Evolutionary and ontogenetic changes of the anatomical organization and modularity in the skull of archosaurs

Comparative anatomy studies of the skull of archosaurs provide insights on the mechanisms of evolution for the morphologically and functionally diverse species of crocodiles and birds. One of the key attributes of skull evolution is the anatomical changes associated with the physical arrangement of cranial bones. Here, we compare the changes in anatomical organization and modularity of the skull of extinct and extant archosaurs using an Anatomical Network Analysis approach. We show that the number of bones, their topological arrangement, and modular organization can discriminate birds from non-avian dinosaurs, and crurotarsans. We could also discriminate extant taxa from extinct species when adult birds were included. By comparing within the same framework, juveniles and adults for crown birds and alligator (Alligator mississippiensis), we find that adult and juvenile alligator skulls are topologically similar, whereas juvenile bird skulls have a morphological complexity and anisomerism more similar to those of non-avian dinosaurs and crurotarsans than of their own adult forms. Clade-specific ontogenetic differences in skull organization, such as extensive postnatal fusion of cranial bones in crown birds, can explain this pattern. The fact that juvenile and adult skulls in birds do share a similar anatomical integration suggests the presence of a specific constraint to their ontogenetic growth.

. Anatomical network models. Example of the network models for three archosaurian skulls: (A) Aetosaurus from Schoch (2007) 63 ; (B) Plateosaurus from Prieto-Marquez and Norell (2011) 107 ; (C) Gallus from Digimorph. The pair-wise articulations among the bones of skulls (left) are formalized as network models (middle) and later analyzed, for example, to identify the skull anatomical node-based modules (right). See "Materials and methods" for details.
Phylogenetic context. We created a phylogenetic tree (Fig. 2) based on the previous studies [34][35][36][37][39][40][41][42][43][44] . The tree was calibrated using the R package paleotree 45 by the conservative "equal" method 46,47 ; branching events were constrained using the minimum dates for known internal nodes based on fossil data from Benton and Donoghue 48 (listed in Supplementary Table S3) and the first and last occurrences of all 21 species from the Paleobiology Database using the paleobioDB package 49 in R. Because there were two extinct Nothura species in the Paleobiology Database, the last occurrence for extant Nothura species was adjusted to 0 (Supplementary Table S2).
Network modelling. We built anatomical network models for each archosaur skull in our sample set based on detailed literature descriptions and CT scans of complete skulls (see Supplementary Information 1). Skull bones were represented as the nodes of the network model and their pair-wise articulations (e.g. sutures and synchondroses) were represented as links between pairs of nodes ( Fig. 1). Skull network models were formalized as binary adjacency matrices, in which a 1 codes for two bones articulating and a 0 codes for absence of articulation. Bones that were fused together without trace of a suture in the specimens examined were formalized as a single individual bone. Figure 2. Phylogenetic framework. A phylogenetic tree was created based on the evolutionary relations among taxa as detailed in previous work [34][35][36][37][38][39][40][41][42][43] . Bifurcation times were calibrated based on fossil dates from Benton and Donoghue 48 using the equal method in the paleotree package [45][46][47] . First and last occurrences were from Paleobiology Database (details listed in Supplementary Table S2). Silhouettes were from Phylopic.org. See methods for details. each network model: the number of nodes (N), the number of links (K), the density of connections (D), the mean clustering coefficient (C), the mean path length (L), the heterogeneity of connections (H), the assortativity of connections (A), and the parcellation (P). The morphological interpretation of these topological variables has been detailed elsewhere 28 . A summary is provided here. N and K represent the direct count of the number of individual bones and articulations observed in the skull. D is the number of connections divided by the maximum number of possible connections (it ranges from 0 to 1); D is a proxy measure for morphological complexity. C is the average number of neighboring bones that connect to one another in a network (i.e., actual triangles of nodes compared to the maximum possible): a value close to 1 shows all neighboring bones connect to each other while a value close to 0 shows neighboring bones do not connect to each other; C is a proxy measure for anatomical integration derived from co-dependency between bones. L measures average number of links separating two nodes (it ranges from 1 to N − 1); L is a proxy measure of anatomical integration derived from the effective proximity between bones. H measures how heterogeneous connections are in a network: skulls composed of bones with a different number of articulations have higher H values. If all bones had the same number of connections (i.e., H = 0), it means that all bones were connected in the same way and the skull had a regular shape. A measures whether nodes with the same number of connections connect to each other (it ranges from − 1 to 1); H and A are a proxy measure for anisomerism or diversification of bones. P measures the number of modules and the uniformity in the number of bones they group (it ranges from 0 to 1); P is a proxy for the degree of modularity in the skull. Calculating P requires a given partition of the network into modules (see next below).
