SUPPLEMENTARY INFORMATION

doi:10.1038/nature13086 Part I. Supplementary Notes A: Detailed Description of Cotylocara macei gen. et sp. nov. Part II. Table of Measurements for holotype of Cotylocara macei (CCNHM-101) Part III. Supplementary Discussion Part IV. Supplementary Notes B: Morphological Character List and Codings for Cotylocara macei gen. et sp. nov. Part I. Supplementary Notes A: Detailed Description of Cotylocara macei gen. et sp. nov. The skull has an elongate rostrum, which, as preserved, comprises 66% of condylobasal length (see Part II of Supplementary Information). Overall the rostrum is fairly narrow, and its anterior quarter to third is fairly uniform in width. Posterior to that the rostrum gradually widens. Relative to the basicranial stem, the rostrum is deflected 20 ventrally (Extended Fig. 1). The WWW.NATURE.COM/NATURE 1

premaxillae are sutured, not fused, to the maxillae, and the suture is quite tight and lacks a groove. The premaxillae have elongate palatal processes that contact each other and are wedged between the maxillae (Extended Fig. 4b: plp). The processes are incomplete, although based on the right premaxilla, they extend at least to the level of the 7 th from the end maxillary tooth. Dorsally the premaxillae roof over the mesorostral gutter on the rostrum, although it is unclear if they originally contacted each other at any point. The anterior half of the preserved portion of the premaxilla is fairly flat and faces dorsolaterally. Posterior to that an anteroposteriorly aligned sulcus gradually deepens and leads to the premaxillary foramina. Lateral to the sulcus the premaxilla is convex, whereas medial to it the premaxilla ascends to form a sharp thin crest that borders the mesorostral groove. The crests bordering the mesorostral gutter are asymmetrical; the left one is bowed laterally and overturned (Fig. 1b). Lateral to the highest part of these crests the premaxilla is deeply concave, forming a premaxillary sac fossa. In this fossa there is at least one premaxillary foramen on the right side and at least on three the left side (Extended Fig. 4a). The most salient feature of the maxilla is a deep basin at the base of the rostrum (i.e. the rostral basin), immediately anterior to the antorbital notch, which we suggest was excavated by a ventrolateral extension of the premaxillary air sac (Figs. 1, 2, Extended Fig. 5). The excavation is so prominent that much of the lateral wall of the infraorbital canal is absent, and at least some of its contents (e.g. infraorbital nerve, accompanying vessels) reentered the maxillary bone to then emerge a short distance anteriorly through multiple foramina that are probably homologous to the infraorbital foramina of other mammals (Extended Fig. 4a: rif,dif). The infraorbital foramina are not preserved on the right side, but on the left side there are two; a large, laterally-facing foramen just ventral to the premaxilla/maxilla suture and a smaller one in a more ventrolateral position. On the floor of each rostral basin is a bulge that contains the roots of the last maxillary WWW.NATURE.COM/NATURE 2

tooth. Although the right maxilla is damaged anterior to this bulge, it is clear that the antorbital basin did not extend more than 25 mm anterior to the bulge. By contrast, on the left side, the basin extends ca. 50 mm anterior to the bulge and reaches the level of the third to the last maxillary tooth. At approximately the level of the second to last maxillary tooth, the left basin is partially subdivided by a transverse ridge. The posterior limits of the rostral basins are unclear, but they certainly extended into the region medial to the antorbital notch. CT data reveals that in this area the maxilla has an anteroposteriorly elongate window through which the premaxilla is visible (Fig. 1f). Whether this window is the result of resorption caused in part by the premaxillary air sinus or is the result of a thin portion of maxilla not being preserved is unclear. The proximal end of the infraorbital canal is either a single a large opening (ca. 17 mm in diameter on the left side) or two smaller foramina (right side). The rostrum has a series of embrasure pits that accommodated the apices of the lower teeth (Fig. 1d). Anteriorly the pits are positioned at the intersection of the ventral and lateral sides of the maxillae and then at the diastema between the n-6 and n-7 maxillary teeth they become completely situated on the ventral side (see description of teeth below for explanation of dental notation). The embrasure pits continue posteriorly between the alveoli, although the penultimate diastema has a shallow embrasure pit and the last diastema appears to lack one entirely (Extended Fig. 4b). Between the tooth rows the palate is fairly flat. The palate bears a greater palatine foramen, one on each side, at the level of the last maxillary tooth and slightly anterior to the maxilla/palatine suture (Extended Fig. 4b). That foramen leads into a deeply entrenched palatal suclus that gradually shallows anteriorly until terminating approximately at the level of the last single-rooted maxillary tooth. At its posterior end, the palatine sulcus has a branch that diverges at a ca. 25 degree angle and is directed toward the third from the last WWW.NATURE.COM/NATURE 3

