPT 282; 52 steps; CI 0.7500; HI 0.3654; RI 0.8116) (Fig. 3 C ) recovered MOR 3045 as basal to U3 specimens and as more derived than UCMP 113697 and MOR 3027, which cluster together. Stratocladistic Analysis. Stratocladistics incorporates stratigraphic data into cladistic analyses (see, for example, refs. 43 – 48). A stratocladistic analysis was performed using the program StrataPhy, which produces trees that can indicate possible ancestor- descendant relationships (49). The multistate dataset was used for the analysis, with the specimens MOR 981, MOR 1604, and MOR 2978 removed from the analysis due to ambiguity over their precise stratigraphic position. Rather than coding specimens separately, specimens from the lower M3, upper M3, lower U3, and upper U3 were combined into operational units based on stratigraphic position. MOR 3081 and MOR 3005 were considered separately from other specimens from the same stratigraphic zones due to the distinct ontogenetic [(2) or, alternatively, taxonomic (4 – 6)] morphological differences between these specimens. MOR 3005 is a fragmentary specimen, but preserves thin sections of frill and thus may represent the Torosaurus morphology. A single stratigraphic character was added [stratigraphic position: (position 0) stratigraphically below the HCF; (position 1) lower L3; (position 2) upper L3; (position 3) lower M3; (position 4) upper M3; (position 5) lower U3; (position 6) upper U3]. Arrhinoceratops (ROM 796) was designated the outgroup. MAXTREES was set to 250,000, and all other pa- rameters were StrataPhy ’ s default settings (49). The initial analysis produced 61 trees with nine topologies (total debt = 64) (Fig. S6 A ). Aside from one tree that suggests all operational units arose via cladogenesis, specimens from the upper half of the formation were consistently found to represent an anagenetic succession. The position of operational units from the lower half of the formation varied and were not always consistent with stratigraphic position. This result is likely influenced by the fact that specimens from the lower half of M3 do not preserve features of the parietal-squamosal frill that would allow them to be distinguished from the Torosaurus morphology. MOR 2982 preserves an anterolateral projection of the squamosal, which is consistent with the morphology expressed in several other HCF specimens, including the Torosaurus specimen MOR 3081. Incorporation of Torosaurus specimens into Triceratops operational units (total debt = 67, nine trees, three topologies) (Fig. S6 B ) produced a single tree suggesting that all operational units arose via cladogenesis and two additional topologies that include ancestor-descendant relationships. In four trees, all operational units were recovered within an anagenetic lineage except the lower M3 group. This operational unit was recovered as basal to the upper L3 operational unit, suggesting a cladogenetic event. The remaining four trees exhibited a bifurcation event in L3 giving rise to two lineages. Given the lack of frill characters for the lower M3 operational unit, the influence of Torosaurus specimens on the results was examined by pruning all Torosaurus from the analysis. This pruning resulted in reduced total debt (57) and 12 trees (Fig. S6 C ). Four trees indicate that all HCF operational units represent a single anagenetic lineage with specimens exhibiting the T. horridus morphology evolving into T. prorsus (Fig. 4 A ). Eight trees recovered two lineages suggested to diverge at some point in L3 or before the deposition of the HCF. One lineage gave rise to lower M3 specimens and the other to U3 specimens. This result suggests that two anagenetic lineages, one comprising specimens referable to T. horridus and the other giving rise to T. prorsus , coexisted in the HCF (for at least some time) (Fig. 4 B ). Characters Incorporated in Cladistic Analysis. The first use in a cladistic study is cited. 1 ) Postorbital horn-core length: (code 0) long (postorbital horn-core/basal-skull length ratio: ≥ 0.64); (code 1) short (postorbital horn-core/basal-skull length ratio: < 0.64). [(50) character 58 modified; (12) character 2 modified]. 2 ) Cross-section of postorbital horn core: (code 0) circular to subcircular; (code 1) narrow. The postorbital horn cores of some specimens of Triceratops (e.g., MOR 2702 and MOR 2923) exhibit a markedly narrow morphology that does not appear to be a product of taphonomic distortion. MOR 2923 exhibits no evidence of lateral compression, and yet the postorbital horn cores of this specimen have a pronounced ventral keel. Specimens for which apparently laterally compressed postorbital horn cores are likely a result of taphonomic processes (e.g., MOR 2982 and MOR 3027) have been coded as “ ? ” . 3 ) Rostrum shape: (code 0) primary axis of nasal process of premaxilla (NPP) is strongly posteriorly inclined; (code 1) NPP vertical or nearly vertical [(12, 50) character 4 modified; (5) Fig. S2]. 4 ) Frontoparietal fontanelle: (code 0) open fontanelle; (code 1) ...