Network parameters were quantified in R 50 using the igraph package 51 . Networks visualization was made using the visNetwork package 52 Supplementary Information 4). First, we performed the tests listed above for all archosaurs. Then, we repeated these tests for a sub-sample that included all archosaurs, except for all modern birds. Next, we repeated these tests for a sub-sample that included all archosaurs, except for adult birds.

Modularity analysis.
To find the optimal partition into network modules we used a node-based informed modularity strategy 54 . This method starting with the local modularity around every individual node, using clus-ter_spinglass function in igraph 51 , then it returns the modular organization of the network by merging nonredundant modules and assessing their intersection statistically using combinatorial theory 55 .
Ethical approval. All methods were carried out in accordance with relevant guidelines and regulations from Imperial College ethics committee and were approved by Imperial College.  Supplementary  Fig. S1C). However, we find no statistically significant difference in morphospace occupation between crurotarsans and avemetatarsalians (F 1,23 = 1.46, p = 0.2002, Supplementary Fig. S1D).

Topological discrimination of skull bones.
When all avians are excluded from the comparison, the first three PCs now explain 80.6% of the total variation (Supplementary Figs. S4-S6). PC1 (38.6%) discriminates skulls by the density of their inter-bone connections (D) and effective proximity (L). PC2 (22.6%) discriminates skulls by the number of bones and their articulations (N and K). Finally, PC3 (19.5%) now discriminates skulls by their anisomerism (H) and whether bones with the same number of connections connect to each (A). PERMANOVA tests could not discriminate between Crurotarsi and non-avian Dinosauria (F 1,17 = 1.235, p = 0.3022; Supplementary Fig. S4D), and between extant and extinct species (F 1,17 = 2.274, p = 0.06399; Supplementary Fig. S4C).
When only adult birds are excluded, the first three PCs explain 79.7% of the topological variation (Supplementary Figs. S7-S9). PC1 (35.8%), PC2 (24.5%), and PC3 (19.5%) discriminate skull similarly as when all birds are excluded (see above). PERMANOVA tests also could not discriminate between juvenile birds, crurotarsans, and non-avian dinosaurs (F 2,19 = 1.682, p = 0.09649; Supplementary Fig. S7D), and between extant and extinct species (F 1,20 = 2.119, p = 0.06169; Supplementary Fig. S7C). www.nature.com/scientificreports/ Regardless of the sub-sample compared, we found no statistically significant difference in morphospace occupation between taxa stratified by flying ability and diet ( Supplementary Fig. S1E, see Supplementary Information 4 for details). This suggests that at least for the given sample set changes in cranial network-anatomy (i.e. how bones connect to each other) are independent of both dietary adaptations and the ability to fly.
Number of network modules. The number of network modules identified in archosaur skulls ranged from one (i.e. fully integrated skull) in adult birds Nothura maculosa (the spotted tinamou) and Geospiza fortis (medium ground finch) to eight in the non-avian dinosaur Citipati (Supplementary Table S10). The number of network modules within the studied taxa decreases during evolution of both major archosaurian clades: from 6 (Riojasuchus) to 4 (Desmatosuchus,) and from 6 (Dibothrosuchus) to 4 (Dakosaurus and all adult crocodilians) modules in Crurotarsi; from 6 (Coelophysis) to 4 (Dilophosaurus and Compsognathus), and from 8 (Citipati) to 4 (Velociraptor, Archaeopteryx, Ichthyornis, and juvenile modern birds) modules in theropod-juvenile bird transition ( Fig. 4A,B, Supplementary Table S10). We found no modular division of the skull in adult Nothura and Geospiza. This is most likely because these skulls are highly integrated due to the extensive cranial bone fusion in adults, which, in turn, results in a network with very few nodes. In general, skull networks are partitioned into overlapping modules.