maxillary tooth. The maxilla/palatine suture is unfused and is M-shaped, with posteriorly projecting maxillary processes on each side of the sagittal plane forming the middle of the M. Each palatine has 2-3 conspicuous foramina on its ventral side, and CT imagery reveals that these lead into canals that join internally to possibly drain the diploe. Posterior to these foramina the palatine bears a ridge that is anteriorly convex, which may demarcate the anterior edge of the attachment of the medial pterygoid muscle. The width of the skull across the orbits is much greater than that of the base of the rostrum, and the two are separated by wide and open antorbital notches (Fig. 1b). Although the preorbital process is poorly developed, the postorbital process is short and stout with a prominent postorbital ridge (Extended Fig. 4). The ascending processes of the maxillae overlie the supraorbital processes and roof over nearly all of the temporal fossa, terminating just 25 mm shy of the supraoccipital. The lateral portion of the frontal is covered by an expansive dorsal wing of the lacrimal, which we here name the ascending process of the lacrimal (Extended Fig. 4a: apl). This process is another feature unique to xenorophids 6. The lacrimal bone terminates slightly anterior to the level of the squamosal fossa. As in other xenorphiids, the premaxilla is expanded on the dorsal surface of the supraorbital process and underlies part of the expanded ascending process of the maxilla (also known as the nasal process of the maxilla). The premaxilla is exposed on the roof of the temporal fossa (Fig. 1e and Extended Fig. 4b), although the amount of original exposure is somewhat unclear due to breakage in this area. Much of the exposed surface has an irregular surface with islands of a thin veneer of frontal (Extended Fig. 4b: tlf). We interpret that this thin veneer covered most, if not all, of the ventral side of the premaxilla. The veneer of frontal appears to thin laterally suggesting that lateral to the premaxillary exposure on the roof of the temporal fossa was a narrow (ca. 2-4 mm) strip of maxilla, and WWW.NATURE.COM/NATURE 4

lateral to that, a much wider exposure of lacrimal (Fig. 1e,f). The maxillary exposure, if real, is oriented anteromedial to posterolateral. Similar exposures of lacrimal, maxilla, and/or premaxilla are seen in Xenorophus sloanii and Albertocetus mefordorum, although descriptions of both taxa do not note this morphological oddity 6,31. For example, one study 6 incorrectly labeled the exposure of the maxilla as that of the frontal (ref. 6, fig. 6; Fr). It could be that previous authors assumed that the exposures were preservational artifacts, a hypothesis that cannot be ruled out for the holotype skull of Cotylocara macei. The external bony nares are at the level of the anterior half of the orbit. Lateral to the external bony nares the premaxillae are slightly concave and face anterodorsally. Their lateral edges form sharp crests that overhang the maxillae by as much as 12 mm (Fig. 1f,g). The sutural surface for the maxilla continues onto the backside (i.e., posteroventral side) of the overhang. Whereas the crest is directed laterally in the region of the nares, it smoothly decreases in height and becomes directed dorsally at the level of the posterior edge of the nasals before disappearing completely. At the level of the antorbital notch, the crest on the premaxilla is thickened for a span of 15 to 20 mm. The nasals are quite thick dorsoventrally. The anterior edge of each nasal bears a sharp, medially compressed ridge near its lateral margin that is separated from the adjacent premaxilla by a distinct gap. In most other Oligocene cetaceans (e.g. Simocetus), the anterior edges of the nasals are sharp and distinctly separate the dorsal and ventral sides. By contrast, in Cotylocara macei it is a smooth, anteriorly-convex curve that joins the dorsal and ventral sides (Extended Fig. 5). The nasals are quite long (right = 69.0 mm, left = 72.5 mm). Overall they are similar in width from anterior to posterior, although at a point 17 mm from the anterior edge on the right side and 25 mm from the anterior edge on the left side, they are slightly compressed transversely. WWW.NATURE.COM/NATURE 5

