Ontogenetic variability of the intertympanic sinus distinguishes lineages within Crocodylia

Abstract The phylogenetic relationships within crown Crocodylia remain contentious due to conflicts between molecular and morphological hypotheses. However, morphology‐based datasets are mostly constructed on external characters, overlooking internal structures. Here, we use 3D geometric morphometrics to study the shape of the intertympanic sinus system in crown crocodylians during ontogeny, in order to assess its significance in a taxonomic context. Intertympanic sinus shape was found to be highly correlated with size and modulated by cranial shape during development. Still, adult sinus morphology distinguishes specimens at the family, genus and species level. We observe a clear distinction between Alligatoridae and Longirostres, a separation of different Crocodylus species and the subfossil Malagasy genus Voay, and a distinction between the Tomistoma and Gavialis lineages. Our approach is independent of molecular methods but concurs with the molecular topologies. Therefore, sinus characters could add significantly to morphological datasets, offering an alternative viewpoint to resolve problems in crocodylian relationships.

Crocodylomorpha and their pseudosuchian stem-groups stand out in being characterised by an expanded set of paratympanic sinuses, a system of endocranial pneumatic cavities linked to the auditory system and the pharynx, invading the braincase bones (Dufeau & Witmer, 2015;Kuzmin et al., 2021). Among mammals and archosaurs, previous studies have investigated the use of endocranial sinuses to resolve ecological, phylogenetic or biomechanical questions (Witmer, 1999). The shape of such structures has often been revealed to be correlated with the development of cranial features (Curtis et al., 2015;Farke, 2010;Ito & Nishimura, 2016).
Sinus shape has also been proposed to be linked to cranial stress dissipation (Sharp & Rich, 2016), and shape differentiation has been observed between phylogenetic groupings or biogeographically distinct populations (Billet et al., 2017;Curtis et al., 2015;Curtis & Van Valkenburgh, 2014;Farke, 2010;Rossie, 2008). Sinus morphology also seems to be impacted by the living environment, showing substantial volume reduction in tetrapod lineages that underwent land to marine environment transition (Brusatte et al., 2016;Cowgill et al., 2021;Curtis et al., 2015;Fernández & Herrera, 2021). The potential relevance of these structures for systematics and ecological studies thus deserves attention in crocodylian species, with some fossil lineages showing debated phylogenetic positions or undergoing drastic habitat transitions (e.g. Thalattosuchia, Dyrosauridae, Sebecidae).
The complex morphologies of the crocodylian paratympanic sinuses were initially described on the basis of dissections and mechanical tomography (Colbert, 1946;Owen, 1850;Tarsitano, 1985;Van Beneden, 1882). The recent development of non-invasive analytical X-ray micro-computed tomography techniques (μCT) has facilitated further investigation of crocodylian cranial anatomy: thus, paratympanic structures have recently received renewed interest and resulted in recent revisions to traditional sinus nomenclature (Dufeau & Witmer, 2015;Kuzmin et al., 2021). In the last decade, many papers have examined the neuroanatomy of fossil crocodylomorphs, pointing out that such structures may be important for inferring ecological and evolutionary patterns (Bona et al., 2015;Brusatte et al., 2016;Erb & Turner, 2021;Martin et al., 2022;Pochat-Cottilloux et al., 2021;Serrano-Martínez et al., 2021;. Therefore, as these approaches are multiplying, it has become timely to get an as complete as possible perspective on the morphological variability of these structures studied across extant crocodylian lineages. Among extant Crocodylia, a few studies already highlighted several endocranial and sinus structures as an additional proxy to refine the taxonomic determination of extant and fossil specimens, then proposed their potential use in phylogenies (Kuzmin et al., 2021;Martin et al., 2022). Furthermore, several works have shown that the crocodylian skull and endocranial system are heavily modified during posthatching development (Dufeau & Witmer, 2015;Hu et al., 2021;Kuzmin et al., 2021;Lessner et al., 2022;Tarsitano, 1985). Cranial morphology is plastic across ontogeny, especially regarding the shape of the snout, which is the most variable skull region in extant species. The shape of the braincase, containing the endocranial organs, also displays important modifications during development such as verticalisation, skull table flattening, quadrate extension and enlargement of temporal fenestrae (Cossette et al., 2021;Morris et al., 2019Morris et al., , 2021Piras et al., 2010Piras et al., , 2014. Assessing the ontogenetic changes in the paratympanic sinuses from a developmental point of view is thus necessary to discuss their morphology and evolution. In the present paper, we focus specifically on the morphological variability of the intertympanic sinus system (Figure 1), a part of the paratympanic sinuses that displays noticeable differences across extant crocodylian species. The aim of this study was to provide a detailed description of the ontogeny of the intertympanic sinus and associated diverticula in extant crocodylian species, to establish an overview of its variability and provide new tools for taxonomic identification and future phylogenetic analyses. We use 3D geometric morphometric quantification to assess the morphological variations of the intertympanic sinus system in 17 modern and two subfossil species (Voay robustus and Crocodylus sp.), reconstruct ontogenetic trajectories and discuss morphological features regarding the crocodylian phylogenetic framework.

| Specimen sampling
The braincases of 64 extant specimens were examined for 3D reconstructions of their endocranial structures (Table 1) Crocodylus palustris, are represented by at least two adult or subadult specimens. All specimens were retrieved from museum collections or online databases and no living specimens were used or euthanised for the purpose of this study.
Three specimens of the subfossil species V. robustus from the Holocene of Madagascar were included in the analyses along with extant crocodylian species, as this genus was still present until less than 2000 years cal BP and was contemporaneous of the genus Crocodylus on the island (Hekkala et al., 2021;Martin et al., 2022).