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... from upper M3, producing a more convex rostrum morphology, which was previously found to characterize T. prorsus (12, 23). The frontoparietal fontanelle is open in late-stage subadults/young adults (UCMP 113697). U3 Triceratops. Specimens from U3 exhibit the features Forster (12) found to characterize T. prorsus . U3 Triceratops possess an elongate, relatively narrow nasal horn (average length/width > 2) (Fig. 2 A and Dataset S1). The NPP is more vertically inclined, producing a convex rostrum lacking the low, elongate profile noted in T. horridus [although the largest, and presumably oldest, known specimens (e.g., MOR 004 and MOR 1625) exhibit pro- portionally longer rostra] (Fig. 2 E and Dataset S1). The NPP is anteroposteriorly expanded, and the anteromedial process of the nasal is greatly reduced (Fig. S3) (27). The frontoparietal fontanelle becomes constricted and eventually closed in late-stage subadults/young adults (e.g., MOR 2923 and MOR 2979), ontogenetically earlier than in L3 and M3. The postorbital horn cores are short ( < 0.64 basal-skull length) (Fig. 2 D ). Further, U3 Triceratops seem to exhibit nasals that are more elongate than Triceratops from the lower half of the HCF (Fig. 2 F and Dataset S1). Shifts in Morphology over Time. Epinasals exhibit a directional morphologic trend; average length increases throughout the formation (Fig. 2 A and Dataset S1) (Spearman ’ s rank coefficient = 0.824, P = 4.15E − 07). A protuberance just posterior to the epinasal, observed in specimens from L3 and M3 (Fig. 1), is partic- ularly pronounced in UCMP 113697 from the uppermost M3 (Fig. 1 E ). U3 Triceratops either do not exhibit this feature or express only a subtle ridge in the homologous location. Concurrent with elongation of the epinasal was an expansion of the NPP (Fig. 2 B ) (Spearman ’ s rank coefficient = − 0.969, P = 3.74E − 06) and an increase in the angle between the NPP and the narial strut of the premaxilla (Fig. 2 C and Dataset S1) (Spearman ’ s rank coefficient = 0.802, P = .000186). Nasals also become more elongate relative to basal skull length (although only three specimens with complete nasals have thus far been recorded from the lower half of the formation) (Fig. 2 F and Dataset S1) (Spearman ’ s rank coefficient = 0.804, P = 0.00894). Postorbital horn-core length appears to be variable throughout L3 and M3 and is consistently short in U3 Triceratops (Fig. 2 D and Dataset S1) [Spearman ’ s rank coefficient is negative ( − 0.197) and not statistically significant ( P = 0.392)]. Large juvenile U3 Triceratops (e.g., MOR 1110) can possess more elongate postorbital horn cores (0.64 basal-skull length). Whereas U3 postorbital horn core length falls within the range of variation observed lower in the formation (Fig. 2 D ), elongate postorbital horn cores have thus far not been found in post-juvenile stage Triceratops from U3. Many large Triceratops (e.g., MOR 1122 and MOR 3000) (3) exhibit evidence of postorbital horn-core resorption, suggesting that maximum length is reached earlier in ontogeny. Maximum postorbital horn-core length may have been expressed later in development (or for a longer duration) in Triceratops from lower in the formation. Triceratops from the upper half of the HCF exhibit a more vertically inclined NPP (Fig. 2 C ), which contributes to a rostrum that appears shorter and more convex in lateral profile (a feature Forster noted in T. prorsus ) (12). However, we note that a Spearman ’ s rank correlation test found apparent reduction in rostrum length to be statistically insignificant (Spearman ’ s rank coefficient 0.018, P = 0.966). Large specimens from U3 (e.g., MOR 004) possess a more elongate rostrum relative to basal- skull length (Fig. 2 E and Dataset S1); however, the shape of U3 rostra appears to be consistently convex. Eotriceratops xerinsularis , found in the stratigraphically older uppermost Horseshoe Canyon Formation ( ∼ 68 Ma) (28), expresses morphologies (elongate postorbital horn cores, small nasal horn) consistent with its stratigraphic position relative to Triceratops . Cladistic and Stratocladistic Analyses. Initial cladistic analyses recovered a polytomy of all HCF specimens, with the 50% majority tree producing a succession of Triceratops that largely correlates with stratigraphic placement (Fig. S5 and SI Text ). Removal of the more fragmentary material recovered Torosaurus specimens as basal to a stratigraphic succession of Triceratops , including a polytomy of specimens from the upper half of the formation (Fig. 3 A ). A similar topology was recovered when specimens not exhibiting codeable features of the parietal squamosal frill were removed from the analysis (Fig. 3 B ). Removal of MOR 2924, a specimen from the base of U3 that does not preserve postorbital horn cores ( SI Text ), recovers specimens from the upper part of M3 as basal to U3 Triceratops . In the analysis of the most reduced dataset, UCMP 113697 and MOR 3027 cluster together (Fig. 3 C ). These specimens exhibit a combination of characters found in Triceratops from L3 and M3. The epinasal of UCMP 113697 is morphologically in- termediate between L3 and U3 Triceratops (the epinasal of MOR 3027 is incomplete). These specimens each exhibit large postorbital horn cores (a feature expressed in some L3 Triceratops ) and a more vertically inclined NPP (found in U3 Triceratops ). MOR 3045 is recovered as being more derived than UCMP 113697 and MOR 3027 (Fig. 3) based on its possession of relatively short postorbital horn cores, a more expanded NPP, and a pronounced step bordering the “ incipient fenestrae ” (sensu ref. 3) ( SI Text ). This specimen exhibits the basal condition of the anteromedial nasal process and expresses a pronounced upturn of the posterior surface of the epinasal, suggesting the presence of a protuberance in life. MOR 3045 exhibits a fairly elongate epinasal (estimated length/width, ∼ 1.88), with a posterior surface that is broader than is seen in most U3 specimens and, like UCMP 113697, MOR 3027, and U3 Triceratops , exhibits a more vertically inclined NPP. Stratocladistic analyses, in which specimens were grouped into operational units based on stratigraphic position, were performed in the program StrataPhy (29). Torosaurus specimens were initially considered separately from other specimens ( SI Text ). Initial results suggested that specimens from the upper half of the HCF represented a sequence of ancestors and descendants but differed on the position of operational units from the lower half of the formation (Fig. S6 A ). This result was likely influenced by missing data for specimens from the lower half of the formation; no specimens from lower M3 preserve frill characters that can distinguish them from the Torosaurus morphology. When Torosaurus specimens were incorporated into Triceratops operational units, three topologies were produced: a strictly cladogenetic result, a topology in which all operational units except lower M3 were recovered in a transformational sequence, and a topology in which the HCF operational units were recovered in two lineages (an upper L3/lower M3 lineage and an upper M3/U3 lineage) that had diverged at some point in the deposition of L3 (Fig. S6 B ). Pruning of Torosaurus specimens from the dataset produced two topologies that incorporated morphological transformation: one topology in which all HCF operational units fell into a single lineage and another topology presenting two HCF lineages that diverged either in L3 or before deposition of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved elsewhere and migrated into the HCF, eventually replacing the incumbent HCF Triceratops population by the beginning of the deposition of U3. Upper M3 specimens represent early members (or close relatives of) this group that would come to dominate the ecosystem. ii ) Variation between MOR 3045, MOR 3027, and UCMP 113697 represents intraspecific (or intrapopulation) variation. As the HCF Triceratops lineage evolved, some individuals expressed ...