Discussion
Occupation of morphospace and evolution of skull architecture. The two major groups of archosaurs (Crurotarsi and Avemetatarsalia) show an analogous trend towards a reduction in the number of skull bones (Supplementary Table S8; Supplementary Information 3), in line with the Williston's Law, which states that vertebrate skulls tend to become more specialized with fewer bones as a result of fusions of neighboring bones during evolution 25,56,57 . This reduction in the number of bones and articulations, together with an increase in density, is also observed within aetosaurs and sphenosuchians (Supplementary Table S8). Likewise, we observed fusion of paired bones into new unpaired ones: for example, left and right frontals, parietals, and palatines are fused through their midline suture in the more derived taxa, such as the crocodilians (Supplementary Table S6). Bone fusion in extant species produced skulls that are more densely connected than the skulls of extinct species (Supplementary Fig. S1C). It was previously suggested that the more connected skulls would have more developmental and functional inter-dependences among bones, and, hence, they would be more evolutionarily constrained 22,23 . Similarly, avian cranium with its strongly correlated traits has lower evolutionary rates and bird skulls are less diverse overall 12 . Bhullar et al. pointed out that avian kinesis relies on their loosely integrated skulls with less contact and, thus, skulls with highly overlapping bones would be akinetic 58 . This contradicts our observations here in that kinetic crown birds have more complex and integrated skulls than the akinetic crurotarsans and the partially kinetic Riojasuchus 59   www.nature.com/scientificreports/ points each bone has, but not the total number of connections possible from the number of bones in these taxa. The total number of articulations possible is the denominator used to calculate density. More recently, Werneburg and colleagues showed Tyrannosaurus, suspected to have kinesis, also has a higher density when compared to akinetic Alligator but lower density when compared to the more derived and clearly kinetic Gallus skull 29 .
When compared with modules identified by Felice et al. 60 , the node-based modules, such as the rostral and neurocranial modules (shown as blue and red modules in Fig. 4), are composed of elements essentially similar to those described as variational modules (more details in Supplementary Information 2). The supraoccipital and basioccipital bones were part of the same topology-defined ( Supplementary Information 2, Fig. 4) and shape-defined module in most taxa, likely due to its functional importance in connecting the vertebral column with the skull 60 .
Crurotarsi. The aetosaurs, Aetosaurus and Desmatosuchus, and the sphenosuchians, Sphenosuchus and Dibothrosuchus, show an increase in complexity within their lineages. The more derived aetosaur Desmatosuchus has a fused skull roof (parietal fused with supraoccipital, laterosphenoid, prootic and opisthotic) and toothless premaxilla that are absent in the less derived aetosaur Aetosaurus [61][62][63] . In contrast, basal and derived sphenosuchian are more topologically similar. Their main difference is that basipterygoid and epiotic are separate in Sphenosuchus but are fused with other bones in the more derived Dibothrosuchus 64,65 . When we compared aetosaurs and sphenosuchians, we found that sphenosuchians have a skull roof intermediately fused condition between Aetosaurus and Dibothrosuchus: interparietal sutures in both sphenosuchians are fused while supraoccipital, laterosphenoid, opisthotic, and prootic remain separate.
To understand cranial topology in Thalattosuchia, a clade with adaptations specialized for marine life, we included Dakosaurus andiniensis. These adaptations comprise nasal salt glands 66 , hypocercal tail, paddle-like forelimbs, ziphodont dentition, fusion of the inter-premaxillary suture, a fused vomer, and a short and high snout 67,68 . Despite these adaptations, Dakosaurus has a cranial complexity closer to that of extant crocodilians by similarly having inter-frontal and inter-parietal fusions 67,68 . In addition to the fused frontals and parietals, both Crocodylus and Alligator have a fused palate and a fused pterygoid bones.
In turn, crurotarsans first fuse the skull roof and skull base, followed by the fusion of the face (more details on Supplementary Table S6). Interestingly, this resonates with the pattern of sutural fusion in alligator ontogeny, which cranial (i.e. frontoparietal) has the highest degree of suture closure followed by skull base (i.e. basioccipitalexoccipital) and then the face (i.e. internasal) 69 suggesting that the same mechanism may control topological changes in both ontogeny and evolution.
Avemetatarsalia. Avemetatarsalian transition is marked with a faster ontogenetic bone growth in more derived taxa, indicated by higher degree of vascularization, growth marks, and vascular canal arrangement (reviewed by Bailleul 70 ), more pneumatized skulls (reviewed by Gold 71 ), and an increase in complexity reminiscent of what is observed in crurotarsans. The basal ornithischian Psittaosaurus lujiatunensis and basal saurischian Eoraptor lunensis are relatively close to each other on the morphospace (Fig. 3), with the Psittacosaurus skull showing slightly more density because of fused palatines, a trait which is also observed in extant crocodilians and some birds, and its extra rostral bone as observed in other ceratopsians 72 .