| X-ray micro-computed tomography
Thirty specimens were scanned at the Laboratoire Mateis (INSA),

using a V|tome|X CT instrument (GE Sensing & Inspection
Technologies Phoenix X-Ray) for skulls smaller than 50 cm, and a DTHE (Double Tomographe Haute Energie by RX Solutions) for larger skulls. One specimen was scanned at MNHN Viscom France; two at the ISEM (RX Solutions EasyTom 150); the eight specimens from the SMNK were scanned at the KIT IPS and seven were scanned at the NHMUK (Nikon Metrology XT H 225 ST). The rest of the specimens comes from CT data available in the online databases Morphosource (https://www.morph osour ce.org/) and Digimorph (http://www.digim orph.org/). Additional information on the μCT parameters, including voxel size, can be found in Data S1.

| Image processing
Raw CT data were imported into the software ImageJ (Schneider et al., 2012), where 16-bit image stacks were converted into 8-bit to reduce file weight and contrast was enhanced between cranial bones and cavities. The resulting files were imported into the software Avizo Lite (version 7, 8.1, 9 and 9.5) for digital segmentation, volume rendering and visualisation of the endocranial structures. Segmentation was performed by multiple authors, and anatomical descriptions are outlined in Section 3.1. It was either done semi-automatically with inter-slice interpolation for most extant specimens, or manually slice by slice for subfossil specimens due to the sediment filling. We follow the nomenclature of Kuzmin et al. (2021) (and references therein) regarding endocranial terminology. Due to the size limitations of the Phoenix instrument, μCT acquisition of large specimens was, in this case, restricted to the basicranium: metrical measurements were thus obtained on the complete skulls when they were available. The most recent μCT acquisitions were conducted on the DTHE (INSA Lyon), where size limitations were no longer a problem, allowing for the largest skulls in our database to be μCT-scanned entirely. Total skull length (SL) was measured from the anterior margin of the premaxillae to the posterior margin of the supraoccipital. All volume renderings are available on MorphoMuseum (https://www.morphomuseum.com/) for 3D visualisation . F I G U R E 1 Intertympanic sinus system of Osteolaemus tetraspis (MHNM 9095.0). (a) Oblique view of the skull; (b) semi-transparent view of the skull showing the position of the intertympanic sinus system; (c) oblique, (d) dorsal, (e) left lateral views of the intertympanic sinus system. app, anterolateral pre-parietal process; IntPR, intertympanic pneumatic recess; OsInt, ostium between intertympanic pneumatic recess and middle ear; OtoPR, otoccipital pneumatic recess; ppp, posteromedial pre-parietal process; PPR, parietal pneumatic recess; PropIntPR, prootic part of intertympanic pneumatic recess. Scale bars: 1 cm. TA B L E 1 List of extant specimens studied along with their total skull length and ontogenetic stage.

| Ontogenetic stage determination
Crocodylians undergo continuous growth during development, precluding a clear osteological assessment of ontogenetic stages and making it difficult to attribute precise size boundaries which would also differ for each species (Morris et al., 2019;Schwab et al., 2021).
Therefore, extant specimens were classified into four size classes (hatchling, juvenile, sub-adult and adult) based on their total SL and respective genus (see Table 1, Table S1), in order to compare sinus shape between specimens of different sizes. Our dataset includes eight hatchlings, 13 juveniles, 14 sub-adults and 34 adults (Table 1). As rostrum size is greatly variable between species, and as the development of each individual of a species can also be different depending on food access and environmental condition, we also provide the skull width (SW) for each specimen (or the braincase width for incomplete fossils) in addition to the inferred ontogenetic stage when addressing a specific individual. This is because this size proxy is less influenced by rostrum length than is SL (O'Brien et al., 2019).

| Taxonomical issues
Uncertainty over taxonomic distributions of museum specimens can be a problem, especially in the genus Crocodylus where determination at the species level is difficult for juvenile and subadult specimens. Indeed, the differences between species of this genus often become clearly visible only in sub-adults or adults, while some relevant post-cranial characters are often missing.
Crocodylus siamensis and C. porosus are especially difficult to distinguish, and museum identifications concerning these two species were often erroneous due to their convergent cranial characters; as such, specimens of these two species were considered as a same entity for the linear regressions, pending further work on the precise morphological delineation between these two species.
The case of Crocodylus niloticus is also particularly troubling because this 'morphological' species seems to be paraphyletic according to molecular phylogenies based on mitochondrial and nuclear

| Landmark protocol
The 3D mesh models of the intertympanic sinus system were exported from the software Avizo as STL files, to be quantified using a 3D geometric morphometric approach. Twenty-five type II landmarks were placed on the surface of the 3D models using the software MorphoDig 1.6.4 (Lebrun, 2018). The landmarks were chosen to reflect the shape and extension of the pneumatic cavities and were placed on the maximal curvatures and maximum extensions of the different structures ( Figure 2, Table 3). Using this so-called 'homology-free' method enables us to compare shape even if a given structure is seemingly absent in a given specimen, by using partly degenerate configurations of landmarks: that is, when a structure is extremely reduced or absent, all landmarks characterising it are placed in the same location, following Polly (2008) and Klingenberg (2008).
The two specimens of Crocodylus rhombifer (MHNL 42006506 and 42006507) were too incomplete to be quantified with the complete set of landmarks. They were only used for descriptive purposes and for comparisons of their dorsal parts with the other Crocodylus specimens but were excluded from the statistical analyses.
Generalised least-squares Procrustes Analysis (GPA) superimposition was performed on the landmark dataset with the function gpagen to correct for differences in size and alignment of specimens.
Principal component analysis (PCA) was used on the Procrustes shape coordinates with the function gm.prcomp to find the major axes of shape variation within our sample. 3D wireframes were produced with plotRefToTarget to visualise shape modifications along PC axes with respect to the mean shape, obtained with mshape and shape.predictor functions. Data visualisation was performed with the package ggplot2 3.3.3 (Wickham, 2011).
First, we ran a PCA on the total dataset to visualise the variation of sinus shape during growth in all our modern Crocodylia samples.
To assess the global effect of size, phylogenetic groupings, skull shape and lifestyle on sinus shape, we performed Procrustes ANOVA on the Procrustes coordinates in the total ontogeny morphospace using the function procD.lm, which corresponds to a non-parametric Permutational Multivariate Analysis of Variance (Anderson, 2001).
To accurately compare ontogenetic trajectories between species, we used Procrustes ANOVA of total shape and PC scores against log transformed centroid size and species (as a factor). A homogeneity of slopes test was performed using the anova function on the unique allometry (size × species) and common allometry (size + species) models to assess if species-specific slopes were more appropriate than parallel allometric trajectories. The pairwise function was  Table 3.
to visualise the axes of shape variation most correlated with size, using ggplot to assess ontogenetic changes in sinus shape.
Additionally, we ran three PCAs within each family (Alligatoridae, Crocodylidae and Gavialidae) to test if the principal axes of variance changed from one subclade to another, and if they could enable a better differentiation between species than in the total Crocodylia dataset (each clade-specific analysis being independent from the total morphospace deformation induced by the differences of variance observed in each family). Statistical tests and linear regression on log-transformed centroid size were performed both in the total dataset and in each subclade.
Both sides of the intertympanic sinus system were landmarked for visualisation purposes. To check how much variation was influenced by the asymmetry in our data, we used the function bilat.
symmetry to quantify the symmetric and asymmetric component of shape variation and compare their statistical significance. The Procrustes ANOVA of the results found that 95.7% of the variation was significantly explained by the differences between individuals, while 0.2% was due to the directional asymmetry between both sides of the 3D models, and 4.1% coming from the fluctuating symmetry between individuals (interaction term). Thus, we considered that the impact of asymmetry on our results was marginal. Additionally, when performing PCA with only the medial and left side landmarks, the results are similar and do not change the interpretations.

