Paralligator, Konjukova, 1954

Braincase osteology of Paralligator

Meatal chamber and major neurovascular passages

The meatal chamber (= outer ear cavity; Montefeltro et al. 2016) is relatively expanded in Paralligator . Its anatomy is best seen in PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3140/502, and PIN 3141/501. The meatal chamber (MC) is dorsoventrally deeper posteriorly, between the squamosal and quadrate and tapers anteriorly ( Fig. 8 View Figure 8 ). Its dorsal boundary is formed by the overhanging skull roof bones—the postorbital and squamosal. The MC is limited by the postorbital bar anteriorly and by the quadratojugal anteroventrally. The quadrate forms the ventral margin of the MC, whereas the posterolateral process of the squamosal limits the MC posteriorly.

A longitudinal sulcus is present along the lateral margin of the postorbital and squamosal ( Figs 5A View Figure 5 , 7B View Figure 7 , 8A View Figure 8 ), which is an osteological correlate for the upper earlid in crocodyliforms ( Montefeltro et al. 2016). This sulcus is variably developed in Paralligator specimens. It is generally weaker anteriorly, along the postorbital, and is more pronounced posteriorly on the squamosal. In some, notably smaller-sized individuals, the sulcus is prominent along its length and expands posteriorly, at the flared lobule of the squamosal: e.g. in PIN 3140/502, PIN 3141/501, PIN 3141/502, and PIN 3905/501-1 ( Figs 7B View Figure 7 , 8A View Figure 8 ). The flared lobule of the squamosal is present in PIN 551/29-1 but the sulcus for the upper earlid does not expand posteriorly, perhaps due to the development of an external ornamentation and co-ossification of a small osteoderm to the lateral surface of the squamosal. The sulcus for the earlid is the weakest in PIN 554/1-1 (holotype of P. gradilifrons ) and PIN 3726/501-1 (holotype of P. major ), both of which represent potentially adult individuals and have relatively flat squamosals. For example, the sulcus fades out at the mid-length of the squamosal in PIN 554/1-1 ( Fig. 5 View Figure 5 ). These differences may represent ontogenetic or individual variation in Paralligator , as has been suggested by Turner (2015) and Skutschas et al. (2015).

The dorsal surface of the quadrate bears a shallow depression—the periotic fossa, which marks the anterior and ventral attachment of the tympanic membrane ( Montefeltro et al. 2016). The fossa is relatively expanded anteroposteriorly and distinctly bilobate in Paralligator (e.g. in PIN 3140/502, PIN 3141/501) ( Figs 6C View Figure 6 , 8A View Figure 8 ). It differs from the more restricted and rounded fossa in extant crocodylians but is similar to that of some fossil mesoeucrocodylian taxa (e.g. Araripesuchus , Sebecus , Shamosuchus : see Montefeltro et al. 2016). A single moderatelysized subtympanic foramen is consistently present at the anteroventral corner of the periotic fossa in Paralligator (e.g. PIN 554/1-1, PIN 3140/502, PIN 3141/501) ( Figs 5C View Figure 5 , 6C View Figure 6 , 7B View Figure 7 , 8A View Figure 8 ).

The principal opening of the bony otic aperture (BOA) sensu Montefeltro et al. (2016) is the external auditory meatus (EAM). It is bordered anteriorly and ventrally by the otic incisure of the quadrate, posteroventrally by the otic buttress, and dorsally by the squamosal. The EAM of Paralligator is ovate in lateral view ( Figs 5B View Figure 5 , 7B View Figure 7 , 8 View Figure 8 ). Its posterior border is less distinct than in extant crocodylians, as the quadrate-squamosal contact is absent and the otic buttress is not prominent.

The neurovascular cranioquadrate passage extends posterolaterally from the posterior corner of BOA and EAM ( Figs 5B View Figure 5 , 7C View Figure 7 , 8 View Figure 8 ). It is a dorsally open groove bounded only by the otoccipital in Paralligator . The quadrate-squamosal contact posterior to BOA and EAM is absent in all but one examined specimen. In PIN 3140/502, a brief contact partially closes the cranioquadrate passage on the left side of the skull but is lacking on the right side ( Fig. 8 View Figure 8 ). This represents a potential individual variation of the feature, with both conditions represented on the two sides of a single cranium.

The dorsal otic incisure in the posterodorsal corner of BOA is not marked on the ventral surface of the squamosal and is not delimited from the EAM. The vascular postquadrate foramen is located deep within BOA, at its posterodorsal corner, as is seen in CT scans of PIN 554/1-1 (holotype of P. gradilifrons ) ( Fig. 9B View Figure 9 ). The postquadrate foramen provides passage for the stapedial/ temporoorbital blood vessels from the cranioquadrate passage into the temporal canal (seePorter et al. 2016, Kuzmin et al. 2021). The narrow temporal canal is clearly observed in CT scans of PIN 554/1-1 ( Fig. 9B View Figure 9 ). It is likely limited by the prootic and otoccipital ventrally and the parietal and squamosal dorsally, but sutural relations are hard to follow due to artefacts in scanning. The temporal canal opens via the anterior temporal foramen anteriorly, on the posterior wall of the supratemporal fossa ( Fig. 9A View Figure 9 ). This foramen is bounded by the parietal and squamosal dorsally and by the quadrate and prootic ventrally. On the occiput, the posttemporal fenestrae are slit-like and limited by the supraoccipital, otoccipital, squamosal, and parietal ( Figs 4A, B View Figure 4 , 6B View Figure 6 ).

Mesethmoid (anterior ossification in olfactory region)

The mesethmoid is a small separate ossification attached to the ventral surface of the frontal, which is preserved in PIN 3141/501 and PIN 3458/501-1 ( Fig. 10 View Figure 10 ). The mesethmoids in both specimens are incomplete but that of PIN 3141/501 is better preserved. Corresponding elevated ridge-like facets are present in PIN 551/29-1 and PIN 554/1-1 (holotype of P. gradilifrons ), indicating that the mesethmoid is a consistent feature in Paralligator , which is either not preserved in situ and was loosely connected to the frontal or was incompletely ossified in these individuals. Similar variability has been noted in the ontogeny of the ‘ethmoid complex’ of tyrannosaurids ( Ali et al. 2008).

The mesethmoid is located on the ventral surface of the frontal, close to its anterior edge, and just anterior to the bases of the prefrontal pillars ( Fig. 10A View Figure 10 ). It is diamond-shaped in ventral view and longer than deep in lateral view. The posterior margin of the mesethmoid forms an acute wedge that divides the impressions of the olfactory bulbs on the ventral surface of the frontal. The mesethmoid may be subdivided into the dorsal plate and the ventral median septum (see Ali et al. 2008). The dorsal plate is slightly lateromedially expanded and sutures to the frontal. The median septum of the mesethmoid is subdivided anteriorly by a deep furrow. Each lateral margin bears two or more longitudinal ridges that delineate shallow sulci. The dorsal sulcus is twice as deep dorsoventrally than the ventral sulci and is here interpreted as an osteological correlate of the medial or common nasal vein (see Porter et al. 2016). The ventral smaller sulci are considered correlates for the olfactory nerve (CN I), as in Efimov (1988) and Ali et al. (2008).

