Tyrannosaurus rex Osborn 1905

Cladistic analyses The reduced cladistic analysis of 31 specimens, following the New Technology and Traditional searches, recovered one most parsimonious tree (i.e., ontogram) of 3,053 steps, with an ensemble Consistency Index (CI) excluding uninformative characters of 0.65, an ensemble Homoplasy Index (HI) of 0.35, an ensemble Retention Index (RI) of 0.72, and an ensemble Rescaled Consistency Index (RCI) of 0.50. The ontogram recovered 21 growth stages; in the adult region of the ontogram several branches contain multiple specimens; these are most simply interpreted as specimens of the same maturity (Fig. 2). Bremer, jackknife, and bootstrap values are shown in Fig. 1B. The ontogram is composed of 21 growth stages, including the group of most mature specimens, and all but the first and third are supported by unambiguously optimized synontomorphies (Data S4). Despite the addition of 26 specimens and 1,766 characters, these results are congruent with those obtained by Carr & Williamson (2004), where LACM 28471, CMNH 7541, LACM 23845, AMNH FARB 5027, and LACM 23844 were again recovered at progressively mature growth stages (Figs. 1B and 2). The a posteriori analysis that included an artificial adult resulted in seven 3,071-step MPTs that, in a strict consensus ontogram did not group with a single, presumably most mature, specimen. Therefore, a different approach was taken, specifically the greatest distance from the root. Of that group, FMNH PR2081 possessed the greatest number of autontomorphies, 19 character changes, in contrast to the five others; ergo, that specimen was regarded as the most mature of the group, having undergone the greatest amount of change, and so represents the twenty-first growth stage (i.e., the terminus of the growth series). In contrast, the massive specimen RSM 2523.8, previously regarded as the most mature individual T. rex (Persons, Currie & Erickson, 2019), was recovered as one of the least mature adults. The two purported female specimens (BMRP 2006.4.4, MOR 1125), a sex identification based on the presence of femoral medullary bone (Schweitzer, Wittmeyer & Horner, 2005; Woodward et al., 2020; this assessment has been challenged by O’ Connor et al., 2018), were recovered as a subadult and a young adult, respectively (Fig. 2). Sexual dimorphism was presumed here to be expressed in one of two ways: either the ontogram would split into separate male and female branches, or sexually diagnostic characters might be optimized as individual variation. In the first instance, a split of the ontogram into separate branches is not seen. In the second, the individual variation of MOR 1125 was compared with that of other specimens. Sexually informative variation, in this case female variation, was assumed to be expressed as multiple homologous character changes seen in MOR 1125 and a repeated set of specimens (i.e., the identical set of specimens for each shared homologous character change). The comparison found eight homologous character changes shared between MOR 1125 and five other specimens; however, the character changes are not shared with a uniform set of specimens (Table 2). Therefore, there is no skeletodental evidence for sexual dimorphism in the data set (i.e., males and females are skeletally identical aside from the presence of medullary bone); otherwise, the ontogram would have divided into separate male and female branches or homologous character changes would have singled out MOR 1125 and an associated set of specimens. This test is not dependent upon MOR 1125 being a female (O’ Connor et al., 2018); if in actuality it is a male, then the set of shared characters would be evidence of that sex. Wildcard specimens Thirteen wildcard specimens were identified; in each case, the analyses that included them resulted in multiple ontograms that collapsed into one or several polytomies; the regions of collapse are enclosed by ellipses in Fig. 1B. Upon comparison of the polytomies, the wildcard specimens could be divided into two groups, where resolution was lost either rootward or distalward relative to BMRP 2002.4.1, the most complete specimen in the dataset; that is, that specimen was not part of either polytomy. The partial adult specimen, CM 1400, is shown in a polytomy with two other specimens at the end of a branch (Fig. 1B); however, structure was lost elsewhere in the ontogram when this specimen was included in the analysis, and so it was excluded from the backbone topology (Figs. 1B and 2). Despite the fact that the wildcards are coded for less than 7% of the characters, some occupy a relatively precise location of the ontogram (e.g., CM 1400, CM 9401, DDM 35.1, MOR 3044, MOR 2925, RSM 2347.1), whereas others collapse entire regions (e.g., BMRP 2001.4.70, DDM 1536.1, DDM 1562.14, DDM 1863.1, FMNH PR2411, MOR 002, TMM 41436-1). Of these specimens, many are single bones (BMRP 2001.4.70, DDM 35.1, DDM 1536.8, FMNH PR2411, MOR 2925, MOR 3044, RSM 2347.1, TMM 41436-1) or teeth (DDM 1562.14, DDM 1863.1), whereas only two are a partial skull (CM 1400) or skull and skeleton (MOR 002). Overview of frequencies of growth changes Influence of specimen completeness The effect of specimen completeness upon the number of synontomorphies at each node was quantified through a Spearman rank correlation test. Examination of the raw data as histograms with a fitted normal curve showed they are positively