Geometric Morphometrics

The results of my GM analyses do not support the use of the method for quantitative tests of taxonomic hypotheses. When the identities of the specimen are known a priori, it is trivial to visualize the two ontogenetic trajectories in PC space (Fig. 2) and to recognize that the taxa share occupy fully nonoverlapping shape spaces. However, agglomerative hierarchical clustering (a method that does not consider a priori classifications, only the data) fails to recover these morphospaces as “clusters” (Fig. 3), indicating that the species morphospaces are not statistically emergent (i.e., the data do not form discoverable clusters). With PC 1 included, the ontogenetic signal overwhelms any phylogenetic signal; while it is unlikely that the clusters would be interpreted as pertaining to many distinct taxa, due to their obvious differences in size and maturity, it would be impossible to quantitatively determine which individuals belonged to which taxon, and how many taxa were present. Excluding PC 1 from the clustering analysis (Fig. 4) effectively factors ontogeny out, but typically overcorrects to a single cluster solution, because the two Alligator species are, overall, quite similar—they are separated along PC 2, but there is more variation within each taxon along that axis than there is range separating them. The only instances in which the clustering algorithm came close to finding the correct taxonomy were those in which either the adult Alligator sinensis or the juvenile Alligator mississippiensis were excluded from the analyses. This is unsurprising, because these are the groups that come closest to each other along PC 2, which is the only axis that separates the two taxa. Elimination of one group thus inflates the apparent difference between the morphospaces occupied by each Alligator species. In sum, GM fails to empirically recover the known taxonomy of the trial dataset.

Furthermore, in all iterations of the GM analysis, the Caiman crocodilus individual clustered within a species of Alligator. The Alligator ontogenetic series dominate the variation in the sample and thus also dominate the signal inherent in the PC space. In a dataset like this, the singleton taxon would need to be radically different from all other specimens to fall clearly outside the morphospaces of the other taxa—but in this case, it seems unlikely that workers would mistakenly include it in the ontogenetic series in the first place. Despite the numerous character differences between Alligator and Caiman, nothing in the morphospace plots would suggest that the Caiman individual was not an alligator. Even large samples of both Alligator species were not statistically emergent, and this problem is only compounded when acknowledging the possibility that some specimens may pertain to an unexpected third taxon. We should expect that extinct ecosystems hosted multiple closely related species, just as modern ecosystems do today even at high trophic levels, and therefore this phenomenon is troubling. It is difficult to envision how a GM analysis of a fossil dataset could adequately account for the possibility that unsuspected new taxa are included, especially if only one or a paucity of the individuals sampled pertain to that new taxon. Given that the two Alligator species do clearly separate in PC space, it may appear that visual examination of morphospace plots is the most effective way to interpret the results of GM analyses. However, this practice is not repeatable or empirical and does little more than add a quantitative veneer to a fundamentally qualitative taxonomic assessment. The data must speak for themselves if we seek to draw species boundaries based on multivariate statistics alone.

The failure of the data to do so in the present analysis is concerning. While the two Alligator species are overall quite similar, they are morphologically distinguishable and have never been suggested to be synonymous. The failure of morphometric methods to recover obviously distinct groups in morphospace suggests that GM cannot effectively discriminate between anatomically similar species, especially when faced with ontogenetic and polymorphic variation within both. It is worth noting that GM analyses of closely related extant species often recover significant morphospace overlap between closely related species, and were their identities not known a priori, it is unclear how close an agnostic analysis would come to the accepted taxonomy (e.g., Ruane Reference Ruane2015; Ferreira-Cardoso et al. Reference Ferreira-Cardoso, Billet, Gaubert, Delsuc and Hautier2020; Baird et al. Reference Baird, Ernst, Waurick, Blom and Bibi2023; Viacava et al. Reference Viacava, Blomberg and Weisbecker2023). GM may be seen, then, as highly susceptible to type II error (false negatives, or failures to recognize species that are present in a dataset). Furthermore, sampling biases also introduce significant potential for type I error (false positives, or erroneous recognition of new taxa). No morphospace is free of gaps—individuals within populations vary independent of growth stage, sometimes significantly. If intermediate individuals are unknown, it is very possible that individuals from two extremes of a taxon’s morphospace would be mistaken for members of separate species, with the presence of a morphological gap between them taken as evidence in favor of separation. For example, two recent studies have suggested that one specimen of Velociraptor mongoliensis (Mongolian Academy of Sciences [MPC-D] 100/982) pertains to a new species due to an apparent gap in morphospace between it and other Velociraptor specimens (Powers et al. Reference Powers, Sullivan and Currie2020, Reference Powers, Fabbri, Doschak, Bhullar, Evans, Norell and Currie2022). While this is certainly plausible, with only four specimens included in the analysis, it remains possible that we are simply missing morphologically intermediate V. mongoliensis individuals and that this “gap” is a sampling artifact attributable solely to the low sample size. GM may, however, serve as an effective “first pass” to identify morphologically divergent specimens that may represent distinct species and to aid identification of diagnostic characters between species delimited under other criteria. Campione and Evans (Reference Campione and Evans2011) identified diagnostic characters for the two accepted species of Edmontosaurus in light of their morphometric analyses, and in the present study, GM revealed that A. sinensis is characterized by a dorsoventrally taller skull than A. mississippiensis throughout ontogeny. However, for the reasons noted, I do not consider morphometric analyses alone to be methodologically or epistemologically sufficient for testing taxonomic hypotheses.