| Ancestral state reconstruction and phylogenetic mapping
A calibrated molecular phylogenetic tree was produced with  Maximum anterior extension of right anterior pre-parietal process branches. As species were represented by a small number of specimens (between three and 10), most 95% confidence intervals of the ancestral trajectories overlapped. Thus, we could hypothesise heterochronic shifts that occurred, following Alberch et al., 1979, based on the changes in rate and intercepts of the ontogenetic trajectory of a species compared to its ancestors, but these results have to be interpreted carefully. As such, a decrease or increase in slope corresponds to a deceleration or acceleration, implying a slowing or speeding in the rate of shape change. A decrease or increase in intercept corresponds to a post-or pre-displacement, implying a change in the onset of development of the structure (occurring sooner or later in development respectively).
Finally, we used a consensus of the molecular topologies of

| Comparative description of the intertympanic sinus system
A diverticulum is a soft-tissue pocket of epithelial origin filled with air, forming a pneumatic sinus. Its development hollows out a 'recess', a cavity in the bone, generated by the growth of the pneumatic diverticulum (Kuzmin et al., 2021). In order to help appreciate the morphological variability occurring in our morphometric dataset, a comparative description of the intertympanic sinus system is provided for all modern crocodylian genera except Paleosuchus. the intertympanic diverticulum, parietal diverticulum and otoccipital diverticulum, which are more closely connected to each other than with the pharyngotympanic sinus system (Dufeau & Witmer, 2015), making it possible to study them as a separate unit.

| Alligator mississippiensis
Alligator mississippiensis displays an anteroposteriorly and dorsoventrally large intertympanic pneumatic recess; its prootic part connects with the prootic facial recess in juveniles and adults alike (Figure 4a-e).  is thick and expands anterodorsally during ontogeny. The anterolateral portion of the parietal bears a pair of prootic-parietal processes that connects with the prootic part of the intertympanic diverticulum through a large ostium (Figure 4). The three diverticula of the system are greatly fused in the adult specimen ( Figure 4e).

| Caiman
Caiman possesses a similar

| Melanosuchus
Adult M. niger present an intertympanic sinus system less expanded than in adult A. mississippiensis and Caiman. Like other Alligatoridae genera, the prootic part of the intertympanic pneumatic recess is connected to the prootic facial recess ventrally and to the PPR dorsomedially ( Figure S3). The intertympanic recess is more compressed anteroposteriorly and the bony walls separating it from the otoccipital recess are thick, making the two recesses well differentiated. The otoccipital pneumatic recess displays a tubular aspect, protruding posteriorly, but showing a verticalised crescent shape in posterior view like adult specimens of Caiman ( Figure S3). The posteromedial pair of pre-parietal processes is absent while the anterolateral pair is expanded, creating large cylindric cavities that merge anteriorly with the prootic-parietal process, forming a tubular PPR.

| Crocodylus
The intertympanic sinus system of Crocodylus is anteroposteriorly short and laterally elongated in adults. In juveniles, it is rounded and bulky; it undergoes an anteroposterior and dorsoventral compression as size increases, which is more prominent in the medial part of the intertympanic diverticulum (Figure 5a-e). In this genus, the morphology of the intertympanic sinus system differs between species, with respect to the dorsoventral thickness of the intertympanic diverticulum, the development of the parietal diverticulum and the reduction of the otoccipital diverticulum at adult stages ( Figures S4   and S5).
In C. niloticus, hatchling and juvenile specimens possess a de-  Figure S5). Crocodylus rhombifer displays an intertympanic diverticulum more similar to C. niloticus: the PPR has its posteromedial parietal processes oriented dorsally, and is small or nearly absent, whereas the anterolateral parietal processes are larger and merged in the medial part of the parietal ( Figure S5). However, our available C. rhombifer specimens are internally damaged, which prevented a proper assessment of the ventral part of the sinus system.

| Osteolaemus
Osteolaemus tetraspis presents a voluminous sinus system throughout all stages studied, with few differences between juveniles and adults. The intertympanic pneumatic recess is anteroposteriorly and dorsoventrally large. Its prootic part protrudes anteriorly and is generally connected with the prootic facial recess ventrally (see also Kuzmin et al., 2021). The otoccipital pneumatic recess is highly developed and connected to the intertympanic pneumatic recess through large ostia, remaining well separated from the latter when size increases. It maintains its relative volume throughout ontogeny, despite a slight compression of its ventral part. The anterolateral pair of pre-parietal processes is large and expanded in voluminous paired parietal cavities developed anteroposteriorly and laterally. In adult stages, these paired cavities merge into a single PPR. The posteromedial pre-parietal processes form two bulges oriented vertically and are anteriorly connected to the parietal recess (Figures 1 and 3 and Figure S6).