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... producing a convex rostrum lacking the low, elongate profile noted in T. horridus [although the largest, and presumably oldest, known specimens (e.g., MOR 004 and MOR 1625) exhibit pro- portionally longer rostra] (Fig. 2 E and Dataset S1). The NPP is anteroposteriorly expanded, and the anteromedial process of the nasal is greatly reduced (Fig. S3) (27). The frontoparietal fontanelle becomes constricted and eventually closed in late-stage subadults/young adults (e.g., MOR 2923 and MOR 2979), ontogenetically earlier than in L3 and M3. The postorbital horn cores are short ( < 0.64 basal-skull length) (Fig. 2 D ). Further, U3 Triceratops seem to exhibit nasals that are more elongate than Triceratops from the lower half of the HCF (Fig. 2 F and Dataset S1). Shifts in Morphology over Time. Epinasals exhibit a directional morphologic trend; average length increases throughout the formation (Fig. 2 A and Dataset S1) (Spearman ’ s rank coefficient = 0.824, P = 4.15E − 07). A protuberance just posterior to the epinasal, observed in specimens from L3 and M3 (Fig. 1), is partic- ularly pronounced in UCMP 113697 from the uppermost M3 (Fig. 1 E ). U3 Triceratops either do not exhibit this feature or express only a subtle ridge in the homologous location. Concurrent with elongation of the epinasal was an expansion of the NPP (Fig. 2 B ) (Spearman ’ s rank coefficient = − 0.969, P = 3.74E − 06) and an increase in the angle between the NPP and the narial strut of the premaxilla (Fig. 2 C and Dataset S1) (Spearman ’ s rank coefficient = 0.802, P = .000186). Nasals also become more elongate relative to basal skull length (although only three specimens with complete nasals have thus far been recorded from the lower half of the formation) (Fig. 2 F and Dataset S1) (Spearman ’ s rank coefficient = 0.804, P = 0.00894). Postorbital horn-core length appears to be variable throughout L3 and M3 and is consistently short in U3 Triceratops (Fig. 2 D and Dataset S1) [Spearman ’ s rank coefficient is negative ( − 0.197) and not statistically significant ( P = 0.392)]. Large juvenile U3 Triceratops (e.g., MOR 1110) can possess more elongate postorbital horn cores (0.64 basal-skull length). Whereas U3 postorbital horn core length falls within the range of variation observed lower in the formation (Fig. 2 D ), elongate postorbital horn cores have thus far not been found in post-juvenile stage Triceratops from U3. Many large Triceratops (e.g., MOR 1122 and MOR 3000) (3) exhibit evidence of postorbital horn-core resorption, suggesting that maximum length is reached earlier in ontogeny. Maximum postorbital horn-core length may have been expressed later in development (or for a longer duration) in Triceratops from lower in the formation. Triceratops from the upper half of the HCF exhibit a more vertically inclined NPP (Fig. 2 C ), which contributes to a rostrum that appears shorter and more convex in lateral profile (a feature Forster noted in T. prorsus ) (12). However, we note that a Spearman ’ s rank correlation test found apparent reduction in rostrum length to be statistically insignificant (Spearman ’ s rank coefficient 0.018, P = 0.966). Large specimens from U3 (e.g., MOR 004) possess a more elongate rostrum relative to basal- skull length (Fig. 2 E and Dataset S1); however, the shape of U3 rostra appears to be consistently convex. Eotriceratops xerinsularis , found in the stratigraphically older uppermost Horseshoe Canyon Formation ( ∼ 68 Ma) (28), expresses morphologies (elongate postorbital horn cores, small nasal horn) consistent with its stratigraphic position relative to Triceratops . Cladistic and Stratocladistic Analyses. Initial cladistic analyses recovered a polytomy of all HCF specimens, with the 50% majority tree producing a succession of Triceratops that largely correlates with stratigraphic placement (Fig. S5 and SI Text ). Removal of the more fragmentary material recovered Torosaurus specimens as basal to a stratigraphic succession of Triceratops , including a polytomy of specimens from the upper half of the formation (Fig. 3 A ). A similar topology was recovered when specimens not exhibiting codeable features of the parietal squamosal frill were removed from the analysis (Fig. 3 B ). Removal of MOR 2924, a specimen from the base of U3 that does not preserve postorbital horn cores ( SI Text ), recovers specimens from the upper part of M3 as basal to U3 Triceratops . In the analysis of the most reduced dataset, UCMP 113697 and MOR 3027 cluster together (Fig. 3 C ). These specimens exhibit a combination of characters found in Triceratops from L3 and M3. The epinasal of UCMP 113697 is morphologically in- termediate between L3 and U3 Triceratops (the epinasal of MOR 3027 is incomplete). These specimens each exhibit large postorbital horn cores (a feature expressed in some L3 Triceratops ) and a more vertically inclined NPP (found in U3 Triceratops ). MOR 3045 is recovered as being more derived than UCMP 113697 and MOR 3027 (Fig. 3) based on its possession of relatively short postorbital horn cores, a more expanded NPP, and a pronounced step bordering the “ incipient fenestrae ” (sensu ref. 3) ( SI Text ). This specimen exhibits the basal condition of the anteromedial nasal process and expresses a pronounced upturn of the posterior surface of the epinasal, suggesting the presence of a protuberance in life. MOR 3045 exhibits a fairly elongate epinasal (estimated length/width, ∼ 1.88), with a posterior surface that is broader than is seen in most U3 specimens and, like UCMP 113697, MOR 3027, and U3 Triceratops , exhibits a more vertically inclined NPP. Stratocladistic analyses, in which specimens were grouped into operational units based on stratigraphic position, were performed in the program StrataPhy (29). Torosaurus specimens were initially considered separately from other specimens ( SI Text ). Initial results suggested that specimens from the upper half of the HCF represented a sequence of ancestors and descendants but differed on the position of operational units from the lower half of the formation (Fig. S6 A ). This result was likely influenced by missing data for specimens from the lower half of the formation; no specimens from lower M3 preserve frill characters that can distinguish them from the Torosaurus morphology. When Torosaurus specimens were incorporated into Triceratops operational units, three topologies were produced: a strictly cladogenetic result, a topology in which all operational units except lower M3 were recovered in a transformational sequence, and a topology in which the HCF operational units were recovered in two lineages (an upper L3/lower M3 lineage and an upper M3/U3 lineage) that had diverged at some point in the deposition of L3 (Fig. S6 B ). Pruning of Torosaurus specimens from the dataset produced two topologies that incorporated morphological transformation: one topology in which all HCF operational units fell into a single lineage and another topology presenting two HCF lineages that diverged either in L3 or before deposition of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved elsewhere and migrated into the HCF, eventually replacing the incumbent HCF Triceratops population by the beginning of the deposition of U3. Upper M3 specimens represent early members (or close relatives of) this group that would come to dominate the ecosystem. ii ) Variation between MOR 3045, MOR 3027, and UCMP 113697 represents intraspecific (or intrapopulation) variation. As the HCF Triceratops lineage evolved, some individuals expressed more of the features that would eventually dominate the population. Over time, these traits were se- lected for and characterized U3 Triceratops. This is a purely anagenetic scenario. iii ) A bifurcation event is recorded in the HCF and occurred at some point before the deposition of U3, resulting in two lineages that differ primarily in the morphology of the epinasal and rostrum (consistent with Forster ’ s diagnoses for T. horridus and T. prorsus ). MOR 3045 represents an ...