skewed, and a Shapiro – Wilk test of normality found that they were not normally distributed (completeness, p = 0.001; synontomorphies, p = 0.000) and so the data were normalized by converting them to ranks (Table 3; Fig. 3). A Shapiro-Wilk test of normality found that the ranked completeness and ranked number of synontomorphies were normally distributed (p = 0.217, 0.134, respectively). A Spearman rank correlation test resulted in a nonsignificant (p = 0.423) correlation coefficient ( rS = 0.149), indicating that the peaks of synontomorphies at each node are not dependent upon the completeness of the specimens that extend from each branch. Synontomorphy trends The overall distribution of growth changes is unimodal (Fig. 4): the highest number occurs early, peaking at the subadult growth category, which then precipitously drops, aside from several low peaks in the adult growth stages. In total, there are five peaks, and four of them mark the onset of growth categories. The peak at growth stage 6 marks the beginning of the subadult growth category, where an increase in the height of the skull frame and inflation of the bones that enclose the antorbital sinus are seen, as well as changes to the pectoral girdle and limb, and pes. The peak at growth stage 8 marks the onset of the young adult growth category. The peak at growth stage 13 marks the onset of adulthood, where the External Fundamental System (EFS; a narrow band of lines of arrested growth that indicate near cessation of appositional growth) is first seen as well as changes to the antorbital sinus system and the origin of the adductor musculature. The peak at growth stage 19 marks extensive changes to the skull and postcranial skeleton, but by itself does not define a new growth category. Finally, the peak of changes at growth stage 21 correspond to the extensive changes in the skeleton of FMNH PR2081, the most mature and second-best sampled specimen in the data set. Given their abundance in the character matrix, nonphylogenetic synontomorphies are more numerous at each node than phylogenetic synontomorphies, but they broadly follow the same pattern of peaks and valleys (Fig. 5), aside from growth stages 6, 8, 10, and 21, where phylogenetic changes tend to decrease in frequency whereas nonphylogenetic changes increase. This difference in frequency distribution shows that the number of phylogenetic changes is not controlled by the number of characters scored. Phylogenetic changes are frequent (i.e., more than five) early in growth (stages 2 – 9), whereas they are less common among adults (stages 10, 12, 13, 18 – 21); if ontogeny is congruent with phylogeny then this gross pattern should be expected since fewer phylogenetic synontomorphies should occur among adults, which presumably would only express characters at the level of species. A comparison of the frequency of cranial and postcranial changes shows that cranial synontomorphies are the most frequent (Fig. 6). Both sets of changes follow the same general pattern; cranial changes are dominant in terms of number and the pattern of the frequency distribution, whereas postcranial changes do not always occur. Cranial and postcranial changes are most frequent at growth stage 6, and thereafter they show less than 22 changes per growth stage. This indicates that once the adult morphotype (i.e., tall skull, inflated antorbital sinuses) is achieved, the rate of change, as shown by the number of changes per growth stage, greatly decreases. During adulthood, cranial changes generally outnumber postcranial changes, which tend to cease altogether. Cranial changes are nearly continuous and have five peaks, whereas only three are seen postcranially that are often preceded and followed by one or more growth stages of no change. The absence of postcranial changes in growth stage 5 is an artifact of the least mature specimens lacking postcranial material. The abundance of postcranial changes at growth stage 7 is an artifact of the exemplar specimen having an incomplete skull and a relatively complete hindlimb. In contrast, the absence of postcranial change seen from growth stage 9 – 12 reflects a signal of quiescence given that several specimens in that interval do include postcranial bones. When the frequencies of changes to the cranium and mandible are compared, both follow the same overall pattern (Fig. 7), but the cranial changes generally outnumber those of the mandible. Mandibular changes occur in a series of three low peaks (i.e., less than 8 synontomorphies per growth stage) throughout ontogeny; the highest number of changes (7) occurs early in the 5th growth stage, but this trend does not continue into the sustained and extremely high number of changes seen in the cranium at the 6th stage. This difference results from the absence of mandibular bones in the sample of subadults at the fifth stage. In contrast, the exemplar of the seventh growth stage, LACM 23845, is represented by an incomplete mandibular ramus, but, notably, it does not result in mandibular synontomorphies at that growth stage; presumably those changes occurred earlier, at growth stage 5. The absence of changes at the 7th growth stage indicates that the completion of the progression of changes in the mandibular ramus, which produces the dorsoventrally deep skull frame, precedes that of the cranium. In adulthood, the number of changes in the cranium exceeds that of the mandible