| Gavialis
Gavialis gangeticus displays a compressed intertympanic sinus system in adult stages (Figures 5i,j and 6a pairs of pre-parietal processes are present but not well developed ( Figure 5f). In the sub-adult specimen, the otoccipital pneumatic recess is compressed anteroposteriorly and slightly reduced ventrally.
The anterolateral pair of pre-parietal processes is inflated, anteroposteriorly large and slightly verticalised, whereas the posteromedial pair is extremely reduced (Figure 5g). In adults, the intertympanic sinus system is highly modified: the intertympanic pneumatic recess is elongated laterally and compressed anteroposteriorly and dorsoventrally, and it is narrower in its medial part. Its lateral parts are slightly oriented ventrally, showing a convex roof in transverse view (Figures 5h-j and 6a,b, Figure S8). The otoccipital pneumatic recess is nearly completely merged with the intertympanic pneumatic recess, with little ventral expansion. The PPR is only formed by the anterolateral pre-parietal processes. They form paired bulges projected dorsally, which then extend anteriorly, coalescing when size increases (Figure 5h-j). Large specimens show a voluminous PPR which is elongated anteroposteriorly, while the posteromedial preparietal processes are completely absent (Figure 5j).

| Tomistoma
Tomistoma possesses an anteroposteriorly compressed intertympanic sinus system which does not bear any developed PPR (Figure 6c,d, Figure S9). The intertympanic pneumatic recess is elongated laterally during growth and undergoes a prominent compression of its medial part when size increases, both in the anteroposterior and dorsoventral directions. The lateral parts of the intertympanic sinus are slightly oriented dorsally, showing a concave roof in transverse view (Figure 6c,d). Sub-adult specimens still display a developed otoccipital recess, which is rapidly reduced ventrally and laterally during growth ( Figure S9). This recess is thinner in adults but still distinguishable from the intertympanic pneumatic recess. The PPR is completely absent in all stages studied. In juvenile and sub-adult specimens, the pre-parietal processes are reduced. During ontogeny, the anteroposterior compression of the system is accompanied with a nearly complete reduction of the anterolateral pre-parietal processes, which become thin and end at the supraoccipital-parietal suture. The posteromedial pre-parietal processes are present and oriented vertically but without entering the parietal (Figure 6c,d).

| Voay
The intertympanic sinus system of V. robustus displays an expanded pneumatisation (Figure 11a and Figure S10). The intertympanic pneumatic recess is anteroposteriorly and dorsoventrally large in adults. Its prootic part is voluminous and developed anteriorly, and it is connected anteroventrally to the prootic facial recess like in Osteolaemus. The otoccipital pneumatic recess is voluminous with almost no lateral compression: it is well developed ventrally, and it is connected through large ostia to the rhomboidal sinus (Figure 11a).
The anterolateral pre-parietal processes are directed anteriorly and merged in a single bulbous cavity in two out of the three specimens studied. The posteromedial pre-parietal processes are directed vertically and can be connected anteriorly to the anterolateral processes. The development of the PPR seems to differ in each individual studied ( Figure S10). In MNHN-F-1908-5 it is greatly inflated, and merges with a great pneumatic cavity oriented anteriorly that reaches the frontal. In the NHMUK specimens it is less expanded, and the anterolateral pre-parietal processes is also developed in the posterior direction in NHMUK-PV-R-36685, like some specimens of Osteolaemus ( Figure S6).

| QUANTIFI C ATI ON OF INTERT YMPANI C S IN US S HAPE
Procrustes ANOVA revealed a significant effect of both size and taxonomic grouping on sinus shape (p = 0.001), with size accounting for 21.1% of the overall variation, while 42.4% of the variability is linked to the species-specific intertympanic sinus morphology. The snout shape of the specimens (brevirostrine, mesorostrine or longirostrine, see Table 1) also accounts for 14.5% of the variation (Table S2).
The first two principal components of the complete ontoge-

| ONTOG ENE TI C TR A JEC TORIE S AND AN CE S TR AL TRENDS RECON S TRUC TI ON
Procrustes ANOVA revealed significant differences in allometric trajectories between species (interaction term size: species, p = 0.001, see Table S2). Comparisons of the allometry models showed that species-specific allometric trends were significantly better than a common allometry model. However, due to the heterogeneity in ontogenetic sampling and the scarcity of specimens in some species, the pairwise comparisons of ontogenetic trajectories in the unique allometry model did not reveal any significant pairwise differences, whereas pairwise comparisons in the common allometry model revealed significant differences between most studied trajectories (Data S6 and S7).

F I G U R E 7
Ontogenetic morphospace of intertympanic sinus system shape showing differences between the distributions of Alligatoridae (red), Crocodylidae (green), Tomistoma (purple) and Gavialis (blue) for the four size classes in the first two principal components. Extreme shapes for each PC axis are given with wireframes in dorsal view. The zone shaded in pink is the region of the morphospace containing all studied hatchlings (CHR, 'common hatchling region').
Only species that showed substantial positive allometry, resolved ontogenetic series and a small variance display statistically significant ontogenetic trends (Figures S17, S18, A. mississippiensis still presents a slightly negative allometric trajectory, which is consistent with our qualitative observations that demonstrate an inflation of the intertympanic sinus system during growth rather than a compression (Figure 4a-e, Figure S17)  Figure S18). Additionally, Mecistops shows a negative trend on PC2, corresponding to a flattening of the parietal recess during growth ( Figure S22b). Yet, as we were not able to study hatchlings and juveniles of this genus, the complete trajectory remains unknown. The ontogenetic trends obtained on PC1 and PC2 were used to estimate the ancestral trends on each node ( Figure S19, Table S6).
Hypothetical developmental patterns of ancestral nodes were obtained by maximum likelihood from previous trend parameters ( Figures S20 and S21). As such, most of the confidence intervals overlap due to gaps in our ontogenetic series (Table S6)