Context 6

... Torosaurus specimens as basal to a stratigraphic succession of Triceratops , including a polytomy of specimens from the upper half of the formation (Fig. 3 A ). A similar topology was recovered when specimens not exhibiting codeable features of the parietal squamosal frill were removed from the analysis (Fig. 3 B ). Removal of MOR 2924, a specimen from the base of U3 that does not preserve postorbital horn cores ( SI Text ), recovers specimens from the upper part of M3 as basal to U3 Triceratops . In the analysis of the most reduced dataset, UCMP 113697 and MOR 3027 cluster together (Fig. 3 C ). These specimens exhibit a combination of characters found in Triceratops from L3 and M3. The epinasal of UCMP 113697 is morphologically in- termediate between L3 and U3 Triceratops (the epinasal of MOR 3027 is incomplete). These specimens each exhibit large postorbital horn cores (a feature expressed in some L3 Triceratops ) and a more vertically inclined NPP (found in U3 Triceratops ). MOR 3045 is recovered as being more derived than UCMP 113697 and MOR 3027 (Fig. 3) based on its possession of relatively short postorbital horn cores, a more expanded NPP, and a pronounced step bordering the “ incipient fenestrae ” (sensu ref. 3) ( SI Text ). This specimen exhibits the basal condition of the anteromedial nasal process and expresses a pronounced upturn of the posterior surface of the epinasal, suggesting the presence of a protuberance in life. MOR 3045 exhibits a fairly elongate epinasal (estimated length/width, ∼ 1.88), with a posterior surface that is broader than is seen in most U3 specimens and, like UCMP 113697, MOR 3027, and U3 Triceratops , exhibits a more vertically inclined NPP. Stratocladistic analyses, in which specimens were grouped into operational units based on stratigraphic position, were performed in the program StrataPhy (29). Torosaurus specimens were initially considered separately from other specimens ( SI Text ). Initial results suggested that specimens from the upper half of the HCF represented a sequence of ancestors and descendants but differed on the position of operational units from the lower half of the formation (Fig. S6 A ). This result was likely influenced by missing data for specimens from the lower half of the formation; no specimens from lower M3 preserve frill characters that can distinguish them from the Torosaurus morphology. When Torosaurus specimens were incorporated into Triceratops operational units, three topologies were produced: a strictly cladogenetic result, a topology in which all operational units except lower M3 were recovered in a transformational sequence, and a topology in which the HCF operational units were recovered in two lineages (an upper L3/lower M3 lineage and an upper M3/U3 lineage) that had diverged at some point in the deposition of L3 (Fig. S6 B ). Pruning of Torosaurus specimens from the dataset produced two topologies that incorporated morphological transformation: one topology in which all HCF operational units fell into a single lineage and another topology presenting two HCF lineages that diverged either in L3 or before deposition of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved elsewhere and migrated into the HCF, eventually replacing the incumbent HCF Triceratops population by the beginning of the deposition of U3. Upper M3 specimens represent early members (or close relatives of) this group that would come to dominate the ecosystem. ii ) Variation between MOR 3045, MOR 3027, and UCMP 113697 represents intraspecific (or intrapopulation) variation. As the HCF Triceratops lineage evolved, some individuals expressed more of the features that would eventually dominate the population. Over time, these traits were se- lected for and characterized U3 Triceratops. This is a purely anagenetic scenario. iii ) A bifurcation event is recorded in the HCF and occurred at some point before the deposition of U3, resulting in two lineages that differ primarily in the morphology of the epinasal and rostrum (consistent with Forster ’ s diagnoses for T. horridus and T. prorsus ). MOR 3045 represents an early member of a lineage that evolved into U3 Triceratops. This scenario incorporates anagenesis (38) and is presented in some trees produced by the stratocladistic analysis (Fig. S6). iv ) The evolution of Triceratops was characterized by a series of cladogenetic events that produced at least five taxa over the course of the deposition of the HCF (the L3 clade, the lower M3 clade, the MOR 3027 clade, the MOR 3045 clade, and the U3 clade). This strictly cladogenetic scenario suggests that no Triceratops found lower in the HCF underwent evolutionary transformation into forms found higher in the formation. A Biogeographic Signal? The Hell Creek Project ’ s stratigraphic record of Triceratops is primarily restricted to northeastern Montana. It has been hypothesized that T. horridus and T. prorsus were largely biogeographically separated, with T. prorsus generally restricted to the Hell Creek and Frenchman Formations and T. horridus commonly found in the more southern Lance, Laramie, and Denver Formations (15, 17). However, this suggested biogeographic segregation may represent an artifact of the stratigraphic record. Specimens that have thus far been described from neighboring coeval formations exhibit morphologies consistent with their stratigraphic position relative to the HCF (39, 40) ( SI Text ). Anagenesis and Cladogenesis. If the morphological trends noted in Triceratops were purely the result of cladogenetic branching (consistent with punctuated equilibrium) (32) (Fig. 4 C and D ), we would expect to find the full U3 morphology coexisting with Triceratops found lower in the formation, or alternatively, specimens exhibiting the L3 morphology in U3. Such specimens have yet to be discovered ( SI Text ). Specimens from the upper part of M3 exhibit transitional features relative to L3 and U3 Triceratops , a pattern consistent with anagenesis. Some cladistic analyses distinguish MOR 3045 from other upper M3 Triceratops based on variation in the length of the postorbital horn cores, width of the NPP, and the thickened regions of the parietal (Fig. 3, Fig. S5, and SI Text ). Triceratops collected from a multiindividual bonebed in U3 (MOR locality no. HC-430) (44) show variable morphology of the premaxillae and parietal between individuals (Fig. S2) (41). This finding suggests that the variation between upper M3 specimens may represent intrapopulational, not taxonomic, variation (10). Indi- viduals exhibiting more pronounced U3 character states may have become increasingly abundant in the HCF Triceratops population over time until, by the end of the Cretaceous, all Triceratops exhibited these character states (Fig. 4 A ). Alternatively, MOR 3045 may represent an early member of a U3 ( T. prorsus ) lineage, with MOR 3027 representing a separate lineage. Stratocladistic analyses suggest the possibility of two lineages in the HCF (Fig. 4 B and Fig. S6); however, this scenario would require the independent evolution of an enlarged epinasal-nasal protuberance. A purely cladogenetic interpretation of the HCF Triceratops dataset suggests the presence of at least five stratigraphically overlapping taxa in the formation (Fig. 4 C and D ). This scenario is possible, but we would argue that interpretations that incorporate populational transformation (anagenesis) are more conservative. Specimens from upper M3 exhibit a combination of primitive and derived characters, as well as more developed states of characters expressed in L3 Triceratops . Forster (12) noted that, whereas T. prorsus exhibited derived characters, no autapomor- phic characters were recognized in T. horridus . This finding is consistent with the hypothesis that the evolution of Triceratops incorporated anagenesis and illustrates the potential difficulties with defining species in evolving populations (6, 35). The HCF dataset underscores the importance of considering morphologies in a populational, rather ...

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... to be formed by the combination of a posterior projection on the epinasal (Fig. S4) and the anteriormost nasal. A homologous morphology is observed in specimens from L3 and the lower half of M3 (MOR 1120, MOR 2982, and MOR 3010). UCMP 128561, from the upper half of M3, exhibits a low nasal boss (25, 26) ( SI Text ). The anteromedial process of the nasal is pronounced in Triceratops from M3, and the NPP is more vertically inclined in specimens from upper M3, producing a more convex rostrum morphology, which was previously found to characterize T. prorsus (12, 23). The frontoparietal fontanelle is open in late-stage subadults/young adults (UCMP 113697). U3 Triceratops. Specimens from U3 exhibit the features Forster (12) found to characterize T. prorsus . U3 Triceratops possess an elongate, relatively narrow nasal horn (average length/width > 2) (Fig. 2 A and Dataset S1). The NPP is more vertically inclined, producing a convex rostrum lacking the low, elongate profile noted in T. horridus [although the largest, and presumably oldest, known specimens (e.g., MOR 004 and MOR 1625) exhibit pro- portionally longer rostra] (Fig. 2 E and Dataset S1). The NPP is anteroposteriorly expanded, and the anteromedial process of the nasal is greatly reduced (Fig. S3) (27). The frontoparietal fontanelle becomes constricted and eventually closed in late-stage subadults/young adults (e.g., MOR 2923 and MOR 2979), ontogenetically earlier than in L3 and M3. The postorbital horn cores are short ( < 0.64 basal-skull length) (Fig. 2 D ). Further, U3 Triceratops seem to exhibit nasals that are more elongate than Triceratops from the lower half of the HCF (Fig. 2 F and Dataset S1). Shifts in Morphology over Time. Epinasals exhibit a directional morphologic trend; average length increases throughout the formation (Fig. 2 A and Dataset S1) (Spearman ’ s rank coefficient = 0.824, P = 4.15E − 07). A protuberance just posterior to the epinasal, observed in specimens from L3 and M3 (Fig. 1), is partic- ularly pronounced in UCMP 113697 from the uppermost M3 (Fig. 1 E ). U3 Triceratops either do not exhibit this feature or express only a subtle ridge in the homologous location. Concurrent with elongation of the epinasal was an expansion of the NPP (Fig. 2 B ) (Spearman ’ s rank coefficient = − 0.969, P = 3.74E − 06) and an increase in the angle between the NPP and the narial strut of the premaxilla (Fig. 2 C and Dataset S1) (Spearman ’ s rank coefficient = 0.802, P = .000186). Nasals also become more elongate relative to basal skull length (although only three specimens with complete nasals have thus far been recorded from the lower half of the formation) (Fig. 2 F and Dataset S1) (Spearman ’ s rank coefficient = 0.804, P = 0.00894). Postorbital horn-core length appears to be variable throughout L3 and M3 and is consistently short in U3 Triceratops (Fig. 2 D and Dataset S1) [Spearman ’ s rank coefficient is negative ( − 0.197) and not statistically significant ( P = 0.392)]. Large juvenile U3 Triceratops (e.g., MOR 1110) can possess more elongate postorbital horn cores (0.64 basal-skull length). Whereas U3 postorbital horn core length falls within the range of variation observed lower in the formation (Fig. 2 D ), elongate postorbital horn cores have thus far not been found in post-juvenile stage Triceratops from U3. Many large Triceratops (e.g., MOR 1122 and MOR 3000) (3) exhibit evidence of postorbital horn-core resorption, suggesting that maximum length is reached earlier in ontogeny. Maximum postorbital horn-core length may have been expressed later in development (or for a longer duration) in Triceratops from lower in the formation. Triceratops from the upper half of the HCF exhibit a more vertically inclined NPP (Fig. 2 C ), which contributes to a rostrum that appears shorter and more convex in lateral profile (a feature Forster noted in T. prorsus ) (12). However, we note that a Spearman ’ s rank correlation test found apparent reduction in rostrum length to be statistically insignificant (Spearman ’ s rank coefficient 0.018, P = 0.966). Large specimens from U3 (e.g., MOR 004) possess a more elongate rostrum relative to basal- skull length (Fig. 2 E and Dataset S1); however, the shape of U3 rostra appears to be consistently convex. Eotriceratops xerinsularis , found in the stratigraphically older uppermost Horseshoe Canyon Formation ( ∼ 68 Ma) (28), expresses morphologies (elongate postorbital horn cores, small nasal horn) consistent with its stratigraphic position relative to Triceratops . Cladistic and Stratocladistic Analyses. Initial cladistic analyses recovered a polytomy of all HCF specimens, with the 50% majority tree producing a succession of