Cladistic Analysis of Ontogeny

Four of my attempts at cladistic analysis of ontogeny fail to yield consensus topologies that indicate the correct phylogenetic and ontogenetic status of the specimens in my dataset (Fig. 5). None of these analyses corroborated the prediction by Zietlow (Reference Zietlow2020) that cladistic analysis of ontogeny would recover a clean divergence between the sampled species. While two out-group protocols did recover strict consensus trees with basal divergences, these divergences did not sort OTUs along clearly phylogenetic or ontogenetic lines. Instead, one clade comprised only juvenile A. mississippiensis, and the other an apparent growth series of A. sinensis, with C. crocodilus and adult A. mississippiensis placed as its most mature members (forming Clade A). Thus, these topologies have the dubious distinction of conveying both misleading phylogenetic signal and misleading ontogenetic signal. In a paleontological study where species identity is unknown (or the question of focus), it would be impossible to determine how many species are represented within the ontogram based on its topology alone. Two other protocols recover a highly asymmetrical strict consensus topology without a basal divergence, and in each, A. sinensis is placed within the A. mississippiensis growth series. Zietlow (Reference Zietlow2020) suggested that such a topology could also be consistent with multiple species, if terminal branches showed “homologous sets of intraspecific variation.” This tree would, presumably, represent one in which the ontogenetic signal is dominant (perhaps due to similar ontogenetic sequences in both taxa), forcing traits specific to one species to optimize as convergences at different points along the ontogenetic trajectory. However, this pattern does not manifest in the present analysis. Rather, putative ontogenetic characters (which are, actually, the phylogenetic characters that distinguish the two species) optimize with two state changes—one from the condition in A. mississippiensis to that in A. sinensis, followed by a reversal to the plesiomorphic state in adults of the former species. This is important to note, because apparent reversals of large suites of ontogenetic characters have been found in prior studies employing cladistic ontogeny—most notably, Carr (Reference Carr2020) reported many reversals to putatively juvenile states among adult Tyrannosaurus rex. My results suggest that these patterns warrant scrutiny. In summary, cladistic analysis of ontogeny did not recover a correct taxonomy, nor did it accurately describe the sequence of character changes that occur during ontogeny in either taxon in four of five analytical trials. One analytical protocol does, however, yield a result that conforms to expectations articulated by Zietlow (Reference Zietlow2020). When C. crocodilus is excluded from the analysis, and the analysis is rooted on the artificial embryo OTU, the single resultant ontogram topology does feature a basal bifurcation into two clades (Fig. 6A), each corresponding to a single species, and in which more “derived” positions are occupied by larger and presumably more mature specimens. While this may seem to validate use of cladistic analysis of ontogeny for paleontological datasets, I consider it to be essentially a “fluke” arising from ideal conditions. My artificial embryo OTU is a mosaic of scores derived from the juvenile exemplars of A. mississippiensis and A. sinensis; while most scores were identical to the A. sinensis exemplar (the smallest specimen), characters describing the presence or absence of features seen in A. sinensis but not A. mississippiensis were scored “absent” in the artificial embryo. This polarized the analysis such that autapomorphies of both taxa were treated as absent at the base of the tree, allowing the analysis to recover reciprocally monophyletic species “clades.” Basing the artificial embryo out-group solely on the exemplar juvenile of A. sinensis (mimicking the typical approach, in which the smallest specimen to preserve each character is used to score the artificial embryo), this result does not obtain (Fig. 6B). Indeed, with C. crocodilus excluded and the analysis rooted on that specimen, A. sinensis is not monophyletic, and the ontogenetic signal is partially obscured. The situation would only be worse in a case in which adults were overrepresented relative to juveniles, which is common in paleontological studies; if only adult A. mississippiensis were available for study, a researcher would have no reason to base scores for an artificial embryo on character states unique to these large specimens (and would, presumably, infer that those features are lost during ontogeny). Furthermore, this analytical iteration is predicated upon exclusion of an “interloper” specimen (C. crocodilus) from the dataset—in other words, it is based to some degree on a priori knowledge that is impossible to obtain for paleontological analyses. In sum, this iteration shows only that in an ideal case, cladistic ontogeny can work as predicted, but given the challenges posed by inclusion of a single specimen belonging to an unrecognized additional species and the practical reality that full ontogenetic series of all included species may not be represented by the fossil record, this is faint praise.

Beyond my own empirical tests, however, it is worth exploring cladistic ontogeny at a deeper level due to its apparent success when applied to fossil datasets. It is possible that my trial dataset differs in some fundamental way from those assembled for fossil datasets. As in exemplar uses of cladistic ontogeny such as those of Carr (Reference Carr2020) and Zietlow (Reference Zietlow2020), I compared specimens over a range of body sizes and presumed ontogenetic stages and strove to codify every morphological character difference that was anatomically unambiguous and repeatably scoreable. My analytical protocol, however, does differ from these previous approaches in three key respects. First, my dataset has a relative paucity of missing data compared with paleontological datasets, but having more data should, if anything, improve my analyses rather than hinder them. Second, Zietlow (Reference Zietlow2020) did not treat multistate characters as ordered. This is clearly problematic when considering ontogenetic characters, which we may expect to change gradually and unidirectionally—for example, several characters in Zietlow’s (Reference Zietlow2020) dataset described the absolute size of certain elements, and treating these characters as unordered did not penalize ontogram topologies that infer growth stages where bones grow quite suddenly without passing through intermediate character states or topologies in which a bone may actually shrink before growing again. Carr (Reference Carr2020) did, however, use ordered characters in his analysis, so my use of ordered characters is not at odds with all prior implementations of this method. More problematically, Carr (Reference Carr2020) reported an analytical protocol in which taxa were iteratively added to the ontogram search to determine which specimens induced the recovery of multiple MPTs; these specimens were considered wildcards and were removed from the analysis a priori. Treatment of wildcard specimens in phylogenetic analyses is a topic worthy of discussion in its own right; some OTUs may be so incomplete that they result in a net loss of information from the tree search, but this is an extreme case, and I concur with perspectives generally favoring inclusion of labile OTUs in the tree search, but removing them a posteriori to report reduced strict consensus tree topologies (Wilkinson Reference Wilkinson1995; Kearney and Clark Reference Kearney and Clark2003; Goloboff and Szumik Reference Goloboff and Szumik2015). In any case, identifying any OTU with multiple most parsimonious positions as a “wildcard” seems like an exaggeration, and the result is an analysis that purposefully eliminates alternative most parsimonious topologies and does not correctly communicate what ambiguity may exist within the dataset. My use of conventional tree search approaches and consensus trees, therefore, may not precisely mirror Carr (Reference Carr2020), but may be seen as indicating the kinds of alternative topologies that his analytical protocol eliminates from consideration.

A further consideration is the possibility that A. mississippiensis and A. sinensis are more dissimilar from one another than any undetected fossil species would be, and thus that Alligator is an unsuitable model system for assessing the efficacy of cladistic ontogeny. It is true that the two taxa differ in many characters, including many that are ontogenetically invariant and others that appear during growth. However, the presence of a “split” manifesting in an ontogram containing multiple taxa, as predicted by Zietlow (Reference Zietlow2020), would logically be more likely to occur in situations where the two taxa are differentiated by a large number of characters. The two species of Alligator diverged in the Eocene and have had about 50 million years of independent evolution to acquire autapomorphies (Wu et al. Reference Wu, Wang, Zhou, Zhu, Nie and Wang2003). If cladistic ontogeny cannot reliably detect the difference between two species that diverged shortly after the extinction of the non-avian dinosaurs, it is difficult to envision how it could possibly be a reliable means of delimiting shallowly diverged, possibly sympatric species that are known only from an incomplete fossil record.