Laterosphenoid

The laterosphenoid is partially preserved in PIN 551/29-1 and is relatively complete in PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3140/502, PIN 3905/501-1, PIN 3141/501, and PIN 3141/502 ( Figs 4 View Figure 4 , 5 View Figure 5 , 6 View Figure 6 , 7 View Figure 7 , 11 View Figure 11 ). The isolated left laterosphenoid PIN 3141/502-9 from the Nogon Tsav locality (Nemegt Formation) is exquisitely preserved showing fine anatomical details ( Fig. 11D–K View Figure 11 ).

The laterosphenoid of Paralligator is generally similar to that of extant crocodylians and fossil crocodyliforms ( Holliday and Witmer 2009, Kuzmin et al. 2021). It forms the anterolateral wall of the braincase and the anterior margin of the trigeminal (= maxillomandibular) fossa and foramen ( Figs 5C View Figure 5 , 7A View Figure 7 , 11 View Figure 11 ). Grooves for the corresponding branches of the trigeminal nerve (CN V) are present on the lateral surface of the laterosphenoid. The lateral bridge subdivides the passages of the ophthalmic (CN V 1) and maxillary (CN V 2) branches of CN V and associated vessels ( Fig. 11F, H View Figure 11 ). The lateral bridge is completely developed and sutures to the pterygoid and quadrate ventrally ( Figs 5 View Figure 5 , 7 View Figure 7 ). The small caudal bridge is present ventrally to the groove for the supraorbital branch of CN V 2 (CN V so) ( Fig. 11D, E View Figure 11 ). It is broken off or imperfectly preserved in most available specimens but apparently contacts the quadrate posteriorly in PIN 3140/502 and PIN 3905/501-1 (Supporting information, Figs S5 View Figure 5 , S 6 View Figure 6 ).

The laterosphenoid body contacts the parabasisphenoid ventrally, the prootic posteriorly, and the quadrate posterolaterally. It is internally pneumatized by the laterosphenoid pneumatic recess (present on both sides of PIN 554/1-1, PIN 3141/501, and in PIN 3141/502-9) ( Fig. 11G, K View Figure 11 ). Medially, a blunt tentorial crest formed by the body delimits the cerebral fossa ( Fig. 11B View Figure 11 ).

Several crests extend on the lateral surface of the laterosphenoid and mark the attachment of various muscles (see Holliday and Witmer 2009, Kuzmin et al. 2021) ( Fig. 11D, E View Figure 11 ). The anterior edge of the lateral bridge corresponds to the tensor crest. It is dorsally continuous with the antotic crest, which extends to the capitate process and subdivides the laterosphenoid into the temporal and orbital aspects. Dorsally, on the temporal surface, there is a faint cotylar crest—osteological correlate for M. pseudotemporalissuperficialis ( Holliday and Witmer 2009). Small crests extend dorsally and ventrally to the groove of CN V so. They are anteriorly continuous with the antotic crest and posteriorly – with the crest A’ on the quadrate ( Fig.5A, C View Figure 5 ). These crests delimit a shallow fossa on the lateral bridge, which is likely an osteological correlate for M. pseudotemporalis profundus ( Holliday and Witmer, 2009) ( Fig. 11E View Figure 11 ).

The postorbital process extends anterodorsally from the laterosphenoid body and forms the temporal aspect of the bone ( Fig. 11A View Figure 11 ). The dorsal surface of the laterosphenoid is sutured to the frontal anteriorly and the parietal posteriorly. The postorbital process is continuous with the anterior process anteriorly and the capitate process laterally. The capitate process terminates distally with a rounded head (capitulum) fitting into a socket on the ventral surface of the postorbital ( Fig. 4C, D View Figure 4 ).

The anterior process is oriented anteromedially and lies anteriorly to the level of the capitate process ( Figs 4D View Figure 4 , 6D View Figure 6 ). It forms the orbital aspect of the element. The anterior process is incomplete medially in all available specimens. The slender process that extends from the anterior process ventromedially (see Kuzmin et al. 2021) is also incomplete; only its base is present in PIN 3141/502-9 ( Fig. 11I, J View Figure 11 ). Thus, the contact between the contralateral laterosphenoids and with the parabasisphenoid rostrum is unknown. The anterior process is pierced by a small canal of the trochlear nerve (CN IV) just dorsal to the base of the slender process ( Fig. 11K View Figure 11 ). A notch posterior to it corresponds to the passage of the oculomotor nerve (CN III) ( Fig. 11J View Figure 11 ).

We have found no evidence of a separate epipterygoid ossification in Paralligator .

Prootic

The prootic is preserved in PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3140/502, PIN 3905/501-1, and PIN 3141/501. Both prootics are segmented in PIN 3141/501, and collectively they provide data on most aspects of its anatomy ( Fig. 12A–I View Figure 12 ). The dorsal portion of the prootic buttress is exposed on the right side of PIN 3905/501-1 due to breakage (Supporting information, Fig. S6E View Figure 6 ). The participation of the prootic in the floor of the temporal canal is observed in PIN 554/1-1, PIN 3905/501-1, and PIN 3141/501 ( Fig. 9A View Figure 9 ).

The prootic of Paralligator is subdivided into the capsular portion, the superior and inferior anterior processes, the dorsolateral lamina, and the prootic buttress, as in extant crocodylians (see Kuzmin et al 2021). It is obscured by the neighbouring bones and is externally observed only through the trigeminal and the anterior temporal foramina ( Figs 5 View Figure 5 , 7 View Figure 7 , 9A View Figure 9 ). The anterior inferior and superior processes of the prootic form the posterior portion of the trigeminal fossa and foramen, which is also bounded by the laterosphenoid and quadrate. The prootic has limited exposure here and lacks the external contact with the pterygoid ventrally to CN V foramen in PIN 554/1-1 and apparently in other specimens (e.g. PIN 3140/502, PIN 3905/501-1) ( Fig. 5A, C View Figure 5 ). In PIN 3141/501, the prootic appears to contact the pterygoid ventral to the trigeminal foramen ( Fig. 7A, B View Figure 7 ). However, it is likely due to an incomplete preservation and segmentation of the pterygoid process of the quadrate on both sides, which covers this contact externally in other specimens.

The prootic forms the anterior part of the otic capsule and contains portions of the vestibular recess and the anterior and lateral semicircular canals ( Fig. 12B, G View Figure 12 ). The cochlear prominence is partially preserved ventrolateral to the vestibular recess in the right prootic of PIN 3141/501 ( Fig. 12H View Figure 12 ), but the margin of the fenestra ovalis cannot be reliably observed in any specimen. The capsular portion of the prootic bulges medially into the endocranial cavity and forms the anteroventral part of the otic bulla (sensu Kuzmin et al. 2021). The two small foramina on the endocranial surface ventral to the otic bulla correspond to the passages of the facial nerve (CN VII) and the anterior branch of the vestibulocochlear nerve (CN VIII ab), respectively ( Fig. 12G View Figure 12 ). The floccular fossa is not developed.