Triceratops that largely correlates with stratigraphic placement (Fig. S5 and SI Text ). Removal of the more fragmentary material recovered Torosaurus specimens as basal to a stratigraphic succession of Triceratops , including a polytomy of specimens from the upper half of the formation (Fig. 3 A ). A similar topology was recovered when specimens not exhibiting codeable features of the parietal squamosal frill were removed from the analysis (Fig. 3 B ). Removal of MOR 2924, a specimen from the base of U3 that does not preserve postorbital horn cores ( SI Text ), recovers specimens from the upper part of M3 as basal to U3 Triceratops . In the analysis of the most reduced dataset, UCMP 113697 and MOR 3027 cluster together (Fig. 3 C ). These specimens exhibit a combination of characters found in Triceratops from L3 and M3. The epinasal of UCMP 113697 is morphologically in- termediate between L3 and U3 Triceratops (the epinasal of MOR 3027 is incomplete). These specimens each exhibit large postorbital horn cores (a feature expressed in some L3 Triceratops ) and a more vertically inclined NPP (found in U3 Triceratops ). MOR 3045 is recovered as being more derived than UCMP 113697 and MOR 3027 (Fig. 3) based on its possession of relatively short postorbital horn cores, a more expanded NPP, and a pronounced step bordering the “ incipient fenestrae ” (sensu ref. 3) ( SI Text ). This specimen exhibits the basal condition of the anteromedial nasal process and expresses a pronounced upturn of the posterior surface of the epinasal, suggesting the presence of a protuberance in life. MOR 3045 exhibits a fairly elongate epinasal (estimated length/width, ∼ 1.88), with a posterior surface that is broader than is seen in most U3 specimens and, like UCMP 113697, MOR 3027, and U3 Triceratops , exhibits a more vertically inclined NPP. Stratocladistic analyses, in which specimens were grouped into operational units based on stratigraphic position, were performed in the program StrataPhy (29). Torosaurus specimens were initially considered separately from other specimens ( SI Text ). Initial results suggested that specimens from the upper half of the HCF represented a sequence of ancestors and descendants but differed on the position of operational units from the lower half of the formation (Fig. S6 A ). This result was likely influenced by missing data for specimens from the lower half of the formation; no specimens from lower M3 preserve frill characters that can distinguish them from the Torosaurus morphology. When Torosaurus specimens were incorporated into Triceratops operational units, three topologies were produced: a strictly cladogenetic result, a topology in which all operational units except lower M3 were recovered in a transformational sequence, and a topology in which the HCF operational units were recovered in two lineages (an upper L3/lower M3 lineage and an upper M3/U3 lineage) that had diverged at some point in the deposition of L3 (Fig. S6 B ). Pruning of Torosaurus specimens from the dataset produced two topologies that incorporated morphological transformation: one topology in which all HCF operational units fell into a single lineage and another topology presenting two HCF lineages that diverged either in L3 or before deposition of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved ...

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... of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved elsewhere and migrated into the HCF, eventually replacing the incumbent HCF Triceratops population by the beginning of the deposition of U3. Upper M3 specimens represent early members (or close relatives of) this group that would come to dominate the ecosystem. ii ) Variation between MOR 3045, MOR 3027, and UCMP 113697 represents intraspecific (or intrapopulation) variation. As the HCF Triceratops lineage evolved, some individuals expressed more of the features that would eventually dominate the population. Over time, these traits were se- lected for and characterized U3 Triceratops. This is a purely anagenetic scenario. iii ) A bifurcation event is recorded in the HCF and occurred at some point before the deposition of U3, resulting in two lineages that differ primarily in the morphology of the epinasal and rostrum (consistent with Forster ’ s diagnoses for T. horridus and T. prorsus ). MOR 3045 represents an early member of a lineage that evolved into U3 Triceratops. This scenario incorporates anagenesis (38) and is presented in some trees produced by the stratocladistic analysis (Fig. S6). iv ) The evolution of Triceratops was characterized by a series of cladogenetic events that produced at least five taxa over the course of the deposition of the HCF (the L3 clade, the lower M3 clade, the MOR 3027 clade, the MOR 3045 clade, and the U3 clade). This strictly cladogenetic scenario suggests that no Triceratops found lower in the HCF underwent evolutionary transformation into forms found higher in the formation. A Biogeographic Signal? The Hell Creek Project ’ s stratigraphic record of Triceratops is primarily restricted to northeastern Montana. It has been hypothesized that T. horridus and T. prorsus were largely biogeographically separated, with T. prorsus generally restricted to the Hell Creek and Frenchman Formations and T. horridus commonly found in the more southern Lance, Laramie, and Denver Formations (15, 17). However, this suggested biogeographic segregation may represent an artifact of the stratigraphic record. Specimens that have thus far been described from neighboring coeval formations exhibit morphologies consistent with their stratigraphic position relative to the HCF (39, 40) ( SI Text ). Anagenesis and Cladogenesis. If the morphological trends noted in Triceratops were purely the result of cladogenetic branching (consistent with punctuated equilibrium) (32) (Fig. 4 C and D ), we would expect to find the full U3 morphology coexisting with Triceratops found lower in the formation, or alternatively, specimens exhibiting the L3 morphology in U3. Such specimens have yet to be discovered ( SI Text ). Specimens from the upper part of M3 exhibit transitional features relative to L3 and U3 Triceratops , a pattern consistent with anagenesis. Some cladistic analyses distinguish MOR 3045 from other upper M3 Triceratops based on variation in the length of the postorbital horn cores, width of the NPP, and