Dorsally, the combined nasals bear a very shallow, median trough for the anteriormost 50 mm of their length, but this trough is then replaced posteriorly with a median ridge that gradually gains in height. That ridge is continuous with a median crest of interparietal that separates the postnarial fossae. Posteriorly, the ends of the nasals are rounded and they drop into the deep postnarial fossae (Extended Fig.1a), where they articulate with the frontals along an interdigitating suture. The internasal suture is gently sigmoidal, with the right nasal being as much as 6 mm wider than the left anteriorly, and then the two are subequal near the origin of the median nasal crest. The postnarial fossae (new term) are deep bilateral pits (one on each side) that are situated between the nasals and the cranial vertex and on each side of the median plane. Portions of the nasals, premaxillae, frontals, parietals, interparietal, and supraoccipital participate in the formation of the fossae, which have sheer and nearly vertical sides (Fig. 1e). The fossae are deepest anteriorly and gradually decrease in depth posteriorly. The interparietal forms a sharp, 40 mm long median crest that separates the right and left postnarial fossae; posterior to that the right and left fossae are continuous. The frontals form the floors of the deepest parts of the fossae and part of their anterior walls. On the anterior wall of the postnarial fossa, the frontal bears a sharp crest that subdivides this fossa into a very small dorsomedial portion and a much larger posterior portion (Fig. 1e). The crest is more salient on the left side, and this is related to the fact that the right postnarial fossa extends farther anteriorly. The frontals also extend upward onto the base of the interparietal spine and are sutured medially to it. Whereas the anterior walls of the postnarial fossae are pocketed as is typical of air sinus fossae, the lateral sides, which are formed by the premaxillae, are sheer and nearly featureless. Posterior to the premaxillae the postnarial fossae are not as well-defined; the lateral sides are defined by fairly low, posteriorly-diverging ridges WWW.NATURE.COM/NATURE 6

that mark the edges of the temporal muscle fossae. In this region the frontals overlie, and are sutured to, the parietals. Immediately posterior to this suture, the parietals receive a single median fossa that is compressed anteroposteriorly (ca. 5 mm) but is wide transversely (ca. 24 mm), which may have housed a small air sinus fossa (Extended Fig. 4a: asf?). The posterior wall of this median fossa is continuous with a near vertical plate (maximum height ca. 40 mm) composed of parietals and supraoccipital. Laterally this plate is continuous with the nuchal crests, and its posterior surface comprises the occiput. In anterior view, it can be seen that the parietals do not cover the entire anterior surface of this plate, instead there is a median, triangular shaped exposure of supraoccipital, with the apex of the triangle pointing ventrally. The interparietal suture is shifted as much as 7 mm to the left relative to a thickening of the supraoccipital centered on the median plane. In posterior view the nearly vertical occiput is somewhat spatula shaped; it is narrowest at a level slightly dorsal to the condyles, widens dorsally, and terminates dorsally as a gentle arc (Fig. 2c). The dorsal quarter of the supraoccipital is convex and has three elevations: a median nuchal ridge and two triangular rugosities, one on each side, which based on comparison to extant mysticetes and odontocetes likely served as attachments for the semispinalis capitus muscles 32,33. Ventral to that, the right and left sides of the supraoccipital are broadly excavated and separated by a low median ridge. The occipital condyles are situated on short necks, which are best developed ventrally. The foramen magnum comes to a dorsal apex, its lateral sides are oriented ventrolaterally, and its ventral margin is curved and convex ventrally. In posterior view, the paroccipital process extends ventrally to the same level as the basioccipital crest, although the shape of the jugular notch between the processes cannot be determined because of damage to the basioccipital crest on both sides. For the same reason it is unclear if the hypoglossal foramen WWW.NATURE.COM/NATURE 7