Beyond my empirical failure to validate the method, there are several epistemological considerations that make cladistic analysis of ontogeny an unsuitable method for testing taxonomic hypotheses. The use of an “artificial embryo” as the out-group OTU is fraught with difficulty. The artificial embryo OTU is, in practice, a collation of the hypothesized immature states for each character, based upon the least mature specimens for which each character is preserved. This runs the obvious risk of inferring an “embryonic” condition that is actually informed by individuals that have already progressed significantly far along their ontogenetic trajectory. The most extreme case was a recent cladistic ontogeny analysis of growth among alioramin tyrannosaurids, in which the approximately 9-year-old holotype specimen of Alioramus altai was used as the sole source of “immature” characters and was scored identically to the artificial embryo (Foster et al. Reference Foster, Brusatte, Carr, Williamson, Yi and Lü2022). Determination of which specimens are “least mature” is typically made based on size, rather than osteohistological data—and indeed, several analyses include absolute size among their ontogenetic characters (Ezcurra and Butler Reference Ezcurra and Butler2015; Carr et al. Reference Carr, Varricchio, Sedlmayr, Roberts and Moore2017; Carr Reference Carr2020; Zietlow Reference Zietlow2020). This process results in the out-group OTU representing the character states observed in the smallest specimens to display each character, meaning that it is a composite that may not represent the true combination of characters at any stage of development, and thus forcing the analysis to interpret these states as “immature” and enforcing the ontogenetic trajectory that had previously been inferred based on size alone. Therefore, despite claims that cladistic ontogeny is advantageous in offering a size-independent means of maturity estimation (Brochu Reference Brochu1996; Carr Reference Carr2020; Zietlow Reference Zietlow2020), these analyses are not size independent in practice. It is perhaps unsurprising, then, that published analyses employing cladistic ontogeny typically find a robust correlation between size and maturity. If the ontogenetic character matrix includes multiple species, the artificial embryo will represent a combination of ontogenetic and phylogenetic information, making it very difficult to interpret the resultant ontogram topology. Any node may be supported by a mixture of ontogenetic and phylogenetic characters, making it difficult to determine which “clades” represent growth stages, which represent species, and which represent some combination of both (e.g., a valid species and immature members of a larger sister taxon). A similar problem has emerged in invertebrate paleontology through the use of “semaphoront coding” (Lamsdell and Selden Reference Lamsdell and Selden2013), which scores immature and adult members of species as separate OTUs, and thereby generates “phylogenetic trees” that do not actually contain a purely phylogenetic signal (Sharma et al. Reference Sharma, Clouse and Wheeler2017). Both semaphoront coding and cladistic ontogeny, then, produce “tree-shaped objects” (Wheeler and Pickett Reference Wheeler and Pickett2007) from mixed data sources that cannot be readily interpreted. Even if it were simple to distinguish between these data sources on an ontogram topology, published expectations for how different scenarios should manifest in an ontogram lack explicit criteria and include topologies both with and without deep divergences (Zietlow Reference Zietlow2020), essentially meaning that almost any conceivable topology could be interpreted in different ways by different workers. Most fundamentally, progressive ontogenetic change occurs within individual organisms and, as such, does not meet the assumption of hierarchical organization that is inherent to Hennig’s model of phylogenetic systematics (Sharma et al. Reference Sharma, Clouse and Wheeler2017), despite claims to the contrary (Brochu Reference Brochu1996; Zietlow Reference Zietlow2020). “Adult” is not a subgroup of “juvenile” in the way that species are subgroups of larger clades. Thus, it may be debated whether cladistic ontogeny is even philosophically appropriate for establishing ontogenetic sequences or staging criteria when the taxonomy is known a priori. In summary, a host of philosophical and practical challenges make cladistic ontogeny unsuitable for testing taxonomic hypotheses in the fossil record, and I suggest that the results of prior studies using the method be interpreted with healthy skepticism until they can be confirmed through other, more robust analytical protocols.

Ontogenetically Invariant Characters

Multivariate ordination of my discrete character matrix recovers two obvious linear clusters (Fig. 7A), which correspond to the two species of Alligator. Axis 1 correlates closely with centroid size (Fig. 7B) and can be interpreted as the primary ontogenetic trajectory; the two species have approximately parallel trajectories, suggesting broadly similar ontogenetic trends (as we may expect among closely related taxa). Axis 2, then, can be interpreted as the primary phylogenetic axis. Notably, the spectacled caiman individual plots between the two species of Alligator, and is approximately equally spaced from both along axis 2 and in the region of similarly sized Alligator individuals of both species along axis 1. Despite the visually obvious separation of these ontogenetic trajectories, hierarchical clustering analysis does not elucidate a correct taxonomy (Fig. 8); instead, the dendrogram clearly shows a primarily ontogenetic signal in which juveniles diverge from adults, after which each growth stage separates along taxonomic lines (excepting C. crocodilus, which clusters with A. mississippiensis). Removing PCoA axis 1 from the clustering analysis results in a single cluster scenario, so removing the influence of ontogenetic variation does not clarify the taxonomic composition of the sample.

In sum, 23 of 189 characters (~13%) were highly phylogenetically significant, and of these, 20 showed no signs of ontogenetic variation. Thus, we can affirm that closely related living species can and do possess ontogenetically invariant characters that allow confident determination of their identities from apomorphic evidence alone. Therefore, the repeated failure of existing multivariate methods might be of less concern than it would outwardly appear. While ontogenetic variation is predominant in my dataset, and some diagnostic characters do occur in adults only, it is also clear that individuals are born with characters that do not change during ontogeny. Importantly, these characters need not simply be general characters shared by every species in their clade, but can instead be highly diagnostic traits that distinguish close relatives and obviate the need for multivariate statistical approaches. Even very young Alligator displays a suite of ontogenetically invariant characters that show no evidence of polymorphism, and while the two species do become increasingly distinct during growth, this is encouraging evidence that fossils of young animals may similarly already possess important diagnostic characters. The question now becomes whether or not it is possible to predict which characters are ontogenetically invariant in extinct taxa—and therefore, which characters are “good” characters for testing taxonomic hypotheses.

Reviewing the this list of characters, it should be immediately evident that ontogenetically invariant characters are overwhelmingly associated with neurovascular foramina, pneumatic recesses, and the sutural topology of the skull. Characters associated with muscle scars, the shapes of bone margins, ornamental features, and overall proportions show far less tendency to be ontogenetically invariant and are in fact among the most ontogenetically variable character types in my dataset. The asymmetric distribution of ontogenetically invariant characters suggests that their invariance is not some evolutionary quirk unique to Alligator or a similarly exclusive clade; rather, I propose that these characters are invariant due to broadly conserved aspects of the vertebrate developmental program and are thus generally applicable to a range of study systems.