The basal sauropodomorph Plateosaurus engelhardti has the lowest clustering coefficient (i.e. lower integration) of archosaurs, suggesting that skulls of sauropodmorphs are less integrated than those of saurischians 31 , accompanied by poorly connected bones (as seen in the network in Fig. 4C). Poorly connected bones, for example epipterygoid, and some connections, such as the ectopterygoid-jugal articulation, are later lost in neosauropods 43,73 .
Within theropods, the ceratosaurian Coelophysis is more derived and has a slightly more complex and specialized skull than the ceratosaurian Dilophosaurus 42 . Their positions on the morphospace suggest that ceratosaurians occupy a region characterized by a higher mean path length (L), when compared to other archosaurs (Fig. 3). Compsognathus is close to Riojasuchus on the morphospace with a similar mean path length ( Fig. 3 and Supplementary Fig. S4, Supplementary Table S8), its facial bones are also unfused, and it has a similar composition for its facial modules (see facial modules in Compsognathus and nasal modules in Riojasuchus on Supplementary Table S4 and Supplementary Fig. S10). These observations suggest an ancestral facial topology (see Supplementary Tables S6 and S8 for more details) is concomitant to the magnitude of shape change reported for compsognathids 34 . Compsognathus possesses an independent postorbital that is absent from Ichthyornis to modern birds. It also has an independent prefrontal that is absent in most Oviraptorsauria and Paraves 74 , including Citipati, Velociraptor, and from Ichthyornis to modern birds. Despite its ancestral features, the back of the skull and the skull base of Compsognathus are fused, similarly to other Paravians and modern birds.
The oviraptorid Citipati has a skull topology that occupies a morphospace within non-avian theropods, despite its unique vertically-oriented premaxilla and short beak 34,75 . Citipati has an independent epipterygoid that is also present in some non-avian theropods and ancestral archosaurs, such as Plateosaurus erlenbergiensis, but which is absent in extant archosaurs [75][76][77][78] . Citipati also has fused skull roof (with fused interparietals), skull base, and face, marked with fused internasal and the avian-like inter-premaxillary sutures.
Like other dromaeosaurids, Velociraptor's eyes are positioned lateral to the rostrum. Its prefrontal bone is either absent or fused with the lacrimal while it remains separate in other dromaeosaurids [79][80][81] . We observed a loss of the prefrontals from Citipati to modern birds, but not in more ancestral archosaurs or crurotarsans. Bones forming the Velociraptor basicranium, such as basioccipital, and basisphenoid are fused with other members of the basicranium (listed in Supplementary www.nature.com/scientificreports/ Compsognathus and other primitive non-avian dinosaurs, Velociraptor has an ancestral facial topology with separate premaxilla, maxilla, and nasal bones.

Archaeopteryx and Ichthyornis as intermediates between non-avian theropods and modern birds.
The skull of Archaeopteryx occupied a region of the morphospace closer to non-avian dinosaurs and crurotarsans than to juvenile birds (Fig. 3). The distance of Archaeopteryx from crown birds and its proximity in the morphospace to Velociraptor and Citipati along the PC1 axis (Fig. 3) may reflect the evolving relationship between cranial topology and endocranial volume. In fact, Archaeopteryx has an endocranial volume which is intermediate between the ancestral non-avian dinosaurs and crown birds 82,83 and it is within the plesiomorphic range of other non-avian Paraves 84 . This makes Archaoepteryx closer to dromaeosaurid Velociraptor than to oviraptor Citipati, for both its skull anatomy and its endocranial volume 84 . Modifications related to the smaller endocranial volume in Archaeopteryx include the unfused bones in the braincase, the independent reappearance of a separate prefrontal after the loss in Paraves 74 , a separate left and right premaxilla as observed in crocodilian snouts and ancestral dinosaurs, and the presence of separate postorbitals, which might restrict the fitting for a larger brain 34 . Compared to Archaeopteryx, Ichthyornis is phylogenetically closer to modern birds and occupies a region of the morphospace near the juvenile birds and extant crocodilians when adult birds are included in the analysis (Fig. 3), but closer to extant crocodilians when all birds or when adult birds are removed ( Supplementary  Figs. S4-S9). The proximity between Ichthyornis and juvenile birds may be explained by the similar modular division (as observed in Fig. 4B,D; Supplementary Table S4, Supplementary Fig. S10), presence of anatomical features characteristic of modern birds, such as the loss of the postorbital bones, the fusion of the left and right premaxilla to form the beak, a bicondylar quadrate that form a joint with the braincase, and the arrangement of the rostrum, jugal, and quadratojugal required for a functional cranial kinetic system 58,[85][86][87][88] . The proximity between Ichthyornis and extant crocodilians in terms of complexity (Supplementary Figs. S4-S9, Supplementary Table S8) may be explained by the fused frontal and fused parietal, and separate maxilla, nasal, prootic and laterosphenoid (Supplementary Table S6).
