Select cranial traits appearing in multiple lineages of coelurosaurian theropod dinosaurs tested herein as PHTs. Ecomorphological indicators statistically correlated with extrinsic evidence of herbivory (first- and second-order CHTs) are marked with an asterisk. Traits featured on six species representing four coelurosaurian theropod subclades, including the only predominantly folivorous modern bird. (A) Opisthocomus hoazin skull, left lateral view (extant Aves), adapted from http://digimorph.org/. Extinct theropods: (B) Ornithomimus edmontonicus (RTMP 95.110.1) skull, left lateral view (derived Ornithomimosauria); (C) Shenzhousaurus orientalis (NGMC 977–4-002) skull, left oblique dorsolateral view (primitive Ornithomimosauria), adapted from ref. 21; (D) Incisivosaurus gauthieri (IVPP V13326) skull left lateral view (primitive Oviraptorosauria); and (E) Caenagnathus collinsi (CMN 8776) fused lower mandibles, dorsal view (derived Oviraptorosauria; Table S7, and see SI Appendix, Section A3 for trait descriptions.