The dorsolateral lamina extends laterally from the capsular portion of the prootic. It is lateromedially broad in Paralligator ( Fig. 12C View Figure 12 ). The anterolateral surface of the lamina is broadly sutured to the quadrate, whereas its posterior surface is smooth and forms the wall of the pharyngotympanic (middle ear) cavity ( Fig. 12C, H View Figure 12 ). Dorsally, the dorsolateral lamina is continuous with the prootic buttress, which forms a loop over the intertympanic pneumatic recess ( Walker 1990, Kuzmin et al. 2021). Only the base of the prootic buttress is preserved in PIN 3141/501 ( Fig. 12B–D View Figure 12 ), but a corresponding facet on the otoccipital allows to trace its course ( Fig. 13A View Figure 13 ). Additionally, a buttress is observed in PIN 3905/501-1 (due to breakage; Supporting information, Fig. S6E View Figure 6 ) and in CT scans of PIN 554/1-1 (holotype of P. gradilifrons ). The prootic buttress is anteroposteriorly and lateromedially expanded at its base, where it merges with the dorsolateral lamina. Here, it forms the floor of the temporal canal and is broadly exposed through the anterior temporal foramen ( Fig. 9A View Figure 9 ). Its dorsal tip is notched to form the postquadrate foramen—the passage of the temporoorbital vessels ( Kuzmin et al. 2021) (Supporting information, Fig. S6E View Figure 6 ). Posteriorly, the prootic buttress is a thin obliquely oriented strip of bone, which contacts the otoccipital.

The prootic of Paralligator is pierced by several cranial nerves (e.g. CN VII, CN VIII, sympathetic nerve—SN) and by the pneumatic recesses. The spacious intertympanic pneumatic recess is bounded by the capsular portion ventrally, the dorsolateral lamina anteriorly, and by the prootic buttress dorsally and posteriorly. It is connected laterally with the pharyngotympanic (middle ear) cavity and medially is continuous with the recesses in the otoccipital, supraoccipital, and parietal ( Fig. 12C View Figure 12 ). The prootic facial recess is concealed within the bone, anterolaterally to the capsular portion ( Fig. 12C, H View Figure 12 ).

Supraoccipital

The supraoccipital is preserved in several specimens: PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3726/501-1 (holotype of P. major ), PIN 3140/502, PIN 3141/501, PIN 3726/503, and PIN 3905/501-1. Additionally, facets on the ventral surface of the parietal PIN 3141/502 (Supporting information, Fig. S8G, H View Figure 8 ) provide data on the supraoccipital anatomy.

The supraoccipital of Paralligator is a trapezoid-shaped bone built of several laminae (anterior, posterior, dorsal) connected by bony struts. It is wider than deep in posterior view: the lateromedial width is about three times larger than the dorsoventral depth ( Figs 3C View Figure 3 , 4B View Figure 4 , 6B View Figure 6 ). The posterior lamina of the supraoccipital is slightly concave or flat in most specimens but is notably concave in PIN 3726/503 ( Fig. 3 View Figure 3 ). The sagittal nuchal crest is weakly developed (e.g. PIN 3140/502, PIN 3905/501- 1) or absent (e.g. PIN 554/1-1, PIN 3726/503, PIN 3141/501: Figs 4B View Figure 4 , 6B View Figure 6 , 12L View Figure 12 ). If present, the crest does not reach the ventral margin of the supraoccipital (PIN 3905/501-1: Supporting information, Fig. S6C View Figure 6 ) or reaches its ventral margin but is not prominent (PIN 3140/502: Supporting information, Fig. S5B View Figure 5 ). The postoccipital processes are situated at dorsolateral corners of the supraoccipital ( Fig. 12J, L View Figure 12 ). They are widely spaced and project posteriorly. The postoccipital processes are not seen in dorsal view in the smaller-sized specimens (e.g. PIN 3140/502, PIN 3141/501, PIN 3905/501-1), as well as in the large-sized holotype of P. major PIN 3726/501-1. However, the processes are observed in dorsal view in the two relatively large specimens—the holotype of P. gradilifrons PIN 554/1-1 and in PIN 3726/503 ( Fig. 3A View Figure 3 ). It seems difficult to determine at present, whether this represents ontogenetic, inter-, or intraspecific variation in Paralligator .

The dorsal lamina is sutured to the parietal anterodorsally ( Figs 3E View Figure 3 , 12K View Figure 12 ). The supraoccipital is not exposed on the skull table in most specimens except in PIN 3141/502 and PIN 3905/501-1 (Supporting information, Figs S6 View Figure 6 , S 8 View Figure 8 ). In the latter, the posterior margin of the parietal is incised, and the supraoccipital has a small dorsal exposure (Supporting information, Fig. S6A View Figure 6 ). Its lateromedial width is about one third of that of the posterior margin of the parietal. Notably, PIN 3141/501 and PIN 3141/502 are of a similar size, both from the Nogon Tsav locality (Nemegt Formation), and were previously referred to a single taxon ‘ S. tersus ’ ( Efimov 1988) . Yet, the dorsal exposure of the supraoccipital is absent in PIN 3141/501 ( Fig. 6C View Figure 6 ), whereas it is present in PIN 3141/502 (Supporting information, Fig. S8G, H View Figure 8 ). Thus, the dorsal exposure of the supraoccipital on the skull table may represent intraspecific variation in Paralligator .

The anterior lamina and the capsular portion are completely preserved only in PIN 554/1-1 (holotype of P. gradilifrons ), but the sutural relationships with the prootic and otoccipital are hard to trace in the available CT scans. The supraoccipital forms the dorsal part of the otic capsule and its endocranial bulge (otic bulla sensu Kuzmin et al. 2021) and likely contains parts of the anterior and posterior semicircular canals. Internally, it surrounds the voluminous intertympanic pneumatic recess, which is dorsally connected to the parietal recess and is laterally continuous with the intertympanic recess within the prootic and otoccipital on both sides ( Fig. 3E View Figure 3 ).

Otoccipital

The paired otoccipitals of Paralligator form a significant portion of the posterior (occipital) surface of the skull, part of the otic capsule, and arrange passages for the posterior cranial nerves and vessels ( Figs 4B View Figure 4 , 6B View Figure 6 , 13 View Figure 13 ). The element is preserved in most studied specimens but its complex internal anatomy may be currently assessed only in PIN 554/1-1 (holotype of P. gradilifrons ) and PIN 3141/501.

The otoccipital forms the posterior part of the otic capsule, along with the prootic and supraoccipital. The otic capsule is mostly preserved in PIN 554/1-1 and only partly so in PIN 3141/501. Fine details of its structure are not apparent in the CT scans of PIN 554/1-1, but the otoccipital contains posterior portions of the vestibular recess and the lateral semicircular canal. The perilymphatic loop is partly preserved in PIN 3141/501 ( Fig. 13A, C View Figure 13 ). In crocodylomorphs, this structure surrounds the perilymphatic foramen and forms the cochlear prominence, together with the prootic ( Walker 1990, Kuzmin et al. 2021). The small piece preserved in PIN 3141/501 apparently corresponds to the ventral portion of the perilymphatic loop. However, margins of the perilymphatic foramen and the fenestra pseudorotunda cannot be reliably identified.