was present or confluent with the cranial hiatus. The lateral margin of the exoccipital is quite thin, and its suture with the squamosal is interdigitated. The posterior side of the zygomatic process has a fossa, which in extant cetaceans serves as an attachment for the sternomastoid and possibly other muscles 32,34, although the fossa in Cotylocara does not extend onto the lateral side of that process. In lateral view the zygomatic process of the squamosal is deep dorsoventrally and triangular (Fig. 2a). It comes to a distinct anterior apex, its ventral edge is nearly straight, and the posterior two thirds of its dorsal margin is a low rounded ridge, whereas the anterior third of that margin is a narrow ridge. In lateral view, the postglenoid process tapers to a ventral apex. Posterior to it is a narrow but distinct external auditory meatus. The zygomatic process forms the lateral border of a deep squamosal fossa; that is the fossa on the dorsal surface of the glenoid process of the squamosal lateral to the squamosal plate. The squamosal plate forms approximately a quarter of the lateral wall of the braincase. The ventral side of the glenoid process of the squamosal is dominated by the concave glenoid fossa for the mandibular condyle and a prominent postglenoid process. The borders of the glenoid fossa are poorly delineated and there is no trace of the middle sinus fossae. A small, transversely elongate fossa medial to the postglenoid process is most likely for the sigmoid process of the ectotympanic bulla (Extended Fig. 2a), as is seen in basilosaurids 35. Medial to this fossa is a prominent spiny process of the squamosal that articulated with the hiatus epitympanicus of the petrosal, although its exact size is somewhat speculative because it is broken on both sides. Dorsal to the spiny process is a suprameatal pit, which presumably housed an expansion of the peribullar sinus. The paroccipital process is extended posterolaterally but does not reach the level of the posterior margin of the occipital condyle (Fig. 1d). WWW.NATURE.COM/NATURE 8

In ventral view, the skull has elongate fossae, one of each side, that are oriented anteromedially and presumably received the peribullar and pterygoid sinus fossae. The medial wall of each fossa is formed by a high and narrow pharyngeal crest. The posterior part of the pharyngeal crest is formed by the basioccipital whereas the anterior part is formed by the posterior lamina of the pterygoid; the suture between the two is at the level of the falciform process of the squamosal. The falciform process forms part of the lateral wall of the sinus fossa and has an anteroposteriorly broad, but transversely narrow base (Extended Fig. 2a). Its distal end faces ventrolaterally, instead of laterally, and is separated from the rest of the process by a distinct anteroposteriorly oriented ridge. The surface of the distal end of the falciform process appears to have been sutured to another bone, possibly the lateral pterygoid plate (not preserved in CCNHM-101). The peribullar sinus fossa (i.e., periotic fossa) is divided into anterior and posterior portions by a weak transverse ridge, the posterior portion includes a deep circular sinus fossa (Extended Fig. 4b: d,f), and the anterior portion lacks a foramen spinosum. As in Waipatia maerewhenua 29 part of the periotic fossa lies on the parietal. Anterior to the parietal the fossa extends onto the alisphenoid, and the suture between these two bones is level with the posterior margin of the falciform process of the squamosal. A wide cranial hiatus occurs on the roof of the air sinus fossa between the periotic fossa and the basioccipital; however, some of its margins are broken, thus it is possible, although unlikely, that the foramen ovale was originally separate from the hiatus. A groove for the mandibular division of the trigeminal nerve occurs on the ventral side of the alisphenoid and is directed laterally and slightly anteriorly. The groove passes adjacent to the anterior end of the base of the falciform process, and lateral to that, the groove is barely visible and courses on the squamosal. The subtemporal crest is prominent and wraps around the anterior margin of the glenoid process of the squamosal. WWW.NATURE.COM/NATURE 9