Despite the common lay perspective that bones are the “scaffold” or “foundation” for the soft tissues of the body, bones appear fairly late in development, and their patterning and ultimate morphology are shaped by the soft tissues that precede them. Of the most informative character types identified, two (cranial foramina and pneumatic recesses) relate to soft tissue systems that are laid down before the onset of cranial skeletogenesis. In human embryology, cranial nerve development occurs quite early—most cranial nerves appear between developmental days 26–38 (Carnegie Stages 12–15), and by day 53 (end of Carnegie Stage 20), all nerves are both present and have reached their target organs (Smit et al. Reference Smit, Jacobs, Bais, Meijer, Seinen, de Bree and Veldhuis2022). The cranial arteries also appear early in development (Takahashi et al. Reference Takahashi, Tanaka, Fujita and Tomiyama2012) and assume an adult branching pattern by approximately ~52 days of development (Paget Reference Paget1948). The onset of cranial bone development is far later—for example, in humans the sphenoid complex begins to form at 16 weeks (~112 days) of development (Mano et al. Reference Mano, Wood, Oladipupo, Reynolds, Taylor, Durham, Cray, Vinyard, DeLeon and Smith2021). Cranial foramina form not as a result of developing blood vessels and nerves “tunneling” through the bone to reach their targets, but because the developing bones envelop the preexisting neurovasculature as they condense from mesenchyme. Indeed, in black caiman (Melanosuchus niger) embryos, foramina for the hypoglossal nerve appear in the basal plate just as it begins to chondrify and long before ossification (Vieira et al. Reference Vieira, Santos, Hirano, Menezes-Reis, Mendonça and Sebben2019). The neurovascular structures are not passive participants in this process—in chicken (Gallus) embryos, chondrogenesis of the occipital bones is interrupted in the immediate vicinity of primordial jugular, carotid, and hypoglossal foramina, which presumably protects the contents of these foramina from being stenosed or severed by encroachment of the surrounding bone (Akbareian et al. Reference Akbareian, Pitsillides, Macharia and McGonnell2015). It has been suggested that the nerves and blood vessels themselves actually initiate the slowdown in chondrogenesis that leads to the development of a foramen to transmit them (Akbareian et al. Reference Akbareian, Pitsillides, Macharia and McGonnell2015). Cranial nerve foramina form during embryonic development in response to the position of nerves and blood vessels that are laid down very early in development, long before mesenchymal condensation and the later onset of chondro- or osteogenesis. Furthermore, dermal bone osteogenesis follows expansion of capillary networks within mesenchymal condensations, suggesting that these capillaries are a source of signals that promote ossification and that alterations to the vascular pattern can induce changes in skeletal morphology (Percival and Richtsmeier Reference Percival and Richtsmeier2013).

Pneumatic recesses in cranial bones are enigmatic structures of unclear function that show a high degree of variation. The epithelial sinuses housed in these recesses have a documented tendency to expand progressively during life, which has been noted in systems as diverse as Alligator (Witmer Reference Witmer1995; Dufeau and Witmer Reference Dufeau and Witmer2015) and humans (Scuderi et al. Reference Scuderi, Harnsberger and Boyer1993). The growth of cranial sinuses (and therefore the recesses they leave in the cranial skeleton) is often described as “opportunistic,” given the apparent tendency of these sinuses to expand as far as they can. Witmer (Reference Witmer1997) proposed the “epithelial hypothesis” of sinus growth, positing that sinus growth is driven by an intrinsic capacity of the epithelia to invade and excavate bone and is constrained only by the biomechanical integrity of the skull. This hypothesis explains much of the variability that is obvious in cranial sinuses, such as asymmetry and development of pathologic fistulae. Given the abundant observations of how ontogenetically and individually variable sinuses are, I and many of my colleagues have historically shied away from their use as taxonomic characters. And yet, my data for Alligator suggest that the basic pattern of pneumatic invasion of the cranial skeleton is highly diagnostic. While it is true that both Alligator species show progressive expansion of the cranial sinuses, the simple presence or absence of a pneumatic recess was consistent, as were large-scale patterns of pneumatization (such as confluence of the lateral and caviconchal recesses of the maxilla). Perhaps unsurprisingly, the precursors of cranial sinuses also appear early in development as nascent outpocketings of the respiratory cavity that are later enclosed by bone during condensation (Scuderi et al. Reference Scuderi, Harnsberger and Boyer1993; Witmer Reference Witmer1995). Unlike cranial nerves and blood vessels, not all cranial sinuses are present in embryo, but those that are not do appear quite early in postnatal ontogeny. In A. mississippiensis, all sinuses are present within a few months of hatching (Witmer Reference Witmer1995), and humans pneumatize the frontal sinus (the last sinus to form) by the second year of life (Scuderi et al. Reference Scuderi, Harnsberger and Boyer1993). It is possible that epithelial outpocketings are present as sinus precursors in embryo—if so, postnatal appearance of these sinuses may relate simply to the fact that a sinus cannot pneumatize before an animal takes its first breath and allows air to fill the space, or that pneumatization can be inhibited for some period of time due to other anatomical factors. In support of this hypothesis, the human frontal sinus appears to develop as an outgrowth of the anterior ethmoidal sinus (which is present at birth) and invades the frontal only after the red marrow that initially inhabits its space transitions to yellow marrow (Scuderi et al. Reference Scuderi, Harnsberger and Boyer1993). The consistency of which bones are pneumatized within species suggests that the “epithelial hypothesis,” as currently understood, is missing a component of higher-order governance that determines how many pneumatic diverticulae form, which bones they invade, and what terminal morphology they achieve. The similarity in cranial anatomy between the two Alligator species precludes explanation of their divergent pneumatization patterns (e.g., vomerine recess in A. mississippiensis, palatine bulla in A. sinensis) as solely reflecting differences in mechanical constraints on their skulls. While the intertympanic sinus system of crocodylians is not diagnostic in hatchlings, it has been demonstrated that the adult morphology of the intertympanic sinuses is diagnostic at low taxonomic levels (Perrichon et al. Reference Perrichon, Hautier, Pochat-Cottilloux, Raselli, Salaviale, Dailh and Rinder2023), despite overall similarity in cranial shape, which appears to corroborate this interpretation. In humans too, despite a high degree of variation in sinus size and extent, the basic pattern of pneumatization is highly constrained—humans develop sinuses in the maxilla, ethmoid, sphenoid, and frontal, and absence of any sinus is both rare and typically correlated with pathological development of the craniofacial skeleton (Jafari-Pozve et al. Reference Jafari-Pozve, Sheikhi, Ataie-Khorasgani and Jafari-Pozve2014; Grine et al. Reference Grine, Post, Greening, Crevecoeur, Billings, Meyer and Holt2024). The human palatines and vomers, despite being in direct apposition with the respiratory tract, do not pneumatize—and the presence of a pneumatic recess in the extremely thin vomer of Alligator suggests that this is not simply a consequence of their delicate construction. Further research is required to resolve the dichotomy between sinus distribution, which appears tightly regulated, and sinus expansion, which does appear to be fundamentally opportunistic and occasionally leads to pathology.