The extracapsular buttress is partially preserved in PIN 3141/501 and PIN 3905/501-1. As in extant crocodylians ( Kuzmin et al. 2021), it is a bony lamina that extends from the capsular portion ventromedially to the cranioquadrate passage dorsolaterally ( Fig. 13A, D View Figure 13 ). The extracapsular buttress is obliquely oriented and anteriorly concave. It is pierced by a single large foramen for the passage of the sympathetic nerve (SN), glossopharyngeal (CN IX), and vagus cranial nerves (CN X). This foramen is damaged in PIN 3141/501 but the CT data of PIN 554/1-1 confirms the presence of a single opening. The internal foramen of the cerebral carotid artery is located just ventral to the extracapsular buttress and the aforementioned nervous foramen. The extracapsular buttress is continuous with the cranioquadrate passage dorsolaterally and with the anteroventral process ventromedially. The anteroventral process contacts the basioccipital and approaches the prootic anteriorly. It forms the ventral margin of the metotic foramen and is bounded by the rhomboidal pneumatic recess laterally and by the endocranial cavity medially ( Fig. 13D, F View Figure 13 ).

The otic capsule bulges into the endocranial cavity as the otic bulla (sensu Kuzmin et al. 2021). The metotic foramen—a vertically oriented notch between the otic capsule anteriorly and the occipital arch posteriorly—provided passage for the posterior cranial nerves CN IX-X ( Fig. 13F View Figure 13 ). Posterior to the metotic foramen, the occipital arch is pierced by the two foramina for the hypoglossal nerve (CN XII) in PIN 554/1-1 and PIN 3141/501.

The posterior aspect of the otoccipital is formed by the extensive paroccipital (POP) and ventrolateral (VLP) processes and the small occipital arch ( Figs 4B View Figure 4 , 13B, E View Figure 13 ). The occipital arch makes up the lateral and dorsal margins of the foramen magnum and contacts the basioccipital ventrally and the contralateral otoccipital dorsally. The POP and VLP extend laterally from the occipital arch. They are approximately equal in lateromedial length or the VLP appears slightly longer, as opposed to the condition in extant crocodylians ( Iordansky 1973, Kuzmin et al. 2021). The cranioquadrate passage of Paralligator is entirely formed by the otoccipital, without participation of the quadrate ( Figs 6B, C View Figure 6 , 7C View Figure 7 ).

The POP is more prominent—it bulges posteriorly and overhangs the VLP. Its ventral margin forms a ridge-like projection ( Fig. 6B View Figure 6 ). The posterior projection is distinctive and acute in most specimens, including smaller (e.g. PIN 3140/502, PIN 3141/501) and large-sized individuals (PIN 3458/501-1), but is relatively blunt in the adult individual PIN 554/1-1 (holotype of P. gradilifrons ) ( Fig. 4B View Figure 4 ). The occipital surface of the POP is concave. The POP of Paralligator contacts the squamosal dorsally and anteriorly but does not contact the quadrate at its distal end, which is seen in many specimens: e.g. PIN 554/1- 1, PIN 3140/502, PIN 3141/501, PIN 3458/502, and PIN 3905/501-1 ( Figs 4B View Figure 4 , 5B View Figure 5 , 6B, C View Figure 6 , 7C View Figure 7 ; Supporting information, Figs S3G, S View Figure 3 5B, E, S View Figure 5 6C, D View Figure 6 ).

The VLP of Paralligator is well developed. It sutures to the quadrate and parabasisphenoid anteriorly and to the basioccipital ventrally. The VLP is pierced by several external foramina for passage of nerves and blood vessels ( Figs 4B View Figure 4 , 6B View Figure 6 , 13B, E View Figure 13 ). A single foramen for CN IX-X and SN is the lateral-most. There are two to three foramina for branches of CN XII: one or two smaller openings lie adjacent to the foramen for CN IX-X + SN, and a single larger foramen pierces the occipital arch more medially. The single foramen for the cerebral carotid artery is located ventrally and separately from the nervous foramina. The foramina for CN IX-X + SN and for the cerebral carotid artery are of approximately the same size in PIN 554/1-1 and PIN 3141/501 ( Figs 4B View Figure 4 , 6B View Figure 6 , 13E View Figure 13 ).

Parabasisphenoid

The parabasisphenoid is an anterior unpaired ossification of the basicranium in crocodylomorphs ( Iordansky 1973, Walker 1990, Leardi et al. 2020, Kuzmin et al. 2021). It is preserved in many studied specimens of Paralligator but is externally obscured by neighbouring bones. The CT-scanning and segmentation of PIN 3141/501 allows to describe its anatomy in detail, which is supplemented by observations of other specimens.

The parabasisphenoid of Paralligator is sutured to the pterygoids and quadrates laterally, to the laterosphenoids and prootics dorsally, to the basioccipital posteriorly, and to the otoccipitals posterodorsally ( Figs 5 View Figure 5 , 6 View Figure 6 , 7 View Figure 7 ). It is dorsoventrally deep (verticalized sensu Tarsitano 1985), wedge-shaped, and is significantly pneumatized internally ( Fig. 14D–G View Figure 14 ). The parabasisphenoid is subdivided into the rostrum, the central part (body), the posterior descending lamina, and the posterolateral alar processes.

The rostrum is missing its distal part in most specimens except PIN 3140/502, in which it is dorsoventrally deep and lateromedially thin (Supporting information, Fig. S5D View Figure 5 ). The parabasisphenoid rostrum forms the ventral margin of the foramen for CN III, CN VI, and orbital vessels. Two small foramina for the palatine branches of the facial nerve (CN VII pl) are situated ventrolateral to the base of the rostrum ( Figs 6A View Figure 6 , 7A View Figure 7 ). The hypophyseal fossa is circular in cross-section. The paired larger foramina for the cerebral carotid arteries and the two smaller openings for the abducens nerve (CN VI) are present within the fossa ( Fig. 14D View Figure 14 ).

The body of the parabasisphenoid forms the floor of the endocranial cavity, which is concave and bounded laterally by the facets for the laterosphenoid and prootic ( Fig. 14G View Figure 14 ). The parabasisphenoid of Paralligator is slightly exposed on the lateral wall of the braincase, anteroventrally to the trigeminal foramen ( Fig. 7A, B View Figure 7 ). A sulcus lateral to the rostrum is absent—the lateral surfaces of the parabasisphenoid and the pterygoid smoothly merge with each other.

The descending lamina forms the posterior aspect of the body of the parabasisphenoid ( Fig. 14E View Figure 14 ). It is dorsoventrally deep and bears paired facets for the basioccipital, which are divided in the middle by the median pharyngeal canal and laterally bounded by the pharyngotympanic canals. The median pharyngeal (Eustachian) foramen is consistently located ventrally relative to the pharyngotympanic (lateral Eustachian) foramina in Paralligator ( Fig. 6B View Figure 6 ).

The ventral exposure of the parabasisphenoid is anteroposteriorly narrow in all specimens, in which this feature is apparent: e.g. PIN 554/1-1, PIN 3141/501, PIN 3140/502. The parabasisphenoid is significantly exposed in posterior view, ventrally to the basioccipital, in most studied specimens of Paralligator : e.g. PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3141/501, PIN 3905/501-1, and in PIN 3140/502 (obscured by crushing and anterodorsal rotation of braincase) ( Figs 4B View Figure 4 , 6B View Figure 6 ). However, it is virtually not exposed posteriorly in PIN 3726/501-1 (holotype of P. major ) and PIN 3140/502. In PIN 3140/502, it is likely due to crushing, as the posteroventral portion of the pterygoid is incomplete and reconstructed with plaster. However, in PIN 3726/501-1, it appears a natural condition and may be a consistent feature of P. major .