| Alligatoridae
The Alligatoridae-only PCA allows a clear discrimination between Caimaninae and A. mississippiensis in the morphospace created by the two first components, explaining 54.4% of their morphological variation (Figure 9a). PC1 scores are significantly correlated with size (p = 0.001, R 2 = 0.65, see Table S4) The allometric trajectories in this morphospace showed that the main changes that occur during alligatorid growth mainly involve the PPR. PC1 trajectories show that species undergo a continuous anteroposterior development of the parietal recess, which is strongly correlated with size ( Figure 9b and Table S7)

| Crocodylidae
Each crocodylid genus displays a distinct morphology, which can be discriminated, for the most part, in the total ontogeny (Figures S12 and S13) and in the Crocodylidae-only morphospaces (Figure 10, Figure S14). In the latter, the first principal component is only significantly correlated with size (p = 0.001, R 2 = 0.65, Table S4). As such, the morphospace defined by PC2 and PC3, which are both correlated with the species-specific morphology (p = 0.001 and 0.003, Osteolaemus at smaller absolute sizes).

| Gavialidae
The Gavialidae-only PCA highlights the characters that discriminate Gavialis and Tomistoma in intertympanic sinus shape (Figure 12a).
PC1 is correlated with the species-specific morphology (p = 0.005, R 2 = 0.58, see Table S4), and separates the small cluster of Tomistoma in positive values, characterised by a nearly complete obliteration of the parietal processes, from the more dispersed cluster containing all Gavialis specimens in negative values, characterised by an anteriorly and dorsally developed parietal recess.
There is a significant relationship between shape and both size and species individually. However, the interaction term (size: species) was not significant (  (Figures 6, 7, 8, and 12). The two genera display divergent trends on PC1, with Gavialis showing a development of the parietal recess, whereas it is reduced in Tomistoma (Figure 12b). Size strongly influences the anteroposterior compression of the intertympanic sinus system (R 2 = 0.67), with both genera possessing a positive allometric trend on PC2.
However, for a given size, Tomistoma specimens display higher values on PC2, showing a slightly more anteroposteriorly compressed intertympanic sinus than Gavialis specimens (Figure 12c). otoccipital recess (Figures 4a,b,f,g and 5a,b,f,g). These rapid posthatching modifications represent a threshold to differentiate neonates and young juveniles from later stages, regardless of absolute size. These changes are likely to be linked with the 'cranial metamorphosis' (termed in Tarsitano, 1985;Tarsitano et al., 1989;Kuzmin et al., 2021). This term defines the profound osteological changes occurring rapidly in the post-hatching development of the crocodylian braincase. It results in the verticalisation of the braincase elements, especially affecting the basisphenoid, basioccipital and pterygoid bones, and to a lesser extent, the quadrate and the exoccipital. Such modifications would necessarily have an impact on the structures encapsulated in the bony elements (Dufeau & Witmer, 2015;Hu et al., 2021). During this developmental event, the ventral part of the exoccipital is slightly affected by the verticalisation while the quadrates develop laterally, causing the changes in orientation of the otoccipital recess after hatching (Figures 4a,b,f,g and 5a,b,f,g).