The petrosal tightly articulates with the squamosal and parietal at many points, although gaps do occur and were likely formed by the peribullar sinus fossa. In lateral view the anterior process of the petrosal is hatchet shaped, with a concave dorsal margin (Extended Fig. 2g). The dorsal apex of the anterior process is much more pronounced on the left petrosal. The lateral side of the anterior process bears a very faint sulcus for the capsuloparietal emissary vein but no channel for the middle meningeal artery. The dorsal third of the lateral side of the anterior process is concave, is continuous with more posterior portions of the tegmen tympani, and fits onto an elevated rugosity of the parietal. Posterior to the anterior process the petrosal bears a very large and elongate ventrolateral tuberosity (Extended Fig. 2e-h). The tuberosity is shaped like a rectangular flange with three sides, a narrow ventral side, a flat side that faces anteroventrally, and a rugose side that faces posterodorsally. Medial to the base of the ventrolateral tuberosity is a circular fossa for the malleus whose anterior margin is particularly well-defined. Posterior to the fossa for the malleus are two structures: medially the tympanic opening of the facial nerve canal, and laterally a slightly elevated facet for the incus. The latter is partially separated from the fossa for the malleus by a shallow sulcus. Lateral to the facet for the incus is a broad depressed portion of the tegmen tympani, the hiatus epitympanicus (Extended Fig. 2e,h). This portion of the petrosal presumably received the now broken spiny process of the squamosal. Posterior to the hiatus epitympanicus is a small, nearly square facet for the ectotympanic bulla. This facet is situated on the posterior process of the petrosal, which is approximately half the length of the pars cochlearis. In ventral view, the promontorium forms an acute angle with the anterior process, and the anterior and medial margins of the latter meet at an angle instead of a smooth curve (Extended Fig. 2e). Medial to the promontorium is a nearly circular fenestra ovalis, and posteriorly the WWW.NATURE.COM/NATURE 10

promontorium bears a large and dorsally expanded fenestra rotunda. The fenestra rotunda is separated from the stapedial muscle fossa by a distinct caudal tympanic process, and the latter is separated from the posterior process by a clear gap. Nearly circular and subequal apertures for the cochlear and vestibular aqueducts occur on the dorsal side of petrosal (Extended Fig. 2f). Anterior to these foramina is the internal acoustic meatus, which includes the proximal opening of the facial canal. Within the meatus the foramen singular is separated from the spiral cribiform tract and the facial canal by anterior and posterior septa. The latter septum is the higher of the two. Lateral to the internal acoustic meatus and medial to a low dorsal crest is an anteroposteriorly elongate and shallow suprameatal fossa. The ectotympanic bulla, like those in all other cetaceans, has a pachyosteosclerotic medial portion called the involucrum. On the dorsal side of the involucrum are several transverse grooves (Extended Fig. 2c). Lateral to the involucrum is the tympanic cavity, which is encased by the thin-walled outer lip and inflated outer posterior prominence. The floor of a tympanic cavity is divided into an anterior third and a posterior two-thirds two by a low transverse ridge. In ventral view the involucrum and outer posterior prominence are separated by a median furrow. This furrow merges anteriorly with a diffuse concave surface that is centered on the ventral aspect of the bulla. (Extended Fig. 2b). The bulla lacks an anterior spine. The preserved part of the mandibular symphysis of the lower jaw is long, sutured, and unfused. Its posterior termination appears to be situated at the level of the n-5 mandibular tooth (Extended Fig. 1a). The dentaries have a large and high coronoid process that bears a shallow fossa on its lateral side. In our opinion this fossa is too dorsal to be an attachment scar for the masseter muscle, and instead is a byproduct of a more pronounced anterior edge of the coronoid process. This edge likely would have formed part of the attachment for the temporalis muscle. WWW.NATURE.COM/NATURE 11