The alar processes diverge posteriorly and laterally from the body of the parabasisphenoid ( Fig. 14E–G View Figure 14 ). They are wedged between the pterygoid and quadrates laterally and the basioccipital and otoccipitals medially. The alar processes are exposed on the lateral wall of the braincase. The exposed surface is smaller than the anteroposterior length of the adjacent quadrate-pterygoid contact ( Figs 5A, C View Figure 5 , 7A, B View Figure 7 ).

Basioccipital

The basioccipital is preserved in most studied specimens of Paralligator , and segmentation of PIN 3141/501 allows to describe its internal anatomy ( Figs 4B View Figure 4 , 6B View Figure 6 , 14A–C View Figure 14 ). The basioccipital forms part of the posterior (occipital) aspect of the skull and endocranial cavity. It sutures to the parabasisphenoid anteriorly and to the otoccipitals laterally. The occipital condyle is mostly formed by the basioccipital. It is moderately developed—approximately equal in size to the foramen magnum— and offset on a short neck.

The basioccipital plate is well-developed: its lateral margins flare ventrally, such that the plate is twice wider than the condyle in posterior view ( Figs 4B View Figure 4 , 6B View Figure 6 ). It is dorsoventrally deep and verticalized: its height below the condyle is 1.2–1.5 times larger than the condyle height. The basioccipital plate faces posteriorly in PIN 554/1-1 (holotype of P. gradilifrons ), PIN 3141/501, and PIN 3726/501-1 (holotype of P. major ), which is here considered the natural condition of adult and subadult individuals of Paralligator . However, the basioccipital surface is inclined anteriorly and faces posteroventrally in PIN 3140/502, PIN 3458/501-1, and PIN 3905/501-1, which we consider a preservation artefact.

The ventral margin of the basioccipital plate is concave posterior to the median pharyngeal (Eustachian) canal. The ventrolateral margins of the basioccipital are notably incised at the pharyngotympanic (lateral Eustachian) foramina in some specimens (e.g. PIN 3140/502, PIN 3141/501, PIN 3905/501-1), such that the basioccipital plate is subdivided into the four lobes ventrally ( Figs 6B View Figure 6 , 14A View Figure 14 ). However, in PIN 554/1-1 (holotype of P. gradilifrons ) and PIN 3726/501-1 (holotype of P. major ), the lateroventral margins are not incised and are slightly convex, such that the basioccipital plate has the appearance of two lobes ( Fig. 4B View Figure 4 ). The crest-like tuberosities extend along the ventrolateral margins of the basioccipital plate. They and the sagittal crest are well developed in all studied specimens of Paralligator .

A vascular foramen ventral to the occipital condyle is present in most examined specimens. Internally, the basioccipital is hollowed out by the paired basioccipital pneumatic recesses. The anterior surface of the basioccipital plate is grooved by the median pharyngeal and the paired pharyngotympanic pneumatic canals ( Fig. 14B View Figure 14 ).

Quadrate

The quadrate is preserved in most studied specimens of Paralligator . Segmentation of both quadrates in PIN 3141/501 and study of several isolated specimens (e.g. PIN 3458/502- 6, PIN 3458/502-7) allows to describe its internal anatomy in detail. The quadrate may be subdivided into the main body terminating with the mandibular condyles and several processes extending from the body, namely the otic, anterodorsal, anteromedial, and pterygoid processes ( Fig. 15 View Figure 15 ). The quadrate of Paralligator does not participate in the cranioquadrate passage, as opposed to the condition in extant crocodylians ( Iordansky 1973, Montefeltro et al. 2016, Kuzmin et al. 2021).

The body of the quadrate is anteroposteriorly elongated and anteromedially inclined. It is slightly bent posteroventrally posterior to the bony otic aperture ( Figs 5B View Figure 5 , 7B View Figure 7 , 8 View Figure 8 ). The angle between the posterior margin of the quadrate body and the skull table in lateral view is about 40–45 o. The quadrate body sutures to the quadratojugal laterally and to the ventrolateral process of the otoccipital posteromedially. The quadrate of Paralligator does not contact the paraoccipital process.

The quadrate condyles are at the level of the occipital condyle or slightly dorsal to it in posterior view and are offset posteriorly relative to the occiput in dorsal view ( Figs 4 View Figure 4 , 6 View Figure 6 ). The lateral condyle is larger, ovate, and horizontally aligned in posterior view, whereas the medial condyle is smaller, bent ventrally, and aligned dorsoventrally. The intercondylar groove is well developed. The siphonial foramen (foramen aereum) is located at the dorsomedial corner of the quadrate, near the medial condyle.

The quadrate body forms the ventral margin of the otic incisure of the external auditory meatus ( Montefeltro et al. 2016) ( Fig. 8 View Figure 8 ). Here, the dorsal surface of the quadrate is smooth but bears a shallow semilunar depression, the periotic fossa. A single subtympanic foramen is located at the anterior corner of the periotic fossa ( Fig. 15C View Figure 15 ). The otic buttress is not prominent in Paralligator , as opposed to extant crocodylians ( Montefeltro et al. 2016, Kuzmin et al. 2021). It is a small shelf at the posterior corner of the external auditory meatus that does not project anterodorsally ( Fig. 15B, D View Figure 15 ).

The posterior portion of the quadrate body bears a large dorsal crest ( Fig. 13B View Figure 13 ). It extends on the dorsal surface of the quadrate from the periotic fossa anteriorly to the intercondylar groove posteriorly and is continuous with a crest-like dorsal margin of the medial condyle. The dorsal crest of Paralligator is situated somewhat similarly to the posterodorsal process of the quadrate in extant crocodylians (see Kuzmin et al. 2021) and may be homologous to it. However, it lacks sutural contacts with the squamosal and otoccipital, does not border the cranioquadrate passage, and reaches far too posteriorly—to the level of the quadrate condyles. Thus, we consider the posterodorsal process of the quadrate sensu Kuzmin et al. (2021) lacking in Paralligator .

A longitudinal groove extends on the dorsal surface of the quadrate, medial and parallel to the dorsal crest and just lateral to the cranioquadrate passage ( Figs 6C View Figure 6 , 15C View Figure 15 ). It merges with the periotic fossa anteriorly and fades out at the level of the siphonial foramen. The groove is a potential osteological correlate for a nervous branch or a blood vessel.

The otic process arches posterodorsally from the quadrate body and terminates with the quadrate head. It forms the anterior margin of the otic incisure of the external auditory meatus. The otic process contacts the prootic buttress medially and abuts the squamosal dorsally ( Figs 5C View Figure 5 , 7B View Figure 7 , 15A, B View Figure 15 ). The anterodorsal process projects anteriorly from the quadrate body and the otic process. It sutures to the ventral surface of the squamosal and forms the lateral wall of the supratemporal fossa ( Fig. 15C View Figure 15 ). The anteromedial process projects anteriorly and forms the lateral wall of the braincase and the posterodorsal margin of the maxillomandibular foramen (for CN V 2-3) ( Fig. 15A, B View Figure 15 ). The anteromedial process of the quadrate is firmly sutured to the prootic and laterosphenoid ( Fig. 7A View Figure 7 ). Finally, the pterygoid process extends ventrally and contacts the pterygoid, the lateral bridge of the laterosphenoid, and the alar process of the parabasisphenoid ( Figs 7A View Figure 7 , 15E View Figure 15 ). The quadrate-pterygoid contact on the lateral wall of the braincase is obliquely inclined.