One further relevant point is that there is no evidence of any cranial sinus being lost during ontogeny by overgrowth of bone that obliterates its ostium. Nanotyrannus individuals have a pneumatic recess in the quadratojugal that is absent in T. rex (Witmer and Ridgely Reference Witmer and Ridgely2010; Carr Reference Carr2020). An apparent ontogenetic acquisition of this sinus was reported in Daspletosaurus horneri and interpreted as evidence that this feature is ontogenetically variable in tyrannosaurs (Carr et al. Reference Carr, Varricchio, Sedlmayr, Roberts and Moore2017), despite this being directly opposite to the pattern required for Nanotyrannus to grow into T. rex. More recently, it has been proposed that this feature is polymorphic in D. horneri (Coppock et al. Reference Coppock, Powers, Voris and Currie2025), and no evidence for ontogenetic acquisition or loss of this feature exists, but ontogenetic loss of a pneumatic recess is unknown in other species; another large theropod, Allosaurus, appears to have had a the same complement of pneumatic sinuses throughout posthatching ontogeny (Rauhut and Fechner Reference Rauhut and Fechner2005). Larson (Reference Larson, Parrish, Molnar, Currie and Koppelhus2013) similarly reported a “one-to-one” correspondence between pneumatic diverticulae in juvenile and adult Struthio camelus. Dufeau and Witmer (Reference Dufeau and Witmer2015) suggest that the laterosphenoid recess is lost during crocodylian ontogeny, but the pneumatic space within the bone persists in all specimens studied herein; only the ostium of this recess is lost, turning the laterosphenoid recess into a blind cavity. This recess is unique in that it enters the laterosphenoid via the laterosphenoid-prootic sutural surface, rather than an external ostium, and closure of this ostium is likely attributable to increased sutural interdigitation. “Typical” pneumatic recesses with external ostia are not documented to close during ontogeny, and even when the ostium is lost, the pneumatic cavity itself persists as proof that the bone is pneumatic. In sum, we can conclude that the topological distribution of pneumatic recesses is highly species specific and expect that only very young members of a species may lack pneumatic recesses present in the adults. The size and morphology of these recesses may readily change during growth, but growth appears to be unidirectional—we should not expect ontogenetic transformations in which pneumatic recesses shrink or close, as was required to justify Nanotyrannus specimens representing immature Tyrannosaurus specimens.

My data on Alligator also suggest that sutural topology of the cranial skeleton is ontogenetically invariant and shows little polymorphism. By this, I mean not the form of the joint surfaces between bones (which show an obvious ontogenetic trend toward interdigitation), but how the bones contact—which bones form joints with which others, the discrete processes, rami, or laminae of each bone, and how the bones relate to cranial openings. In the present dataset, presence of a subnarial process of the nasal is itself sufficient to identify a specimen as A. mississippiensis, and presence of a descending process of the prefrontal is likewise sufficient to identify a specimen as A. sinensis. The ossification of skull bones follows patterns laid down very early in development, which are dictated by gene expression in the embryonic brain and both sensory and ectodermal epithelia (Noden Reference Noden1988; Hanken and Thorogood Reference Hanken and Thorogood1993; Hu et al. Reference Hu, Marcucio and Helms2003; Wada et al. Reference Wada, Javidan, Nelson, Carney, Kelsh and Schilling2005; Brugmann et al. Reference Brugmann, Goodnough, Gregorieff, Leucht, ten Berge, Fuerer, Clevers, Nusse and Helms2007; Bhullar et al. Reference Bhullar, Morris, Sefton, Tok, Tokita, Namkoong, Camacho, Burnham and Abzhanov2015). While current research has so far allowed confident identification of the mechanisms responsible for mostly “coarse” morphological changes, such as the fusion of the avian premaxillae into a beak (Bhullar et al. Reference Bhullar, Morris, Sefton, Tok, Tokita, Namkoong, Camacho, Burnham and Abzhanov2015), there is no reason to think “finer” details such as the presence or absence of a bony process or the position of a bony contact relative to some landmark are not governed by similar signaling cascades. Indeed, embryos of different galloanseran bird species show distinct developmental trajectories from the first appearance of facial landmarks (Smith et al. Reference Smith, Percival, Young, Hu, Schneider, Marcucio and Hallgrimsson2015), leading the authors to propose that morphological differences among adults of closely related species can and do arise from modification to the early stages of development. The development of the vertebrate skull is complex and represents the influence of multiple soft-tissue systems in addition to pleiotropic interactions between skull bones themselves (Percival et al. Reference Percival, Green, Roseman, Gatti, Morgan, Murray and Donahue2018), and possibly (as described in the functional matrix hypothesis), a strong to potentially overriding influence of postnatal mechanical loading (e.g., Moss Reference Moss1997a,Reference Mossb,Reference Mossc,Reference Mossd). While we certainly lack a general predictive model for skull morphology, available evidence makes it clear that the topological architecture of the skull is governed by early developmental events and that we therefore should not expect architectural changes to the skull during postnatal ontogeny.