F I G U R E 11
The prootic, parietal and supraoccipital bones are barely impacted by this verticalisation, which would allow the intertympanic and parietal recesses to thicken dorsoventrally while retaining their own ontogenetic trajectories independently of dorsoventral constraints.
Arising from this shared intertympanic sinus shape, post-hatching individuals of the three families follow different growth trajectories.
In Alligatoridae, intertympanic sinus morphology is mainly driven by the anterodorsal development of the parietal recess (Figures 7 and 9). This is remarkably similar to the allometric trend for the hypothetical crocodylian ancestor (Figure 8d). Intertympanic recess shape is weakly modified in A. mississippiensis and C. latirostris between juveniles and adults, due to the prominent deceleration in compression and the continuous expansion of their diverticula (Figure 8a), resulting in minimal changes in anteroposterior thickness (Figure 4; low dispersion on PC1, Figure 7). This retention of a juvenile morphology is in line with the recognised paedomorphic nature of alligatorid cranial features (Monteiro & Soares, 1997;Morris et al., 2019).
In Longirostres, the intertympanic sinus system displays more profound changes after the cranial metamorphosis, being much less expanded in adults. In Crocodylidae, there is a high disparity in ontogenetic trajectories and resulting adult morphologies.
However, the crocodylid sinus ontogeny seems to be partitioned in two phases. From hatchlings to juveniles, they first develop the pre-parietal processes, overlapping with Alligatoridae morphology F I G U R E 1 3 Molecular phylogenetic tree of extant Crocodylia, including Voay robustus, associated with skull outlines of each studied species. The tree was constructed as a consensus of the topologies of Oaks & Dudley, 2011;Hekkala et al., 2021;Pan et al., 2021. O., Osteolaeminae; ppp, posteromedial parietal processes; (1) Pre-displacement of intertympanic sinus anteroposterior compression and reduction of otoccipital recess; (2) Reduction of the posteromedial pre-parietal processes; (3) Reduction of the anterolateral pre-parietal processes and absence of parietal recess; (4) Expanded diverticula; (5) Developed and verticalised parietal recess; (6) Reduction of parietal and otoccipital recesses. Characters highlighted in blue correspond to conflicts between the molecular and morphological topologies ( Figure S16).
(displacement towards PC2-positive values, Figure 7). Then, from juveniles to adults, they undergo an anteroposterior compression and lateral expansion of the system, which increases with absolute size, constraining the pneumatic cavities (displacement towards PC1-positive values, Figure 7). This compression mechanism has a different intensity depending on the genus and species: it heavily impacts C. niloticus and Mecistops, while C. siamensis and C. porosus are moderately impacted (Figure 8b, Figure S22). Crocodylus palustris, Osteolaemus and Voay are weakly impacted, showing thicker diverticula in adults (Figure 10a). In Indomalayan Crocodylus species C. siamensis, C. porosus and C. palustris, the parietal recess also displays an increased rate of development, being greatly developed vertically in adults (Figure 8e, Figure S5) and revealing a common developmental event in this lineage (character 5, Figure 13). Finally, the anteroposterior compression seems to start earlier during the ontogeny of Gavialidae (pre-displacement at node VII, Figure 8c).
This would result in the simultaneous development of the parietal and intertympanic recesses; however, the shift in the calculated trajectory at node VII could be mainly driven by the shift in the intercept of the Tomistoma trajectory, which must be taken cautiously in the absence of a hatchling in our dataset. Although they show this common sinus compression pattern, the two genera display a major developmental difference: the acceleration of the parietal recess growth in Gavialis, and its deceleration (or even resorption) in Tomistoma (Figures 8f and 12b).
While the developmental patterns of the parietal diverticulum seem to be clade-specific, intertympanic sinus compression seems to be correlated with the variation in skull shape to some extent.
Indeed, species characterised by blunt skulls with short and broad rostra, tend to possess anteroposteriorly large and expanded diverticula. Such characteristics are likely to be an ancestral feature of Alligatoridae, but were likely independently acquired by Osteolaemus and Voay. This tendency is also present to a lesser extent in C. palustris ( Figure 13). On the other hand, mesorostrine and longirostrine species, that develop more slender skulls with longer and narrower rostra, tend to possess anteroposteriorly compressed and restricted diverticula. This is the case in C. niloticus, C. acutus, Mecistops and the Gavialidae. We hypothesise that these convergences are linked to space availability inside the braincase: during crocodylian cranial growth, the posterior part of the skull table enlarges laterally while the supratemporal fenestrae (STF) become bigger, which reduces room between the latter and the posterior wall of the braincase (Cossette et al., 2021). The size of the STF is linked to the development of the adductor muscles attached to the jaw (i.e. the 'musculus adductor mandibulae externus profundus', Holliday & Witmer, 2007), which presents different shapes depending on skull morphotypes. Brevirostrine taxa possess small semi-circular adductor muscles associated with small STF, while longirostrine taxa possess large circular adductor muscles, associated with larger STF (Holliday & Witmer, 2007). Furthermore, the STF increases in size with snout length in most species: STF development would thus imply an anteroposterior constraint on the intertympanic sinus system, weak in brevirostrine taxa due to smaller STF, but increased in mesorostrine and longirostrine taxa due to the presence of larger STF. The correlation between rostrum and STF sizes, partly controlled by adductor muscle attachments, would thus influence the space available in the braincase for sinus development, linking indirectly rostrum shape and sinus expansion.
In Alligatoridae and Osteolaemus, the shape of the skull table remains rectangular during ontogeny, and the STF size remains small (Cossette et al., 2021), reflecting the deceleration of their rostrumto-braincase relative growth (Morris et al., 2019), which concurs with the retention of juvenile characters. The same bone and sinus developmental patterns seem to characterise Voay, which displays both a blunt skull and large diverticula ( Figure 11). Crocodylus palustris also displays an anteriorly developed sinus system, which explains its differentiation from C. siamensis and C. porosus in the morphospace despite having similar otoccipital and parietal recess characteristics (Figures 10a and 13, Figure S5). In contrast, the already elongated and a small intertympanic sinus that is greatly reduced anteroposteriorly (Erb & Turner, 2021). As an extreme, the Teleosauridae do not possess any intertympanic sinus (Brusatte et al., 2016;Herrera et al., 2018;Wilberg et al., 2021). These Mesozoic aquatic crocodylomorphs were fully aquatic and characterised by long slender snouts, extremely large STF and an anteroposteriorly restricted braincase.
However, as noted by Cossette et al., 2021, the direct link between longirostry and larger STF is likely to be overstated in some clades, as longirostrine osteolaemines make an exception to this rule. Despite their elongated snout, Mecistops and Euthecodon both display moderate STF sizes comparable to mesorostrine spe- cies. Yet, they are still larger than their osteolaemine counterparts, showing that rostrum shape probably has some influence on STF size, but somehow decoupled from intertympanic sinus shape (adult Mecistops having similar compression scores on PC1 as C. niloticus or Gavialis). This implies that potential additional constraints influence the volume and expansion of intertympanic sinus diverticula.

| Is intertympanic sinus shape influenced by ecology?
The sinus system of crocodylians plays an important role in the interaction between the animal and its environment. It is a key part of the hearing process (Carr et al., 2016;Dufeau & Witmer, 2015).
Additionally, thanks to its pneumatic nature, it lightens the skull, and may potentially be useful for controlling the buoyancy of the head in an aquatic environment. However, all extant species of Crocodylia share roughly similar ecological preferences, living in semi-aquatic environments, which makes it difficult to assess environmentalbased differences, and few studies have investigated the behaviour of wild crocodylian species. There are only two genera that represent extremes in behavioural patterns. Among the taxa we sampled, Osteolaemus shows the most 'terrestrial' lifestyle, living in swamps, secluded pools or stagnant water and was reported to take long walks far from water (Eaton, 2010;Waitkuwait, 1986). In contrast, Gavialis shows the most aquatic lifestyle of all extant crocodylians, spending most of its time in water and being the sole extant species to not be able to walk in a semi-upright stance on land (Stevenson & Whitaker, 2010).
The impact of lifestyle on intertympanic sinus shape was thus tested by partitioning the crocodylian species in three classes (semiaquatic for most genera, sub-aquatic for Gavialis and semi-terrestrial for Osteolaemus), revealing a significant correlation (p = 0.003), but accounting for only 7.5% of the overall variation (Table S2). Thus, it is likely that intertympanic sinus characteristics were modulated by ecological parameters during the evolution of the crocodylian lineages. However, we were not able to precisely assess which shape changes could be linked to the living environment with our dataset.
In comparison with other crocodylian clades, we observe that the sinus system bears considerable differences between fossil forms from different living environments. For instance, the Sebecidae, a group of Cretaceous-Cenozoic crocodylomorphs that are interpreted to be fully terrestrial, possesses a sinus system that is impressively large and inflated, with numerous diverticula (Pochat-Cottilloux et al., 2021). On the other hand, in the marine thalattosuchians, the sinus system is compact and reduced, with a complete obliteration of the intertympanic sinus pneumatic recesses (Brusatte et al., 2016;Herrera et al., 2018;Wilberg et al., 2021). We therefore hypothesise that the overall volume of the sinus system, especially the dorsal pneumatic cavities, could be linked to living environments, albeit weakly. In addition to the brevirostry/longirostry constraints mentioned earlier, functional constraints such as head weight and buoyancy could be drivers explaining the selection of sinus volume expansion in more terrestrial species or volume reduction in more aquatic species.
Even so, the shape and arrangement of the pneumatic diverticula, as shown in the present work, are also highly correlated with the species-specific morphology of the specimens studied, making it useful to assess morphological endocranial characters for studying the crown group.