The adductor crests on the ventral surface of the quadrate are well developed in Paralligator ( Figs 4D View Figure 4 , 5 View Figure 5 , 6D View Figure 6 , 7A View Figure 7 , 15E View Figure 15 ). Crest B is the most prominent. It arches from the quadrate-pterygoid contact ventrally and almost reaches the lateral condyle posterodorsally. Crest A is also prominent; it extends parallel to the anterolateral margin of the quadrate body. Crests A and B reach the same level posteriorly and are almost confluent near the lateral condyle. Anteriorly, crest A is continued by an arched crest A’, which forms a distinct shelf at the ventral margin of the supratemporal fossa and overhangs the maxillomandibular foramen. Crest A’ is confluent with crests on the lateral surface of the laterosphenoid.

Internally, the quadrate of Paralligator is significantly pneumatized ( Fig. 15C, D View Figure 15 ). It bounds the pharyngotympanic (middle ear) cavity laterally. There are up to four pneumatic foramina on the medial surface of the quadrate—two larger openings for the infundibular and quadrate recesses, and one or two smaller foramina for the entrance of the siphonium (see Paratympanic pneumatic system).

Neuroanatomy of Paralligator

A relatively complete endocast of the endocranial cavity (‘brain endocast’), the associated neurovascular structures, and the paratympanic pneumatic recesses were segmented for PIN 554/1-1 (holotype of P. gradilifrons ) ( Figs 16 View Figure 16 , 17 View Figure 17 ). The brain endocast lacks the anterior part of the diencephalic portion and the hypophysis. Nerves were imperfectly reconstructed due to incomplete preservation of the laterosphenoids and the parabasisphenoid rostrum anteriorly and insufficient resolution of the CT scans in the posterior portion of the braincase. Due to the latter reason, endocasts of both endosseous labyrinths are also incomplete. The complete paratympanic pneumatic system is reconstructed for PIN 554/1-1 ( Fig. 17 View Figure 17 ). It is missing only small ventral parts of both pharyngotympanic (middle ear) cavities due to symmetrical cracks on both sides of the braincase.

Additionally, partial endocasts of the endocranial cavity and the paratympanic pneumatic recesses were produced for PIN 3141/501 ( Fig. 18 View Figure 18 ). This specimen is preserved in several pieces (see Specimens), and segmentation of the internal cavities was done for the larger braincase piece. This provides information on the ventral and right lateral aspects of the posterior brain endocast, the posterior cranial nerves and vessels, and the median and right lateral paratympanic recesses. The pneumatic and neurovascular cavities in the smaller braincase pieces of PIN 3141/501 were also segmented and assessed, but we did not attempt to reconstruct the complete endocranial anatomy for this specimen due to a large number of missing parts.

Brain endocast

The brain endocast of PIN 554/1-1 (holotype of P. gradilifrons ) is anteroposteriorly elongated and dorsoventrally low ( Fig. 16 View Figure 16 ). It is slightly curved in lateral view: the cephalic and pontine flexures equal 150 o and 156 o, respectively. In lateral view, the dorsal margins of the olfactory tract and cerebral hemispheres are continuous and slightly convex dorsally ( Fig. 16D View Figure 16 ). The highest dorsal point of the endocast in lateral view is above the cerebral hemispheres. The dorsal elevation (dural peak sensu Ristevski 2022) is weakly developed above the cerebellum. The dorsal concavity above the midbrain is shallow in lateral view. The height of the brain endocast is lowest posteriorly, above the medulla oblongata portion. The ventral margin of the hindbrain is relatively straight in lateral view of PIN 554/1-1 but has a sinuous curve in PIN 3141/501 ( Fig. 18A View Figure 18 ). In dorsal view, the brain endocast of PIN 554/1-1 has undulating lateral margins, with a notable expansion at the cerebral hemispheres and a smaller expansion at the level of the cerebellum ( Fig. 16A View Figure 16 ). The endocast is notably constricted at the olfactory tract, midbrain, and medulla oblongata portion.

The forebrain (prosencephalon) is represented by the olfactory complex (bulbs and tract) and the cerebral hemispheres. The olfactory complex is anteroposteriorly elongated: its length approximately equals that of the rest of the brain endocast. The paired olfactory bulbs are divided by the mesethmoid facet and diverge anteriorly at an angle of 25°–30°. They are moderately developed: each bulb has a transverse width equal to that of the constricted part of the tract. The unpaired olfactory tract is elongated and transversally narrow. It expands anteriorly into the olfactory bulbs and posteriorly into the cerebral hemispheres.

The cerebral hemispheres are the widest portion of the brain endocast in dorsal view. They are 2.5 times wider than the olfactory tract and 1.5 times wider than the mesencephalic and the medulla oblongata portions ( Fig. 16A View Figure 16 ). In dorsal view, the hemispheres gradually narrow into the olfactory tract anteriorly and are notably constricted posteriorly. In lateral view, they are ovate with an obliquely inclined longitudinal axis.

The diencephalic portion of the brain endocast is only partially preserved and reconstructed. The thalamic and hypothalamic divisions of the brain are represented by a transversally constricted portion of the endocast ventral to the cerebral hemispheres ( Fig. 16D View Figure 16 ). The optic chiasm and optic nerves (CN II) are not segmented due to imperfect preservation of the anterior processes of laterosphenoids. Most of the infundibulum and the hypophysis are missing. The posterior portion of the hypophysis is rounded in cross-section and directed posteroventrally in PIN 554/1-1 and PIN 3141/501 ( Figs 16D View Figure 16 , 18A, B View Figure 18 ). It receives the paired cerebral carotid arteries. The posterior terminus of the hypophysis reaches the level of the trigeminal nerve posteriorly and is located ventral to the hindbrain in lateral view.

The mesencephalic portion of the brain endocast is posterior to the cerebral hemispheres. It is notably constricted in dorsal view ( Fig. 16A, D View Figure 16 ). The anterior portion of the rhombencephalon (hindbrain)—the cerebellum and pons—lies posteriorly to the midbrain. The corresponding portion of the endocast is expanded dorsoventrally and laterally. The flocculus of the cerebellum is not developed. The medulla oblongata portion of the brain endocast is lateromedially wider than deep. There is a low longitudinal ridge on its ventral surface that corresponds to a vascular structure (most likely basilar artery: Hopson 1979, Porter et al. 2016) ( Figs 16C View Figure 16 , 18A, B View Figure 18 ).

Cranial nerves

The anterior cranial nerves—the olfactory (CN I), optic (CN II), oculomotor (CN III), and trochlear (CN IV) nerves—are not segmented in PIN 554/1-1 due to the imperfect preservation of the laterosphenoids and the absence of the mesethmoid. However, the position of CN III and CN IV in Paralligator can be assessed in the left laterosphenoid of PIN 3141/501 and the isolated left laterosphenoid PIN 3141/502 ( Fig. 11J, K View Figure 11 ). Both nerves were located ventral to the cerebral hemispheres. CN IV is narrow and pierces the anterior process of the laterosphenoid just ventral to the cerebral fossa. CN III is slightly wider than CN IV and left the endocranial cavity posteroventrally to it. Additionally, the lateral sulci on the mesethmoid of PIN 3141/501 mark the course of CN I branches, extending anteriorly into the nasal cavity from the olfactory bulbs ( Fig. 10C, D View Figure 10 ).