or, on occasion, mandibular changes exceed cranial changes at growth stages where the cephalic skeleton is represented solely by mandibular bones (NHMUK R7994) or very few cranial bones (NMMNH P-3698). Changes to the skull and jaws were examined by anatomical domain, which includes discrete regions of the skull such as bony structures associated with the antorbital air sac system or aggregates of functional structures, such as joint surfaces. For ease of comparison, the domains were separated into two groups: pneumatic systems on the one hand, and apneumatic features on the other. The pneumatic systems include the antorbital sinus system (invades the snout), tympanic sinus system (invades the lateral surface of the braincase), median pharyngeal sinus system (invades the sphenoid rostrum and basicranium), and the cervical air sac system (invades the occiput). In descending order, the most frequent pneumatic changes are associated with the antorbital, cervical (=subcondylar) and tympanic sinus systems, and the median pharyngeal sinus system (Fig. 8). Changes associated with the antorbital sinus occur throughout ontogeny, whereas cervical changes begin in adulthood and continue almost to senescence; in contrast, median pharyngeal changes are limited to growth stage 12, at the end of the young adult growth category. Finally, tympanic changes are limited to growth stages 9 – 12, during young adulthood. Apneumatic domains include joint surfaces, muscle scars, the subcutaneous surface, neurovasculature, the occiput, dentition, and the skull frame. The skull frame sees the most changes throughout the growth series (Fig. 9). Change to all other domains are low in frequency (i.e., fewer than 10 changes per growth stage), but most of them also change throughout growth, including joint surfaces (growth stage 4 – 21), the dorsotemporal fossa (growth stage 4 – 21), neurovasculature (growth stage 2 – 21), muscle scars (growth stage 5 – 21), and the subcutaneous surface (growth stage 5 – 21). A limited pattern is seen in the dentition where changes occur from the 5th to 17th growth stages. In contrast, nonmuscular and apneumatic changes to the occiput are limited to the young adult growth category (growth stage 9). In the postcranial skeleton, the greatest number of changes (more than five) are seen in the transition from the subadult to the young adult growth categories (Fig. 10) that include, in descending order, the pes, fibula, scapula, coracoid, and humerus. Thereafter, postcranial changes effectively cease until three clusters of changes in adulthood, at the 14th and 15th stages, the 18th and 19th stages, and a final set at the 21st growth stage. Early changes (juvenile to young adult categories) happen to the pectoral girdle and pes (6th and 7th growth stages), the humerus (6th growth stage), and the fibula (8th growth stage). Later changes (adult to senescent adult categories) are seen in the axial column (15th, 19th, and 21st growth stages), pelvic girdle (14th and 18th growth stages), and the fibula (18th and 19th growth stages). This pattern suggests a relatively instantaneous transition in the pectoral girdle and limb, and the pes; in contrast, changes to the axial column, and to the pelvic girdle and limb, are relatively sustained throughout growth. Craniomandibular modules Recent work has found that the skull of T. rex is organized into six modules of functional integration (Werneburg et al., 2019). The growth series obtained here shows that the modules experience different amounts of ontogenetic change (Fig. 11; Table 4): in descending order, the dorsum of the snout, circumorbital bones, and frontals; the sides of the snout and palate; the mandibular ramus; the braincase; the suspensorium; and the parietal bone. The modular pattern of the skull is considered evidence for a flexible framework (this hypothesis conflicts with inferences based on Finite Element Analysis (FEA) modeling; Cost et al., 2019); in terms of growth, the suspensorium, parietal, and braincase are the modules that change the least (less than 10 changes per growth stage), which is consistent with their stable keystone-like function against which the relatively flexible palate and facial skeleton can passively move and the lower jaws freely rotate. The greatest change across modules (more than 10) occurs in the 5th and 6th growth stages; this corresponds to the transition from small to large juveniles (Fig. 11). The transition from the long and low skulls of juveniles to the tall skulls of subadults imposes 52 changes, where the snout dorsum module is changed from the delicate and thin morphotype of juveniles to the greatly expanded and inflated form of subadults. Changes to the skull roof and mandible are seen throughout ontogeny; changes to the snout and supensorium occur later, from the 5th growth stage onwards. Other modules do not change until young adulthood, including the parietal and braincase; changes to the parietal are limited to young adults and adults, whereas changes to the braincase continue to the last growth stage. These differences in the timing of change to modules is consistent with the hypothesis of modularity, otherwise they would change together if they were integrated. During the interval of greatest change, in the transition from juveniles to subadults (growth stages 5 and 6), the modules that change the most are the skull roof, snout, and