| Relevance of intertympanic sinus morphology for taxonomic determination and phylogenetic analyses
The developmental study of the intertympanic sinus system enables us to examine the ontogenetic trends of different crocodylian genera, leading to different adult sinus morphologies. It now becomes possible to identify characters linked with ontogenetic stages, and highlight the potential diagnostic characters for each studied taxon at adult stage, and eventually, map adult intertympanic sinus morphology in phylogenetic framework ( Figure 13, Figure S16).
Here, we discuss several key features of crocodylian intertympanic sinuses which could help refine phylogenies in the future or ease the taxonomic attribution of fossil specimens, by including observations based on the sinus morphology as a complementary tool to osteological characters. This is a first step towards the inclusion of endocranial characters in phylogenetic character matrices.
In recent morphological phylogenies, only one character related to the intertympanic sinus system has been used since the works of Brochu: the presence/absence of a parietal recess communicating with the paratympanic pneumatic system, based on longitudinal cutting or low-resolution CT-scans (Brochu, 1997(Brochu, , 1999. However, we found that the coding of this character was dependent on ontogenetic variability, and often proved erroneous and inconsistent between publications. Indeed, in the matrices of Brochu (1997Brochu ( , 1999, it corresponds to character 154, stated as present in Alligatoridae and Gavialis (0)  all Longirostres (sensu Harshman et al., 2003) possess only two pairs of pre-parietal processes, with one pair being reduced during ontogeny in Mecistops, Gavialis and Tomistoma ( Figure 13). Thus, it concurs with the recovery of Gavialidae and Crocodylidae as sistergroups in both molecular (Oaks & Dudley, 2011;Pan et al., 2021;Poe, 1996;Roos et al., 2007;Willis et al., 2007) and recent morphological topologies (Lee & Yates, 2018;Rio & Mannion, 2021).
If this pattern is verified in fossil specimens of the three lineages, the presence/absence of the prootic-parietal ostium might be a key character to discriminate alligatoroids from crocodyloids in the fossil record, if the prootic-parietal suture is preserved. Whether this character is an apomorphy of Alligatoridae or simply a character loss in Longirostres lineages ( Figure 13, Figure S16 Figure S3). The shape of the parietal recess, as well as the relative position of the pre-parietal processes can still be coded accordingly.
Additionally, Caimaninae species bear further differences with A.
mississippiensis. Adult Caiman crocodilus and C. yacare share a remarkably similar morphology, as expected for sister-taxa ( Figure S3). Caiman latirostris sinus shape is close to the latter, with a more expanded parietal recess and an inflated intertympanic recess ( Figure S2). Melanosuchus niger morphology falls close to Caiman species in the morphospace, but displays more differentiated diverticula, with more restricted, tubular and well-separated recesses (Figure 9a, Figure S3). Intertympanic sinus morphology within Alligatoridae thus matches molecular-based interspecific relationships (Figure 13).

| Crocodylid characters
Investigation of the intertympanic sinus system was especially relevant to resolve the issues concerning specific determination within African counterpart, concurring with molecular-based biogeographical scenarios (Nicolaï & Matzke, 2019). This partition matches the molecular phylogenetic framework (Figure 13), as Indomalayan species C. siamensis and C. palustris are retrieved as sister taxa in molecular topologies, followed by C. porosus (Pan et al., 2021).
Here, adult C. siamensis and C. porosus form a single cluster; however, as the taxonomic determinations of these specimens may be uncertain, it is impossible to separate the two species without additional specimens. In any case, the biogeographic distribution of these two species greatly overlaps (Nicolaï & Matzke, 2019), and cases of hybridisation between the two species have been reported, and a common sinus morphology is plausible (Fitzsimmons et al., 2002;Lapbenjakul et al., 2017;Simpson & Bezuijen, 2010;Srikulnath et al., 2012). Neotropical crocodiles, on the other hand, are for now insufficiently sampled to draw conclusions on the evolution of their sinus system after their separation from their African ancestors (Delfino et al., 2020;Milián-García et al., 2020;Nicolaï & Matzke, 2019).
The Madagascar subfossil crocodylian material was also subject to taxonomic misinterpretations. Indeed, the Holocene crocodylian fauna was primarily thought to be only represented by the brevirostrine endemic species V. robustus, while the arrival of Crocodylus on the island was assumed to be very recent and following the extinction of Voay around 2000 years ago (Bickelmann & Klein, 2009;Brochu, 2007;Martin et al., 2022). Consequently, much ancient crocodile material was attributed by default to V. robustus. However, Martin et al. (2022) showed, using a combination of external and internal cranial characters, that the occurrence of Crocodylus on the island was at least contemporaneous with the endemic species, and that Malagasy crocodylian material needed to be re-evaluated (Martin et al., 2022). Here, we confirm the distinctive morphological gap between 'true' V. robustus specimens and two subfossil Crocodylus sp. from Madagascar ( Figure 11). Agreeing with the absence of Voay diagnostic traits (pronounced squamosal horns and verticalised snout), the intertympanic sinus of these subfossils of Crocodylus sp. share the same morphology as C. niloticus (Figure 11), that is, a compressed intertympanic sinus, an absence of a developed prootic part, and reduced otoccipital and parietal recesses.
This shows that the Malagasy Crocodylus internal morphology is easily distinguishable from that of V. robustus. Furthermore, it implies that the oldest Crocodylus populations of Madagascar were probably morphologically associated with African C. niloticus populations coming from the African mainland (Hekkala et al., 2021).
Additionally, V. robustus displays a sinus morphology that is close to Osteolaemus: an anteroposteriorly developed intertympanic recess with a protruding prootic part, linked ventrally to the prootic facial recess; an expanded and verticalised otoccipital recess with no lateral compression; and a flat parietal recess developed anteriorly, laterally and posteriorly (Figures 10 and 11, Figures S6 and   S10). These shared characters are in line with their proposed close relationship based on morphological phylogenies ( Figure S16; Brochu, 2007;Rio & Mannion, 2021), but contrast with molecular results which retrieve Voay as a stem-taxon to the Crocodylus lineage (Hekkala et al., 2021). On the other hand, Mecistops, which is considered as the sister-taxon to Osteolaemus in the molecular framework, possess a different and compressed morphology similar to that of Crocodylinae (especially to the sub-longirostrine C. acutus), which rather reflects once again phylogenetic topologies derived from morphological characters, where Mecistops often lies at the base of the Crocodylus lineage ( Figure S16). Voay, Osteolaemus and Mecistops are an example of high disparity in rostrum shape in a putatively single lineage, associated with two very different types of sinus system.
In any case, even if the influence of cranial shape on endocranial features is different in Osteolaeminae, it has not overwritten shared sinus characters in Voay and Osteolaemus. This reinforces the problematic status of osteolaemines, a group that is still phylogenetically debated and composed of morphologically distant taxa. In the future, the investigation of juveniles and fossil osteolaemine relatives may help clarify such questions.