Paleognath and neognath birds. Juvenile birds have a skull roof with relatively less fused bones with the interfrontal, interparietal, and frontoparietal sutures open, and a more fused skull base. Postorbital is already fused in all juvenile birds (i.e. after hatching). Collectively, juvenile neognaths show a skull anatomy with a fused cranial base, relatively less fused roof, and unfused face that resembles the anatomy of ancestral non-avian theropods. Unlike what is observed in non-avian theropods, frontal, parietal, nasal, premaxilla, and maxilla eventually fuse with the rest of the skull in adult modern birds. However, in the palatal region not all the sutures are completely closed: the caudal ends of the vomers remained unfused in adult Nothura, which is a characteristic common in Tinamidae 89 . A similar pattern of suture closure has been described in another paleognath, the emu, in which the sutures of the base of the skull close first and then the cranial and facial sutures close while palatal sutures remain open 69 . The only difference is that in Nothura, where closure of major cranial sutures (frontoparietal, interfrontal, and interparietal) happens after the facial sutures closure. In summary, when compared with neognaths, the skull of the paleognath Nothura is more homogeneous and complex in both juvenile and adult stages. As the skull grows, its bones fuse and both its complexity and heterogeneity increase.
Within the neognaths, the skull of Geospiza fortis is more complex and more homogenous than Gallus gallus in both juvenile and adult stages: bones in Geospiza skull are more likely to connect with bones with the same number of connections than Gallus. These two trajectories illustrate how the connectivity of each bone diversifies and becomes more specialized within a skull as sutures fuse together, as predicted by the Williston's law.
As in crurotarsans, major transitions in Avemetatarsalia are associated with the fusion first of the skull base, then the skull roof, and, finally, with the face (more details on Supplementary Table S6). This is more similar to the temporal pattern of sutural closure during ontogeny in the emu (skull base first, skull roof second, facial third) than to the one observed in the alligator (cranial first, skull base second, facial third) 69 , thus suggesting that the same mechanism for ontogeny may have been co-opted in Avemetatarsalia evolution.

Ontogenetic differences in topology between birds and crocodilians.
Our comparisons on network anatomy found that juvenile birds occupy a region of the morphospace that is closer to the less derived archosaurs and crurotarsans than to that occupied by adult modern birds (Supplementary Fig. S1B). Juvenile birds have a degree of anisomerism of skull bones and skull anatomical complexity closer to that in crurotarsans and non-avian dinosaurs, while their pattern of integration overlaps with that of adult birds, crurotarsans, and non-avian dinosaurs. These similarities in complexity and heterogeneity may be explained by the comparably higher number and symmetrical spatial arrangements of circumorbital ossification centres in early embryonic stages 74 . For example, both crown avians and A. mississippiensis have two ossification centres that fuse into one for lacrimals 74,90 . Meanwhile, ossification centres that form the prefrontal and postorbital, fuse in prenatal birds but remain separate in adult non-avian dinosaurs 74,90,91 . These ossification centres later develop into different, but overlapping, number of bones and their arrangement in juvenile birds (27-34 bones) and adult non-avian theropods (32-44 bones) with discrepancies explained by the heterochronic fusion of the ossification centres (Supplementary Table S8 www.nature.com/scientificreports/ interact as modules with heterogeneity and complexity similar to basal members at juvenile stage, and (3) then fuse and diversify to produce skulls of adult birds. The skulls of birds, crocodilians, and dinosaurs develop from ossification centres with comparable spatial locations in the embryonic head 74 . When both evolutionary and ontogenetic cranial shape variation was compared among crocodilians, Morris and colleagues showed that at mid-to late embryonic stages, cranial shapes originated from a conserved region of skull shape morphospace 92 . They suggested that crocodilian skull morphogenesis at early and late embryonic stages are controlled by signaling molecules that are important in other amniotes as well, such as Bmp4, calmodulin, Sonic hedgehog (Shh); and Indian hedgehog [92][93][94][95][96][97][98][99] . Then, from late prenatal stages onward, snout of crocodilians narrows 100 and elongates following different ontogenetic trajectories to give the full spectrum of crocodilian cranial diversity 92 .