mandible. Ontogram mapped onto growth curve Mapping the ontogram onto a previously published growth curve for T. rex (Erickson et al., 2004) permits refinement of the diagnosis of the higher-level growth categories of Carr (1999) and Erickson et al. (2004), namely juvenile, subadult, young adult, adult, and senescent adult (Fig. 12). This approach provides a framework for comparison with previous studies on functional morphology in T. rex and the evolution of its ontogeny. This template serves as a heuristic device and is not intended to estimate growth rates; for example, the position of BMRP 2006.4.4 on the steepest part of the growth curve conflicts with the histological evidence that the individual was at a moderate growth rate before death (Woodward et al., 2020). At best, the curve is an approximation of the true growth rate. The chronological age of BMRP 2002.4.1 is based on the revised age of Woodward et al. (2020); the age of LACM 23845 (14 years; Erickson et al., 2004) is considered here to be an underestimate since it conflicts with that of the less mature BMRP 2006.4.4 (15 years; Woodward et al., 2020). Growth categories Alignment between the growth series, chronological age, cortical histology, number of growth changes, growth rate, and, to a lesser degree, size and mass, were used to define five growth categories, once the ontogram was mapped onto the growth curve of Erickson et al. (2004), a procedure that was constrained by seven histologically aged specimens (Fig. 12). Although mass is a relevant variable in these comparisons, given the variety of methods used by different workers, the published mass estimates conflict with each other (Table 5); for that reason, the decision for each mention of mass as a relevant diagnostic character is given below. Also, although the masses are given to the nearest kilogram or, in four instances, to the tenth of a kilogram, it is not intended to give the impression of precision, rather the exact estimates are here simply reproduced unaltered from the original sources. To reflect the natural imprecision, mass estimates given in the next section are rounded up in the discussion of diagnostic features of growth categories. Juveniles Juveniles (=adolescent category of Erickson et al., 2004) have a skull length less than 80 cm, long and low skulls with a length to height ratio of 3.0 or greater, are equal to or less than 13 years old, and lack an EFS. This growth category sees 58 unambiguously optimized growth changes, of which 24 have a CI of 1.0 (Table 6). In the skull, most changes are seen in the snout module (sensu Werneburg et al., 2019). This category corresponds to growth stages 1 – 5 of the ontogram (Fig. 2) and to the initial lag phase of the T. rex growth curve of Erickson et al. (2004; Fig. 12). The juvenile stage extends from hatching to the 13th year of life, before the long and low skull proportions are lost at the subadult category. A single mass estimate of 39.9 kg has been published for the small juvenile LACM 28471 by Erickson et al. (2004). Two mass estimates have been published for the large juvenile BMRP 2002.4.1: a range of 639 – 1,269 kg, and a mean of 954 kg was published by Hutchinson et al. (2011) and an estimate of 660.2 kg was published by Snively et al. (2019). The maximum estimate is used here as a point of reference; therefore, juveniles are here considered to have a mass equal to or less than ~1,300 kg. The juvenile growth stage is diagnosed by the possession of a dorsoventrally shallow skull and jaws, the increase in height of which defines the subadult stage. To precisely reflect the primary changes that occur even during this initial phase of life, this growth category is divided into two categories in the following diagnosis, namely small juveniles and large juveniles. A total of five growth changes occur in the small juvenile growth stage, which affect the skull roof and mandible modules of Werneburg et al. (2019). In contrast, 53 changes occur in the large juvenile growth stage that are more widespread across the skull, including modules of the skull roof, snout, suspensorium, and mandible. The large juvenile category marks the earliest onset of sexual maturity (see below). Small juveniles Joint surfaces In the fourth growth stage, there is a clear distinction between the postorbital buttress and the caudal shelf of the frontal bone. Neurovasculature In the second growth stage, the alveolar row of foramina that penetrates the lateral surface of the dentary acquires a sulcus that unites all of the openings. In medial view, the Meckelian sulcus becomes a deeply inset groove. Dorsotemporal fossa In the fourth growth stage, the sagittal crest of the frontal becomes tall and the fossa extends rostrodorsally at a steep angle relative to the level forehead (subcutaneous surface ahead of the fossa). Large juveniles Skull frame In the fifth growth stage, several correlates of an increase in skull height are seen, including the dorsal position of the angulation in the rostral margin of the premaxilla, the rostrodorsal orientation of the nasal process of the premaxilla, an oval orbital fenestra, vertical orientation of the postorbital bar with the presence of a depression and strut on the lateral surface of the postorbital process of the jugal, the inset and braced ventral end of the jugal process of the postorbital, and presence of the subocular process of the postorbital. Some