| Gavialoid characters
The similarity in intertympanic sinus ontogeny in Tomistoma and Gavialis may corroborate their shared ancestry, shown by a common pre-displacement event of sinus compression occurring in the Gavialidae lineage (Figures 8c and 13, Figure S16). This is congruent with the evolution of their cranial ontogeny, because their cranial development also underwent a pre-displacement of both snout elongation and braincase size reduction sometime before the Gavialis-Tomistoma evolutionary split (Morris et al., 2019). Both aspects thus reinforce the phylogenetic placement of Tomistoma and Gavialis as sister-taxa. Furthermore, their seemingly divergent ontogenetic trajectories are consistent with the rapid evolutionary rates retrieved for the gharial lineage, which draws Gavialis morphology far away from its sister-taxon Tomistoma in less than 10 Ma after their separation, around 38 Ma according to tip-dated molecular-clock estimates (Lee & Yates, 2018). However, most morphology-based phylogenetic methods still retrieve divergence time between Tomistominae and Gavialinae around 100 Ma. This is mainly due to the 'thoracosaur' issue, which involves longirostrine taxa that are historically considered as stem-gavialoids and are still retrieved as such in the recent morphological topologies (Rio & Mannion, 2021). Along with other longirostrine fossils, 'thoracosaurs' are convergent with modern gharials due to atavism and reversion of cranial characters in the latter (Gatesy et al., 2003;Lee & Yates, 2018). Their age (from Late Cretaceous to early Palaeocene) indicates the presence of tens of millions of years-long ghost lineages in the branches leading to extant Gavialidae in morphologicalbased topologies (Rio & Mannion, 2021). Therefore, it would be extremely useful to have an insight on thoracosaur internal structures to investigate whether their gharial-like external morphology is independent of their sinus structure, the latter being a potential new morphological proxy to separate these ancient forms from modern gharials.
Finally, the morphological differentiation observed between Gavialis and Tomistoma bears implications among fossil relatives.
If the intertympanic morphological distinctiveness is conserved in the braincase of extinct gavialines and tomistomines, important taxonomic implications are expected within longirostrine forms, circumventing the phylogenetic convergence in snout shape.
Supporting this view, the neuroanatomy of Gryposuchus neogaeus, a Miocene longirostrine crocodylian considered part of the gavialid lineage, represents an interesting case (Bona et al., 2015). Many differences in the shape and extension of the paratympanic sinuses were reported between the specimen and Gavialis gangeticus. Notably, the intertympanic sinus system was well preserved, and showed several recognisable features: a considerable compression of the medial part of the intertympanic recess; a ventral reduction of the otoccipital recess; and the absence of any parietal recesses. This morphology is more reminiscent of Tomistoma than They were described as displaying a combination of tomistomine and gavialine characters, bringing further support for the sister taxon relationships of the two lineages (Iijima et al., 2022;Iijima & Kobayashi, 2019). Therefore, the investigation of the intertympanic sinus of such longirostrine taxa holds important promises to understand the evolution of the internal organs in Gavialidae and longirostrine crocodylians in general.

| CON CLUS ION
The investigation of crocodylian intertympanic sinus systems revealed that endocranial structures bear species-specific differences, which corroborate molecular data at high-and low-level phylogenetic relationships in extant taxa. Alligatoridae are clearly differentiated from Longirostres by the absence of a prootic-parietal ostium in the latter. Sinus post-hatching development begins with a common hatchling shape shared by all studied species, from which ontogenetic trajectories diverge, following different heterochronic modifications resulting in distinct adult characteristics. Sinus anteroposterior compression seems to have been accelerated and predisplaced in mesorostrine and longirostrine species, which we link to cranial constraints due to enlarged STF in taxa with an elongated rostrum. In adults, species are mainly separated by differences in the shape of the otoccipital and parietal recesses, which can now be used to differentiate Caiman from Alligator, Indomalayan from African Crocodylus, C. niloticus from Voay, as well as Tomistoma from Gavialis. These characteristics can be used to accurately discuss the evolution of endocranial sinuses in extinct crocodylians with respect to extant species, and eventually bring more material for the taxo-