I also found no evidence for ontogenetic loss of maxillary tooth positions in modern crocodylians. Expanded data collection from alligatoroid specimens in the AMNH Herpetology collection suggests that variation, if present, is exclusively on the order of ±1 positions, and shows no consistent relationship with body size (Fig. 10)—therefore, I interpret this character as polymorphic, but not ontogenetic. Indeed, Brown et al. (Reference Brown, VanBuren, Larson, Brink, Campione, Vavrek and Evans2015) found a similar pattern in both crocodylians and the Komodo dragon (Varanus komodoensis), suggesting that macropredatory reptiles may be generally characterized by ontogenetically stable maxillary tooth counts; however, the presence of an ontogenetic increase in tooth count in many lizards, basal archosauriforms, basal sauropodomorphs, and ornithischian and perhaps basal theropod dinosaurs (Rauhut and Fechner Reference Rauhut and Fechner2005; Brown et al. Reference Brown, VanBuren, Larson, Brink, Campione, Vavrek and Evans2015; Ezcurra and Butler Reference Ezcurra and Butler2015; Chapelle et al. Reference Chapelle, Barrett, Botha and Choiniere2019) indicates that ontogenetically invariant tooth counts are not a general feature of tetrapods. Maxillary tooth count is also interesting in that it provides direct rebuttal of proposed tooth loss in theropod ontogeny. Carr (Reference Carr1999) partially justified a loss of several maxillary tooth positions during tyrannosaurid ontogeny by analogy to crocodylians, citing Mook (Reference Mook1921), Wermuth (Reference Wermuth1953), and Iordansky (Reference Iordansky, Gans and Parsons1973). However, Carr (Reference Carr1999) did not accurately characterize the ontogenetic tooth loss reported by these authors. Mook (Reference Mook1921) identified the number of maxillary teeth below the orbit as undergoing an ontogenetic reduction in crocodylians; this observation is correct, but does not involve loss of maxillary tooth positions, but simply positive allometry of the snout that draws the entire toothrow forward, causing fewer teeth to lie ventral to the orbit. Both Wermuth (Reference Wermuth1953) and Iordansky (Reference Iordansky, Gans and Parsons1973) describe loss of the second premaxillary tooth in mature crocodylians, not reduction in maxillary or dental tooth count. This observation is correct, but the second premaxillary tooth is lost due to overgrowth of the first dentary tooth, resulting in local resorption and eventual obliteration of the premaxillary alveolus (Wermuth Reference Wermuth1953); however, the space for the former tooth persists, making the original dental formula clear. Therefore, none of these authors document a progressive loss of maxillary tooth positions during ontogeny in living archosaurs. Carr (Reference Carr1999) was therefore mistaken in citing these papers as precedent for an ontogenetic loss of maxillary teeth in tyrannosaurids, and indeed other paleontological research does not corroborate this claim. Carr (Reference Carr1999) proposed an ontogenetic reduction from 15 maxillary teeth in “stage 1” juveniles to 13 in “stage 3” adults of the tyrannosaurid Gorgosaurus libratus based on a sample of only 10 specimens and without any quantitative analysis. Currie (Reference Currie2003a) found no statistical evidence for ontogenetic reduction in tooth count in Gorgosaurus, and two recently described individuals smaller than those studied by Carr (Reference Carr1999) both have 14 maxillary teeth (Voris et al. Reference Voris, Zelenitsky, Therrien, Ridgely, Currie and Witmer2022), which is the most common dental count for this genus. Furthermore, the youngest known individual of Tarbosaurus bataar has only 13 maxillary teeth, like most Tarbosaurus adults (Tsuihiji et al. Reference Tsuihiji, Watabe, Tsogtbaatar, Tsubamoto, Barsbold, Suzuki, Lee, Ridgely, Kawahara and Witmer2011). Carr et al. (Reference Carr, Varricchio, Sedlmayr, Roberts and Moore2017) proposed that another tyrannosaurid, Daspletosaurus torosus, gained and then lost teeth as it grew, but this observation is based upon a long-standing misidentification of a juvenile specimen, which is more convincingly interpreted as a young G. libratus (Voris et al. Reference Voris, Zelenitsky, Therrien and Currie2019). Without this specimen, all D. torosus individuals have between 14 and 16 maxillary tooth positions and thus are consistent with the range of variation seen in crocodylians and other tyrannosaurs. Therefore, the available evidence favors the interpretation that tyrannosaurids, like modern crocodylians, did not lose maxillary tooth positions during growth and instead showed limited variation about a modal tooth count that was particular to each species. Suggestions to the contrary were based upon small sample sizes, misidentified specimens, and erroneous citation of prior literature.

The ontogenetic invariance of dental count is of interest beyond Tyrannosauridae, however, for two main reasons. First, tooth count is a widely applicable and presumably homologous character among most tetrapods, allowing a rare example of directly comparable character states among a wide array of taxa. Second, the generation of teeth is yet another process mediated by epithelial–mesenchymal interaction during development. The first teeth in Alligator appear at approximately the same time as the cranial nerves and arteries, although the ultimate patterning of the toothrow and determination of the final number of functional tooth positions continues to hatching (Westergaard and Ferguson Reference Westergaard and Ferguson1990). While the first embryonic tooth generation is formed from cells derived from odontogenic placodes, an epithelial cell population termed the dental lamina replaces it and persists as a source of odontogenic stem cells throughout life (Tsai et al. Reference Tsai, Abdelhamid, Khan, Elkarargy, Widelitz, Chuong and Wu2016). The persistence of a dental lamina permits Alligator (and toothed amniotes generally) to undergo continuous tooth replacement (polyphyodonty), and this cell population plays a key role in patterning the toothrow, such as determining the number of tooth positions (Westergaard and Ferguson Reference Westergaard and Ferguson1990). Given the previously discussed tendency of epithelial tissues to maintain and create space for themselves, it seems plausible to hypothesize that the persistence of a dental lamina precludes ontogenetic loss of tooth positions. The early-diverging theropod Limusaurus inextricabilis is documented to lose tooth positions ontogenetically, and this appears to result from a complete cessation of tooth replacement that is consistent with degeneration of the dental lamina (Wang et al. Reference Wang, Stiegler, Amiot, Wang, Du, Clark and Xu2017). However, in Limusaurus, void spaces persist in the maxilla and dentary in the former positions of the dental alveoli, suggesting that the dental lamina alternatively may persist but become inactive. In any case, we can observe that, like the other character types described earlier, tooth patterning is a process that occurs early in development (long before the condensation of the eventual tooth-bearing bones) and shows no ontogenetic variation in my model system. This result may be broadly applicable, given that extant macropredatory reptiles also show no sign of ontogenetically variable tooth counts, but the phylogenetic distribution of ontogenetically stable dental counts requires further study (a goal of future work by myself and others).

In summary, characters that derive from patterns and topology laid down in early stages of embryonic development appear to be fixed throughout later ontogeny, irrespective of how the skeleton itself is later modified. The “architectural plan,” so to speak, is fixed from early embryology, and certainly by birth or hatching. While we lack a cohesive understanding of how increasingly granular cranial characters develop, known mechanisms make it clear that the architecture of the cranial skeleton is controlled by the soft tissues that are laid down long before the initiation of osteogenesis and are in fact active signaling centers governing osteogenesis itself. These developmental mechanisms are broadly conserved among vertebrates, so while I welcome further studies in other extant study systems, I am confident that this general principle will hold for species that have comparable developmental programs (e.g., metamorphic amphibians may not be subject to the same constraints). Anecdotal data from disparate systems corroborate my expectation. It is perhaps of note that the single consistent cranial character differentiating lions from tigers (a textbook example of osteologically similar living species) is an architectural character—the posterior level of the nasofrontal suture relative to the maxillofrontal suture (Williams et al. Reference Williams, Loveridge, Newton and Macdonald2015). Similarly, Voris et al. (Reference Voris, Zelenitsky, Therrien, Ridgely, Currie and Witmer2022) and Coppock et al. (Reference Coppock, Powers, Voris, Sharpe and Currie2024) found that an overwhelming majority of apparently ontogenetically invariant characters among derived tyrannosaurid dinosaurs related to the sutural relations of skull bones. The nasal capsule forms before skeletogenesis, perhaps explaining both the ontogenetic invariance of cranial pneumatization in Alligator and the ontogenetically invariant (and apparently autapomorphic) absence of an “S-loop” in the nasal passage of the ornithischian dinosaur Parasaurolophus, despite progressive growth of an elaborate cranial crest containing the nasal passage (Farke et al. Reference Farke, Chok, Herrero, Scolieri and Werning2013). In contrast, my results show that non-architectural characters such as the shape of bone contours, the gross proportions of the skull, dermal bone ornamentation, and muscle scar appearance are characterized by high degrees of ontogenetic variation. That is not to say that any of these characters cannot be diagnostic; for example, my data indicate that A. sinensis is distinguished by a taller posterior skull than A. mississippiensis throughout life, and the apomorphically broad snout of Caiman latirostris is similarly discernible, even in hatchling individuals (Fernandez Blanco et al. Reference Fernandez Blanco, Bona, Olivares and Desojo2015); however, my results do suggest that characters relating to the topological relationships of the cranial skeleton and organ systems are more reliable than characters such as skull proportions, muscle scar development, or degree of ornamentation. These traits have been identified as ontogenetic by generations of anatomists before me, including in work focused specifically upon crocodylians (e.g., Fernandez Blanco et al. Reference Fernandez Blanco, Bona, Olivares and Desojo2015; Morris et al. Reference Morris, Vliet, Abzhanov and Pierce2019); I consider the significant result of the present work identifying not which characters do vary during ontogeny, but rather the identification of those that do not.