the thickened regions of the parietal (Fig. 3, Fig. S5, and SI Text ). Triceratops collected from a multiindividual bonebed in U3 (MOR locality no. HC-430) (44) show variable morphology of the premaxillae and parietal between individuals (Fig. S2) (41). This finding suggests that the variation between upper M3 specimens may represent intrapopulational, not taxonomic, variation (10). Indi- viduals exhibiting more pronounced U3 character states may have become increasingly abundant in the HCF Triceratops population over time until, by the end of the Cretaceous, all Triceratops exhibited these character states (Fig. 4 A ). Alternatively, MOR 3045 may represent an early member of a U3 ( T. prorsus ) lineage, with MOR 3027 representing a separate lineage. Stratocladistic analyses suggest the possibility of two lineages in the HCF (Fig. 4 B and Fig. S6); however, this scenario would require the independent evolution of an enlarged epinasal-nasal protuberance. A purely cladogenetic interpretation of the HCF Triceratops dataset suggests the presence of at least five stratigraphically overlapping taxa in the formation (Fig. 4 C and D ). This scenario is possible, but we would argue that interpretations that incorporate populational transformation (anagenesis) are more conservative. Specimens from upper M3 exhibit a combination of primitive and derived characters, as well as more developed states of characters expressed in L3 Triceratops . Forster (12) noted that, whereas T. prorsus exhibited derived characters, no autapomor- phic characters were recognized in T. horridus . This finding is consistent with the hypothesis that the evolution of Triceratops incorporated anagenesis and illustrates the potential difficulties with defining species in evolving populations (6, 35). The HCF dataset underscores the importance of considering morphologies in a populational, rather than typological, context (42). The documented changes in Triceratops morphology occurred over a geologically short interval of time (1-2 million y) (2). High-resolution stratigraphy is necessary for recognizing fine- scale evolutionary trends. If cladogenesis is considered the primary mode of dinosaur evolution, a problematic inflation of dinosaur diversity occurs. Current evidence suggests that the evolution of Triceratops incorporated anagenesis as there is currently no evidence for biogeographic segregation of contemporaneous Triceratops morphospecies and there is evidence for the morphological transformation of Triceratops throughout the HCF. This dataset supports hypotheses that the evolution of other Cretaceous dinosaurs may have incorporated phyletic change (6, 43, 44) and suggests that many speciation events in the dinosaur record may represent bifurcation events within anagenetic lineages ...

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... from L3 and the lower half of M3 (MOR 1120, MOR 2982, and MOR 3010). UCMP 128561, from the upper half of M3, exhibits a low nasal boss (25, 26) ( SI Text ). The anteromedial process of the nasal is pronounced in Triceratops from M3, and the NPP is more vertically inclined in specimens from upper M3, producing a more convex rostrum morphology, which was previously found to characterize T. prorsus (12, 23). The frontoparietal fontanelle is open in late-stage subadults/young adults (UCMP 113697). U3 Triceratops. Specimens from U3 exhibit the features Forster (12) found to characterize T. prorsus . U3 Triceratops possess an elongate, relatively narrow nasal horn (average length/width > 2) (Fig. 2 A and Dataset S1). The NPP is more vertically inclined, producing a convex rostrum lacking the low, elongate profile noted in T. horridus [although the largest, and presumably oldest, known specimens (e.g., MOR 004 and MOR 1625) exhibit pro- portionally longer rostra] (Fig. 2 E and Dataset S1). The NPP is anteroposteriorly expanded, and the anteromedial process of the nasal is greatly reduced (Fig. S3) (27). The frontoparietal fontanelle becomes constricted and eventually closed in late-stage subadults/young adults (e.g., MOR 2923 and MOR 2979), ontogenetically earlier than in L3 and M3. The postorbital horn cores are short ( < 0.64 basal-skull length) (Fig. 2 D ). Further, U3 Triceratops seem to exhibit nasals that are more elongate than Triceratops from the lower half of the HCF (Fig. 2 F and Dataset S1). Shifts in Morphology over Time. Epinasals exhibit a directional morphologic trend; average length increases throughout the formation (Fig. 2 A and Dataset S1) (Spearman ’ s rank coefficient = 0.824, P = 4.15E − 07). A protuberance just posterior to the epinasal, observed in specimens from L3 and M3 (Fig. 1), is partic- ularly pronounced in UCMP 113697 from the uppermost M3 (Fig. 1 E ). U3 Triceratops either do not exhibit this feature or express only a subtle ridge in the homologous location. Concurrent with elongation of the epinasal was an expansion of the NPP (Fig. 2 B ) (Spearman ’ s rank coefficient = − 0.969, P = 3.74E − 06) and an increase in the angle between the NPP and the narial strut of the premaxilla (Fig. 2 C and Dataset S1) (Spearman ’ s rank coefficient = 0.802, P = .000186). Nasals also become more elongate relative to basal skull length (although only three specimens with complete nasals have thus far been recorded from the lower half of the formation) (Fig. 2 F and Dataset S1) (Spearman ’ s rank coefficient = 0.804, P = 0.00894). Postorbital horn-core length appears to be variable throughout L3 and M3 and is consistently short in U3 Triceratops (Fig. 2 D and Dataset S1) [Spearman ’ s rank coefficient is negative ( − 0.197) and not statistically significant ( P = 0.392)]. Large juvenile U3 Triceratops (e.g., MOR 1110) can possess more elongate postorbital horn cores (0.64 basal-skull length). Whereas U3 postorbital horn core length falls within the range of variation observed lower in the formation (Fig. 2 D ), elongate postorbital horn cores have thus far not been found in post-juvenile stage Triceratops from U3. Many large Triceratops (e.g., MOR 1122 and MOR 3000) (3) exhibit evidence of postorbital horn-core resorption, suggesting that maximum length is reached earlier in ontogeny. Maximum postorbital horn-core length may have been expressed later in development (or for a longer duration) in Triceratops from lower in the formation. Triceratops from the upper half of the HCF exhibit a