The trigeminal nerve (CN V) is the largest reconstructed nerve in Paralligator ( Figs 16 View Figure 16 , 18A, B View Figure 18 ). It leaves the brain endocast at the level of an approximate division between the mesencephalon and rhombencephalon. The diameter of CN V medially, near the brain endocast, equals that of the preserved part of the hypophysis in PIN 554/1-1 but is smaller in PIN 3141/501. Laterally, CN V is expanded into the ganglion, with several branches diverging from it: namely, ophthalmic (CN V 1), maxillary (CN V 2), and mandibular (CN V 3) divisions ( Fig. 16A View Figure 16 ). CN V 3 is the largest branch than extends posterolaterally from the CN V ganglion. CN V 1 and CN V 2 extend anteriorly and are divided by the lateral bridge of the laterosphenoid. A small supraorbital branch (CN V 2so) branches off of the CN V ganglion and extends anterodorsally. Posterodorsally, the branch extending from the pharyngotympanic (middle ear) cavity enters the CN V ganglion. It is here interpreted as the sympathetic nerve (SN) ( Fig. 16A View Figure 16 ).

The abducens nerve (CN VI) was reconstructed both in PIN 554/1-1 and PIN 3141/501 ( Figs 16C View Figure 16 , 18B View Figure 18 ). Its paired branches leave the brain endocast ventrally, at the level of CN V. They extend anteriorly and leave the parabasisphenoid dorsolaterally to the hypophysis. The facial (CN VII) and vestibulocochlear nerves (CN VIII) were segmented only in PIN 3141/501 ( Fig. 18A, B View Figure 18 ). They leave the rhombencephalic portion of the endocast posterior to CN V and just ventral to the endosseous labyrinth. CN VII is represented by a single common branch that pierces the right prootic of PIN 3141/501 and by both palatine branches (CN VII pl). They extend ventrally within the parabasisphenoid, over the medial wall of the pneumatic recessus epitubaricus, then curve anteriorly to exit ventrolaterally to the parabasisphenoid rostrum. In PIN 3141/501, CN VI, the common branch of CN VII, and CN VII pl have an approximately equal diameter. A single preserved branch of CN VIII is narrow and short; it enters the vestibule of the inner ear at the level of the anterior ampulla.

The common canal for CN IX-X and SN within the otoccipital is the second largest among the reconstructed nerves ( Figs 16 View Figure 16 , 18A View Figure 18 ). It pierces the otoccipital and is not subdivided into separate branches at its anterior end both in PIN 554/1-1 and PIN 3141/501, as opposed to extant crocodylians ( Kuzmin et al. 2021). Two or three branches of the hypoglossal nerve (CN XII) are present in Paralligator . Only two branches were segmented in PIN 554/1-1 and PIN 3141/501, but a small foramen on the occiput, ventral to the CN IX-X + SN opening, suggests the presence of a tiny anterior branch, which cannot be located in the CT scans ( Figs 4B View Figure 4 , 6B View Figure 6 ).

Vasculature

The cerebral carotid arteries were segmented both in PIN 554/1-1 and PIN 3141/501 ( Figs 16 View Figure 16 , 18A, B View Figure 18 ). They enter the otoccipitals posteriorly, course through the pharyngotympanic cavity without leaving osteological correlates, then pierce the parabasisphenoid, and finally enter the hypophyseal fossa anteriorly. The diameter of the cerebral carotid arteries approximately equals that of the common canal for CN IX-X and SN. A small branch diverges dorsolaterally from the right cerebral carotid artery in PIN 3141/501 ( Fig. 18A View Figure 18 ). It likely represents a connection between the stapedial and cerebral carotid arteries (e.g. Kuzmin et al. 2021: fig. 5).

Additional vascular elements are present on the ventral surface of the rhombencephalon and within the basioccipital of Paralligator . The paired vessels along the ventral longitudinal ridge were segmented in PIN 3141/501 ( Fig. 18A, B View Figure 18 ). They likely correspond to the basilar artery or its tributaries ( Hopson 1979, Porter et al. 2016). These paired vessels are connected to the vascular plexus within the basioccipital, which opens by a single or paired foramina ventral to the occipital condyle. In PIN 554/1-1, similar vascular canals within the basioccipital are present but were not reconstructed due to the lower resolution of the CT scans.

The dorsal longitudinal venous sinus was present in Paralligator , because the contralateral olfactory tracts and cerebral hemispheres are not divided dorsally on the brain endocast. The dorsal longitudinal sinus extended anteroposteriorly between the tracts and hemispheres, as in extant crocodylians (e.g. Hopson 1979: fig. 2). Its anterior tributaries in extant taxa are the common nasal veins, which lie above the olfactory bulbs and are formed by the fusion of the lateral and medial nasal veins (see Porter et al. 2016). The course of the medial/common nasal veins in Paralligator is potentially marked by the dorsal sulcus on the mesethmoid ( Fig. 10C, D View Figure 10 ). This is consistent with the course of these vessels over the lateral walls of the cartilaginous nasal septum in extant crocodylians ( Porter et al. 2016).

Endosseous labyrinth

Partial endocasts of both endosseous labyrinths were segmented in PIN 554/1-1 and PIN 3141/501 ( Figs 17 View Figure 17 , 18A View Figure 18 ). They correspond to the vestibule and the cochlear duct of the inner ear; the semicircular canals are imperfectly segmented and do not provide relevant anatomical information. The cochlear duct of Paralligator is elongated and located ventrolaterally to the vestibule of the inner ear ( Fig. 18A View Figure 18 ).

Paratympanic pneumatic system

The paratympanic pneumatic system of Paralligator is divided into the two principal components—the median pharyngeal and pharyngotympanic recesses—based on developmental origins in extant crocodylians ( Dufeau and Witmer 2015, Kuzmin et al. 2021). The two recesses and their subdivisions are interconnected and continuous in Paralligator ( Figs 17 View Figure 17 , 18 View Figure 18 ). The pneumatic cavities of both sides are connected ventrally and dorsally and surround the brain endocast ( Figs 9B View Figure 9 , 17 View Figure 17 ).

The median pharyngeal recess in Paralligator invades the parabasisphenoid ( Figs 17A View Figure 17 , 18D View Figure 18 ). It is represented by the single median pharyngeal (= median Eustachian) canal, the paired parabasisphenoid and subcarotid recesses, the single rostral recess, and the variably developed precarotid recesses. The median pharyngeal canal bifurcates into the paired parabasisphenoid recesses anterodorsally and is broadly connected with the basioccipital recesses posterodorsally ( Fig. 18D, E View Figure 18 ). It is bordered anteriorly by the parabasisphenoid and posteriorly by the basioccipital and opens on the ventral surface of the braincase by the median pharyngeal (= median Eustachian) foramen. The canal is dorsoventrally elongated (verticalized) and relatively large—its diameter is approximately twice larger than that of the cerebral carotid artery or the common nervous canal for CN IX-X and SN ( Figs 17 View Figure 17 , 18 View Figure 18 ).

Each parabasisphenoid recess excavates the body of the eponymous element. It is located ventral to the course of the cerebral carotid artery and posterior to CN VII pl. Each parabasisphenoid recess is connected to its counterpart and to the median pharyngeal canal medially. Laterally, it connects to the ventral part of the pharyngotympanic (middle ear) cavity via the narrow recessus epitubaricus ( Figs 17A, B View Figure 17 , 18C, D View Figure 18 ).