I conclude that the answer to the final question posed in the introduction to this manuscript is “yes”—ontogenetically invariant characters both exist and occur following basic principles of embryonic development, even among sister species that are known to develop from a common embryonic morphology and remain superficially similar even in adulthood (Morris et al. Reference Morris, Vliet, Abzhanov and Pierce2019). The presence of differences in skull architecture, therefore, allows us to falsify the hypothesis that the character differences between two specimens are attributable to ontogenetic variation. I hope these results will prove relevant to continued investigations of the proposed “extreme ontogenetic changes” experienced by many extinct clades, most famously including non-avian dinosaurs, as well as taxonomic assessment of new discoveries and historical collections alike. It is certainly tempting to declare that many transformations involving “extreme” ontogenetic changes are invalid, and indeed some prior research has been criticized on developmental grounds—for example, Longrich and Field (Reference Longrich and Field2012) criticized the proposal that Torosaurus is the adult form of Triceratops partially on the grounds that such a hypothesis would require late ontogenetic addition of osteoderms, which is not observed in modern animals or in other ceratopsians (Farke Reference Farke2011). This principle would also cast doubt on the synonymy of Late Cretaceous pachycephalosaur genera, which is partially predicated on rearrangement of osteoderm ornaments (Horner and Goodwin Reference Horner and Goodwin2009; Goodwin and Evans Reference Goodwin and Evans2016). However, we cannot be sure that extinct species with anatomy unlike any modern animal did not have concomitant modifications to the developmental program without corroborating evidence from the fossil record itself. Here, “Rosetta Stone” specimens of potentially intermediate ontogenetic stage and exceptional preservational quality will have renewed importance, for they will allow us to test how applicable models derived from extant study systems are to extinct clades of interest. Several ceratopsians, for example, do appear to show an unexpected ontogenetic character change—exclusion of the supraoccipital from the foramen magnum (Horner and Goodwin Reference Horner and Goodwin2006; Currie et al. Reference Currie, Holmes, Ryan and Coy2016)—which is only recognizable due to plentiful fossil material and exceptional specimens of different ontogenetic stages. It is clear, however, that the results of the present study contrast sharply with prevailing interpretations of ontogeny as a “black box” that can be invoked to explain almost any character difference between specimens, and I predict that if “extreme ontogeny” proves to be real, we will find that it does not involve architectural modification to the skull and its soft tissues, but rather exaggeration of ontogenetic trajectories in proportion, shape, and ornamentation that exist in all amniotes.

Pursuant to the example that has formed a throughline in this paper: the “Dueling Dinosaurs” tyrannosauroid specimen (North Carolina Museum of Natural Sciences [NCSM] 40000) has now been demonstrated to be both somatically mature and apomorphically referable to Nanotyrannus lancensis (Zanno and Napoli Reference Zanno and Napoli2025), confirming that the controversial taxon is valid and not a juvenile form of T. rex and corroborating that characters such as absence of a subnarial foramen, presence of a sinus cavernosus, a laterally positioned vagus foramen, presence of a quadratojugal recess, and high maxillary and dentary tooth counts are phylogenetically informative and ontogenetically invariant in tyrannosauroids. It is worth noting that, as described earlier, continued research on juvenile tyrannosauroids has established that many of the ontogenetic trends required for Nanotyrannus to grow into Tyrannosaurus are not precedented in closely related taxa (Tsuihiji et al. Reference Tsuihiji, Watabe, Tsogtbaatar, Tsubamoto, Barsbold, Suzuki, Lee, Ridgely, Kawahara and Witmer2011; Voris et al. Reference Voris, Zelenitsky, Therrien and Currie2019, Reference Voris, Zelenitsky, Therrien, Ridgely, Currie and Witmer2022; Coppock et al. Reference Coppock, Powers, Voris, Sharpe and Currie2024; Raun et al. Reference Raun, Coppock, Badamgarav, Tsogtbataar and Currie2026), and that Nanotyrannus, contra Voris et al. (Reference Voris, Zelenitsky, Kobayashi, Modesto, Therrien, Tsutsumi, Chinzorig and Tsogtbaatar2025), shares no exclusive apomorphies with Tyrannosaurus (Currie Reference Currie2003b; Zanno and Napoli Reference Zanno and Napoli2025). It appears that the stratigraphic co-occurrence of these taxa and the (perceived) juvenile status of all previously reported specimens of Nanotyrannus were considered to supersede the abundant morphological evidence that they were distinct taxa; these lines of evidence are circumstantial and logically irrelevant to taxonomic hypotheses. To be a juvenile T. rex, a specimen must be both a juvenile and identifiable as T. rex; merely being a juvenile tyrannosauroid does not meet this burden of proof. The implausibility of the “juvenile T. rex hypothesis” is perhaps best evidenced by the fact that Carr (Reference Carr2020) described it as a “secondary metamorphosis” and compared it directly to the abrupt morphological transformations seen in sexual maturity among some teleost fish, rather than any other archosaur. It is difficult to see why the “simplest hypothesis” was that these specimens were juveniles of T. rex, despite sharing no unique characters with T. rex and mounting evidence that other tyrannosaurids did not show comparable ontogenetic trajectories. Perhaps Occam’s razor needs sharpening.