As in other odontocetes and most archaeocetes, the mandible has a huge mandibular foramen that leads anteriorly into an expanded mandibular canal and posteriorly into the large mandibular fossa. The lateral wall of the mandibular canal is thin, suggesting the presence of a pan bone for conducting sound to the intramadibular fat body (but see ref. 22). The body of the right mandible is pathologic. A channel 7-9 mm wide and 5-6 mm deep courses medial to the alveoli, from a point immediately anterior to the alveolus for the n-2 mandibular tooth to a point opposite the posterior end of the mandibular symphysis. The posterior end of the channel is in a medially-placed embrasure pit, and inspection of the upper tooth that fits into that embrasure pit reveals that unlike the other maxillary teeth, it is directed ventromedially instead of ventrally. However, the channel itself cannot be entirely explained by embrasure pits because the channel passes by, and does not incorporate, another embrasure pit. A similar pathologic channel occurs medial to the penultimate and last alveoli of the right dentary, although due to poor preservation its exact morphology is unclear. Based on alveoli and preserved teeth, the maxilla bears 5 single-rooted and 6 doublerooted teeth, and there was at least one tooth in the premaxilla. Given that the total tooth count is unknown, teeth are referred to as n-1, n-2, etc., where n = the total tooth count. Thus, for example, the third from the last tooth in the maxilla is referred to as the n-2 tooth, the penultimate tooth is n-1, and the last tooth is the n tooth. Some teeth were found separate from the skull and were placed in the skull based on fit to an alveolus and overall morphology. We suspect that the n-3 and n-2 teeth on the left side may be reversed (i.e., they were inadvertently placed in each other s alveolus) because their wear patterns do not fit the overall trend in dental wear observed across the toothrow. Our suspicion cannot be confirmed until more specimens of WWW.NATURE.COM/NATURE 12

Cotylocara macei are found, thus for now we refer to teeth according to their current position in the skull, even though they might belong at another locus. In general, the double-rooted teeth have an entocingulum, an ectocingulum, weak striations, and accessory denticles that are smaller than the central primary cusp. Roots are typically inflated with a wasted zone adjacent to the base of the crown. The posterior teeth have elongate wear facets on the mesial and/or distal carinae caused by the opposing dentition, although the facets differ from those of stem cetaceans 36 in being strongly inclined instead of subvertical in orientation. More details on individual teeth are as follows. Mesial denticles are worn off of the last maxillary tooth (Fig. 2a,b). The distal carina bears three denticles; the apical two are subequal in size and the basal one is minute, but all are much smaller than the main denticle. There is an ento- and an ectocingulum, and the labial and lingual sides of the crown bear very faint striations. Although wear is most pronounced along the mesial carina, the distal edge of the central cusp and the apex of the adjacent denticle on the distal carina have slight wear. There is also minor wear on the apex of the main cusp. On the left n-1 tooth, strong mesial and distal wear have obliterated all traces, if there were any, of accessory cusps. These two wear facets converge on the apex of the tooth, and as a result, the current height of the crown likely underestimates its pre-wear height. There is an ectoand an entocingulum as well as some striations, which are most evident on the labial side. The cusp of the right n-1 tooth has been largely reconstructed and is not described here. The left n-2 maxillary tooth has very clear striations that are slightly nodular at the base of the crown. It also bears well developed ecto- and entocingula. The mesial and distal carinae were removed by wear facets, with the mesial wear facet expanded into a deep gouge near the base of the crown. There are at least two denticles on the mesial side and two on the distal side, WWW.NATURE.COM/NATURE 13