The unpaired rostral recess extends anteriorly directly from the median pharyngeal canal in PIN 3141/501 ( Fig. 18C, D View Figure 18 ). In the examined extant crocodylians, the rostral recess is usually formed by the fusion of the paired precarotid recesses extending from each parabasisphenoid recess anteriorly (e.g. Kuzmin et al. 2021: fig. 27). In PIN 3141/501, a narrow precarotid recess extends ventral to the hypophysis and dorsal to CN VII pl, as in extant crocodylians. It connects the rostral and parabasisphenoid recesses on the left side but is absent on the right ( Fig. 18D View Figure 18 ). The rostral recess of Paralligator is narrow posteriorly and expands into a rounded cavity anteriorly, which invades the base of the parabasisphenoid rostrum. The rostral and precarotid recesses are not segmented in PIN 554/1-1 (holotype of P. gradilifrons ) due to incompleteness of the parabasisphenoid anteriorly.

The paired subcarotid recesses extend posteriorly ventral to the cerebral carotid arteries ( Fig. 18D View Figure 18 ). They connect to the parabasisphenoid recess medially, the recessus epitubaricus anteriorly, and to the ventral part of the pharyngotympanic (middle ear) cavity posteriorly. Both in PIN 554/1-1 and PIN 3141/501, the subcarotid recesses are larger than in most adults of extant crocodylians (except Alligator mississippiensis ; see Kuzmin et al. 2021).

The rest of the paratympanic pneumatic cavities belong to the system of the pharyngotympanic recesses ( Dufeau and Witmer 2015, Kuzmin et al. 2021). The principal pharyngotympanic recess (= middle ear cavity) is voluminous and lateromedially expanded in Paralligator ( Figs 17C View Figure 17 , 18C, E View Figure 18 ). Each pharyngotympanic recess is bounded by the quadrate laterally, by the prootic, supraoccipital, and otoccipital medially, and by the parabasisphenoid and basioccipital ventrally. The outgrowths of the pharyngotympanic recess invade every braincase element of Paralligator and are broadly connected with each other and with the median pharyngeal recesses. Each pharyngotympanic cavity opens on the ventral surface of the braincase via the pharyngotympanic (= lateral Eustachian) canal ( Figs 17C View Figure 17 , 18E View Figure 18 ). The paired pharyngotympanic canals are dorsoventrally long but narrow. They are enclosed by the parabasisphenoid anteriorly and basioccipital posteriorly. Their ventral openings—pharyngotympanic or lateral Eustachian foramina—are located dorsally relative to the median pharyngeal foramen.

Ventrally, the extensions of the pharyngotympanic cavities excavate the parabasisphenoid, basioccipital, and otoccipital and are continuous with the median pharyngeal recess. The ventral extensions of the pharyngotympanic cavity include the recessus epitubaricus anteriorly and the rhomboidal and basioccipital recesses posteriorly. The paired basioccipital recesses are largely fused together within the eponymous bone( Figs 17C View Figure 17 , 18E View Figure 18 ). They are broadly connected with each other and with the median pharyngeal canal medially. Ventrolaterally, the pharyngotympanic cavity, the basioccipital recess, and the pharyngotympanic canal merge into the rhomboidal pneumatic recess on each side of the braincase ( Figs 17C View Figure 17 , 18E View Figure 18 ). The latter recess is located ventral and posterior to the course of the cerebral carotid artery. The rhomboidal pneumatic recess is connected to the otoccipital recess dorsally; the communicative canal is located medially to the cerebral carotid artery ( Fig. 18E View Figure 18 ).

The recessus epitubaricus is the paired pneumatic cavity bounded by the parabasisphenoid medially and by the prootic and pterygoid laterally ( Figs 17A, B View Figure 17 , 18C, D View Figure 18 ). It is located anterolaterally to the cerebral carotid artery and ventral to CN V. The recessus epitubaricus is transversally narrow but expanded dorsoventrally. It is continuous with the parabasisphenoid recess medially and is connected to the pharyngotympanic cavity posterodorsally. In Paralligator , there are two additional extensions from the recessus epitubaricus—the pterygoid recess ventrally and the laterosphenoid recess anterodorsally. The laterosphenoid recess invades the body of the eponymous element ( Figs 11G, K View Figure 11 , 17A, B View Figure 17 , 18C View Figure 18 ). It is consistently present in Paralligator (e.g. in PIN 554/1-1, PIN3141/501, PIN3141/502) and maintains the connection with the recessus epitubaricus in studied individuals. The pterygoid recesses are ventral outgrowth of the recessus epitubaricus within the eponymous bones ( Figs 17A View Figure 17 , 18C, D View Figure 18 ). They are undoubtedly present and segmented in PIN 3141/501 and tentatively segmented in PIN 554/1-1 (due to insufficient resolution of CT scans).

The dorsal extensions of the pharyngotympanic cavities—the intertympanic pneumatic recess and its outgrowth—excavate the prootic, otoccipital, and supraoccipital. The intertympanic recess is transversally oriented; it passes throughout the supraoccipital above the otic capsule and connects both pharyngotympanic cavities dorsally, above the brain endocast ( Fig. 17B, C View Figure 17 ). The paired anterodorsal extensions of the prootic and supraoccipital portions of the intertympanic recess merge with the parietal recess. The latter cavity is consistently present in Paralligator (e.g. in PIN 554/1-1, PIN 3141/501, PIN 3141/502, PIN 3726/503) ( Fig. 17A, B View Figure 17 ). Posteriorly, the intertympanic recess is broadly connected to the otoccipital recess, which excavates the eponymous element laterally to the otic capsule ( Figs 17C View Figure 17 , 18E View Figure 18 ).

Anteriorly, there is the prootic facial recess, which excavates the eponymous element anteriorly to the otic capsule and dorsally to CN V ( Figs 17B View Figure 17 , 18C View Figure 18 ). This recess communicates with the main pharyngotympanic cavity posteroventrally and with the intertympanic recess within the prootic posterodorsally. The prootic facial recess is present on both sides of the skull in PIN 554/1-1 and PIN 3141/501 and appears as a consistent feature of Paralligator .

Laterally, the subdivisions of the pharyngotympanic pneumatic recess invade the quadrate ( Figs 17 View Figure 17 , 18C–E View Figure 18 ). Both the infundibular and quadrate recesses are broadly developed and interconnected in Paralligator (e.g. in PIN 554/1-1, PIN 3141/501). The infundibular recess lies anteriorly; it excavates the base of the otic process of the quadrate and opens dorsally via the single subtympanic foramen. The quadrate recess is located posteriorly; it inflates the body of the quadrate. The long posteriorly directed siphonium is present in Paralligator . It opens posteriorly via the foramen aereum medial to the medial quadrate condyle. Anteriorly, the siphonium is directly connected to the pharyngotympanic cavity. There is a presiphonial cavity dorsolateral to each siphonium in Paralligator ( Fig. 18D, E View Figure 18 ). The presiphonial cavity is either connected to the quadrate recess anteriorly or lacks this communication. The feature obviously represents individual variation, as the connection is present on the left side of braincase but is absent on the right in PIN 3141/501.