Another major transformation in archosaurian evolution is the origin of skulls of early and modern birds from the snouted theropods. This transition involved two significant heterochronic shifts 34,101 . First, avians evolved highly paedomorphic skull shapes compared to their ancestors by developmental truncation 34 . This was followed, by a peramorphic shift where primitively paired premaxillary bones fused and the resulting beak bone elongated to occupy much of the new avian face 101 . By comparison, the skull of Alligator undergoes extensive morphological change and closing of the interfrontal and interparietal sutures during embryogenesis is followed by the prolonged postnatal and maturation periods, with the lack of suture closure and even widening of some sutures 102,103 . Bailleul et al. suggested that mechanisms that inhibit suture closure, rather than bone resorption, cause the alligator sutures to remain open during ontogeny 103 . Nevertheless, juvenile and adult alligators share the same cranial topology featuring similar module compositions and both occupy a region of morphospace close to Crocodylus ( Fig. 4D and Supplementary Fig. S10; Supplementary Tables S4 and S8). Such topological arrangement suggests that conserved molecular, cellular, and developmental genetic processes underlie skull composition and topology observed across crocodilians. Likewise, oviraptorid dinosaurs, as represented by Citipati, display their own unique skull shape and ontogenetic transformation 34 , while retaining a topology conserved with other theropods. Combined, this evidence suggests that developmental mechanisms controlling skull composition and interaction among skull elements are conserved among theropods.
The process of osteogenesis underlies the shape and topology of the bony skull. In chicken embryo, inhibition of FGF and WNT signaling pathways prevented fusion of the suture that separates the left and right premaxilla, disconnected the premaxilla-palatine articulation and changed their shapes giving the distal face a primitive snout-like appearance 101 . The site of bone fusion in experimental unfused, snout-like chicken premaxillae showed reduced expression of skeletal markers Runx2, Osteopontin, and the osteogenic marker Col I 101 , implying localized molecular mechanisms regulating suture closure and shape of individual cranial bones. Thus, changes in gene expression during craniofacial patterning in avians 95,96,98,[104][105][106] , non-avian dinosaurs, and crocodilians 92,101 contribute to the clade-specific differences in skull anatomical organization resulting from the similar patterns of bone fusion of bones.
Finally, we observe some network modules where some bones within the same modules in juveniles will later fuse in adult birds, but not in A. mississippiensis ( Supplementary Information 5; Fig. 4E and Supplementary  Fig. S10, Supplementary Table S4). For example, in Nothura, premaxilla, nasal, parasphenoid, pterygoid, vomer, and maxilla grouped in the same juvenile module will later fuse during formation of the upper beak in the adult. In A. mississippiensis, premaxilla, maxilla, nasal, lacrimal, prefrontal, jugal, frontal, and ectopterygoid are also in the same juvenile module, but remain separate structures in adult. These findings suggest that bones within the same module may be more likely to fuse together in ontogeny but doing so is a lineage-specific feature. www.nature.com/scientificreports/ Comparisons of juveniles and adults for extant birds and the alligator revealed ontogenetic changes linked to the evolution of the skull organization in archosaurs. Whereas the anatomical organization of the skull of juvenile alligators resembles that of adults, the anatomy of juvenile modern birds is closer to that of non-avian dinosaurs than to that of adult avians of the same species in terms of morphological complexity and anisomerism, probably due to the spatial arrangements of ossification centres at embryonic stages 74,90,91 . More specifically, the differences in skull organization between crown birds and non-avian dinosaurs could be explained by postnatal fusion of bones.

conclusion
A network-based comparison of the cranial anatomy of archosaurs shows that differences within and among archosaurian clades are associated with an increase of anatomical complexity, a reduction in number of bones (as predicted by the Williston's Law), and an increase of anisomerism marked by bone fusion, for both crurotarsans and avemetatarsalians. Our findings indicate that the anatomical organization of the skull is controlled by developmental mechanisms that diversified across and within each lineage: heterotopic changes in craniofacial patterning genes, heterochronic prenatal fusion of ossification centres 74,90,91 , and lineage-specific postnatal fusion of sutures. Some of these mechanisms have been shown to be conserved in other tetrapods. For example, heterotopy of craniofacial patterning genes also took place between chick and mice embryos 95,96,106 . Hu and Marcucio showed that mouse frontonasal ectodermal zone could alter the development of the avian frontonasal process, suggesting a conserved mechanism for frontonasal development in vertebrates 96 . Our findings illustrate how a comparative analysis of the anatomical organization of the skull can reveal both common and disparate patterns and processes determining skull evolution in vertebrates.