more vertically inclined NPP (Fig. 2 C ), which contributes to a rostrum that appears shorter and more convex in lateral profile (a feature Forster noted in T. prorsus ) (12). However, we note that a Spearman ’ s rank correlation test found apparent reduction in rostrum length to be statistically insignificant (Spearman ’ s rank coefficient 0.018, P = 0.966). Large specimens from U3 (e.g., MOR 004) possess a more elongate rostrum relative to basal- skull length (Fig. 2 E and Dataset S1); however, the shape of U3 rostra appears to be consistently convex. Eotriceratops xerinsularis , found in the stratigraphically older uppermost Horseshoe Canyon Formation ( ∼ 68 Ma) (28), expresses morphologies (elongate postorbital horn cores, small nasal horn) consistent with its stratigraphic position relative to Triceratops . Cladistic and Stratocladistic Analyses. Initial cladistic analyses recovered a polytomy of all HCF specimens, with the 50% majority tree producing a succession of Triceratops that largely correlates with stratigraphic placement (Fig. S5 and SI Text ). Removal of the more fragmentary material recovered Torosaurus specimens as basal to a stratigraphic succession of Triceratops , including a polytomy of specimens from the upper half of the formation (Fig. 3 A ). A similar topology was recovered when specimens not exhibiting codeable features of the parietal squamosal frill were removed from the analysis (Fig. 3 B ). Removal of MOR 2924, a specimen from the base of U3 that does not preserve postorbital horn cores ( SI Text ), recovers specimens from the upper part of M3 as basal to U3 Triceratops . In the analysis of the most reduced dataset, UCMP 113697 and MOR 3027 cluster together (Fig. 3 C ). These specimens exhibit a combination of characters found in Triceratops from L3 and M3. The epinasal of UCMP 113697 is morphologically in- termediate between L3 and U3 Triceratops (the epinasal of MOR 3027 is incomplete). These specimens each exhibit large postorbital horn cores (a feature expressed in some L3 Triceratops ) and a more vertically inclined NPP (found in U3 Triceratops ). MOR 3045 is recovered as being more derived than UCMP 113697 and MOR 3027 (Fig. 3) based on its possession of relatively short postorbital horn cores, a more expanded NPP, and a pronounced step bordering the “ incipient fenestrae ” (sensu ref. 3) ( SI Text ). This specimen exhibits the basal condition of the anteromedial nasal process and expresses a pronounced upturn of the posterior surface of the epinasal, suggesting the presence of a protuberance in life. MOR 3045 exhibits a fairly elongate epinasal (estimated length/width, ∼ 1.88), with a posterior surface that is broader than is seen in most U3 specimens and, like UCMP 113697, MOR 3027, and U3 Triceratops , exhibits a more vertically inclined NPP. Stratocladistic analyses, in which specimens were grouped into operational units based on stratigraphic position, were performed in the program StrataPhy (29). Torosaurus specimens were initially considered separately from other specimens ( SI Text ). Initial results suggested that specimens from the upper half of the HCF represented a sequence of ancestors and descendants but differed on the position of operational units from the lower half of the formation (Fig. S6 A ). This result was likely influenced by missing data for specimens from the lower half of the formation; no specimens from lower M3 preserve frill characters that can distinguish them from the Torosaurus morphology. When Torosaurus specimens were incorporated into Triceratops operational units, three topologies were produced: a strictly cladogenetic result, a topology in which all operational units except lower M3 were recovered in a transformational sequence, and a topology in which the HCF operational units were recovered in two lineages (an upper L3/lower M3 lineage and an upper M3/U3 lineage) that had diverged at some point in the deposition of L3 (Fig. S6 B ). Pruning of Torosaurus specimens from the dataset produced two topologies that incorporated morphological transformation: one topology in which all HCF operational units fell into a single lineage and another topology presenting two HCF lineages that diverged either in L3 or before deposition of the HCF (Fig. S6 C ). Evolutionary Patterns. One of the principle questions in evolutionary biology regards the modes of evolution: what evolutionary patterns are preserved in the fossil record and how prominent are these patterns (30 – 32)? Small sample sizes for most nonavian dinosaur taxa complicate the investigation of evolutionary modes in this group. As such, it is unknown how prominent a role anagenesis (the transformation of lineages over time) (Fig. 4 A ) (33 – 37) played in their evolution or whether the majority of morphologies recorded in the fossil record were a product of cladogenesis (evolution via branching events) (Fig. 4 B – D ) (8, 32, 33, 37, 38). Horner et al. (6) presented evidence for anagenesis in several dinosaur clades within the Cretaceous Two Medicine Formation of Montana. It has been suggested that the ceratopsid sample size presented in that study was too small and that cladogenesis was a more conservative interpretation of the data (7). A combination of large sample size, ontogenetic resolution, and detailed stratigraphic data makes Triceratops an ideal taxon for testing hypotheses regarding evolutionary mode in a nonavian dinosaur. Restriction of the full T. prorsus morphology to U3 renders untenable hypotheses that T. horridus and T. prorsus represent sexual or ontogenetic variation within a single taxon. Triceratops from the upper part of M3 exhibit a combination of features found in L3 and U3 Triceratops . This pattern suggests that the evolution of Triceratops incorporated anagenesis. Strict consensus trees produced by cladistic analyses either recover upper M3 specimens in a polytomy with all HCF specimens, in a polytomy of HCF Triceratops from the upper half of the formation, or UCMP 113697 and MOR 3027 cluster together whereas MOR 3045 shares more features with U3 Triceratops (Fig. 3 and Fig. S5). We will consider four alternative hypotheses for the morphological pattern recorded in the HCF: i ) T. prorsus evolved elsewhere and migrated into the HCF, eventually replacing the incumbent HCF Triceratops population by the beginning of the deposition of U3. Upper M3 specimens ...