The “Dueling Dinosaurs” specimen provided a wealth of anatomical evidence about Nanotyrannus from an individual that was functionally somatically mature, meeting an exceptionally high burden of proof for the validity of Nanotyrannus. Griffin et al. (Reference Griffin, Bugos, Poust, Morris, Sombathy, D’Emic, O’Connor, Petermann, Fabbri and Colleary2025) independently followed this paper with evidence that the holotype of Nanotyrannus itself was mature, which suggests that the entire Nanotyrannus debate was built upon a false premise. But what if these specimens were, like the holotype (Burpee Museum of Natural History [BMRP] 2002.4.1) of the newly recognized species Nanotyrannus lethaeus , rapidly growing juveniles (Woodward et al. Reference Woodward, Tremaine, Williams, Zanno, Horner and Myhrvold2020; Zanno and Napoli Reference Zanno and Napoli2025)? Based upon the results presented herein, I argue that the anatomical evidence alone would have been inconsistent with ontogeny and allowed these specimens to be correctly identified. While osteohistology provides an invaluable wealth of information and can inform taxonomic hypothesis testing, it should not hold a premium over the actual morphological evidence that is used for taxonomy and systematics—especially given that, as I hope I have shown convincingly, ontogenetic character variation is predictable and juveniles do show diagnostic traits of their species from early ontogenetic stages. Ironically, the osteohistological evidence of maturity in Nanotyrannus specimens was needed to prove that such evidence is not required to resolve similar taxonomic debates in the future. The framework I have developed here holds promise to clarify many uncertainties in amniote taxonomy and systematics, especially as similar studies are completed over a greater phylogenetic and taxonomic scope.

The preceding discussion warrants a final word of caution. Establishing that a character is not ontogenetically variable is not equivalent to establishing that it is not intraspecifically variable. The overwhelming focus on ontogeny belies the numerous sources of intraspecific variation that may exist superimposed upon each other. Trait polymorphism is perhaps the most obvious, and as seen earlier can allow even ontogenetically invariant characters to vary within species. For example, the hypoglossal canal in the human skull is partly or fully divided by a bony septum in ~20% of individuals (Guarna et al. Reference Guarna, Lorenzoni, Franci and Agliano2023; Kalthur et al. Reference Kalthur, Padmashali, Bhattarai and Gupta2023). This occurs due to abnormal development of the neurovasculature traversing the canal and is therefore almost surely not ontogenetic variation, but normal polymorphism within Homo sapiens. Indeed, evolution cannot occur in the absence of intraspecific variation, so we should expect that every phylogenetically informative character was, at some point in evolutionary history, polymorphic within a single species. For this reason, I urge circumspection in applying my results to the fossil record. The presence of a putatively ontogenetically invariant difference between two specimens need not mean that the two specimens belong to different species—this difference could always represent polymorphism, especially if there is only one such difference. That said, the present dataset does suggest that polymorphism is uncommon in ontogenetically invariant characters. This is probably not coincidental. Modifying architectural traits necessarily involves alteration to early steps in the developmental program, which increases the risk that they render the embryo nonviable—therefore, we may expect that these changes are developmentally “harder” and would appear less frequently, making it most likely that such character changes are associated with deeper lineage divergences and thus that they are strong evidence of species distinction. If this model holds, these characters would also be those that are least likely to be homoplastic, and therefore they may be the strongest characters for both taxonomic hypothesis testing and phylogenetic analyses. The long-recognized importance of cranial arterial and venous anatomy in mammalian systematics (Wible Reference Wible1986, Reference Wible1987; MacPhee et al. Reference MacPhee, Gaillard, Forasiepi and Sulser2023; Crowell et al. Reference Crowell, Wible and Chester2024) corroborates this expectation, as do observations of a widely conserved topological correspondence between divisions of the tetrapod adductor musculature and branches of the trigeminal nerve (e.g., Holliday and Witmer Reference Holliday and Witmer2007). Recent research has demonstrated that within the appendicular skeleton, later-developing distal limb bones show greater variation than earlier-developing proximal elements and evolve more rapidly (Stepanova and Womack Reference Stepanova and Womack2020; Rothier et al. Reference Rothier, Fabre, Clavel, Benson and Herrel2023), lending further credence to this interpretation. At present, it seems safe to say that early-developing architectural characters are likely to both be ontogenetically invariant and show the least polymorphism, with the caveat that further research on polymorphism itself may modify how paleontologists accommodate it in the fossil record.

While polymorphism remains a potentially problematic unknown, the present results do allow me to articulate guidelines for vetting the possibility of fossil specimens representing an ontogenetic series:

1. 1. Characters relating to the sutural topology of the skull, which is determined by patterns of gene expression in epithelia from early stages of embryonic development, are unlikely to change in posthatching ontogeny. This includes characters such as “bone X contacts bone Y,” “bone X has a distinct process overlapping part of bone Y,” “bone X reaches the posterior level of landmark Z,” and “process A of bone X is longer than process B of bone Y,” among potential others.

2. 2. Characters relating to the pathway of major cranial blood vessels and nerves, which are laid down before and regulate osteogenesis, are unlikely to change during posthatching ontogeny. These include, for example, “foramen bounded by bones X and Y, between bones X and Z, or entirely within bones X, Y, or Z,” “foramen in bone X is single or divided,” “foramen in bone X is on the lateral or anterior surface of bone X,” or “foramen for neurovascular bundle A is present or not present.”

3. 3. Characters related to the distribution of pneumatic recesses (osteological correlates of air sinuses, which begin to form before osteogenesis) are unlikely to vary during posthatching ontogeny, with the possible exception of the very earliest stages of posthatching life. Such characters may include “pneumatic recess present in bone X” and “pneumatic recesses A and B internally communicate,” potentially among others. While the ultimate adult morphology and size of pneumatic recesses may vary, we may also predict that such change will be unidirectional (and result in larger overall size), so shrinking or secondary closure of pneumatic recesses is also unlikely.

4. 4. Tooth counts show clade-specific patterns in ontogenetic variability, but such tendencies either involve ontogenetic addition of tooth positions, or ontogenetically stable tooth positions. In the latter case at least, tooth count usually varies by ±1 from a modal value, fitting general observations that variation in biological systems tends to approximate a normal distribution and that ranges of dental counts have diagnostic utility despite the presence of intraspecific variation. No clade shows a tendency toward a loss of tooth positions, despite published claims to the contrary.

5. 5. Ontogenetically invariant characters overwhelmingly represent characters that arise early in embryonic development. As such, they are also less likely to be polymorphic among species, although it is impossible to fully exclude the possibility that any one character varies among a sample due to polymorphic intraspecific variation.

6. 6. Ontogenetically variable characters, such as bone surface ornamentation, suture fusion, muscle scar development, and proportional and shape changes, tend to show a unidirectional and predictable trend, allowing apparent trend reversals to be independent indicators of species distinction among sufficiently large datasets. For example, “bone X has an ornamental structure” may be on ontogenetically variable character state, but is unlikely to be the juvenile character state; conversely, “bone X lacks a muscle scar” is unlikely to represent the adult state.

Critical appraisal of these predictions both in a range of study systems and through finer resolution of molecular signaling pathways that ultimately generate skeletal morphology, clearly represent important topics for future research.