but wear has made the exact number unclear. The right n-2 has much stronger wear; the mesial and distal wear facets have obliterated all denticles. The size and shape of the wear facets on the right n-2 tooth resemble more those of the left n-1 tooth than those of the left n-2 tooth. The left n-3 tooth has strong wear on its mesial and distal sides, although slightly less wear than that on the left n-1 tooth. Ecto- and entocingula are present, and the latter is slightly crenulated toward its distal end. Striations are also present on both sides of the crown, with some on the lingual side being slightly nodular. The right n-3 tooth has very different wear; there is moderate wear on the mesial edge and essentially no wear on distal edge. It has three denticles on the distal carina; all crowded near the base with the most basal one being minute. It has entoand ectocingula as well as striations. The striations are nodular towards base, particularly those on the lingual side. The right and left n-4 teeth have clear striations on both sides of their crowns that become more nodular towards the base, particularly those on the lingual side. There are well-developed ecto- and entocingula. On the right n-4 tooth it can be seen that the distal carina has four small denticles crowded near the base, but it is unclear if this is the case on the left side because of damage to the crown. It is also unclear if there were any denticles on the mesial carina because of a large gouge that has consumed it and a portion of the lingual side of the crown. The left n-5 tooth is similar to the n-4 tooth except that it has three small denticles on its distal edge instead of four. Based on alveoli there were at least eight lower teeth on each side, although only three lower teeth are preserved. The other lower teeth in CCNHM-101 are casts of teeth from other loci or were sculpted using other teeth as a model. The right n-1 tooth is preserved and has an ento- and an ectocingulum. There are some striations, mainly on the mesial third of the lingual WWW.NATURE.COM/NATURE 14

side of tooth. There is strong wear on the mesial and distal edges, thus it is unclear if this tooth lacked denticles or they were worn off. The right n-5 tooth lacks denticles on the mesial carina, but the distal carina is worn so that the presence or absence of denticles could not be determined. That tooth has an entocingulum, lacks an ectocingulum, and has striations that are primarily restricted to lingual side. The only lower tooth preserved on the left side is the n-4 tooth. On that tooth the mesial and distal carinae have two minute denticles near the base of the crown, and this tooth has well-developed ecto- and entocingula with clear crenulations. The labial side of the n-4 tooth is nearly devoid of striations, but the labial side has clear striations that become nodular toward the crown base. Unlike the other preserved teeth, the n-4 tooth lacks obvious wear. There are three preserved cervical vertebrae, all unfused (Extended Fig. 3h-k). One is clearly the axis (C2), another is likely C3 or C4, and one is probably C6. The axis has a prominent odontoid process with a base slightly wider than its height. The dorsal side of the odontoid has a sagittal ridge that continues onto the floor of the vertebral canal and nearly reaches the posterior side of the centrum. On either side of this ridge is an anteroposteriorly elongate trough. The ventral side of the odontoid process is covered by the articular facet for the atlas. These facets extend laterally across the anterior face of the centrum of the axis and are concave transversely and nearly flat dorsoventrally. The ventral side of the centrum bears a robust hypophysis. Extending ventrolaterally away from the centrum are short, but robust, transverse processes. The distal end of the transverse process is blunt, and the process lacks a transverse foramen. Its posterior side forms a distinct ridge, and dorsal and ventral to that ridge the transverse process is concave. The dorsal margin of the transverse process comes to a sharp crest that connects with the vertebral centrum. The left transverse process is noticeably longer than the right one. The vertebral foramen (i.e. portion of vertebral canal) is roughly an equilateral WWW.NATURE.COM/NATURE 15

triangle, although its lateral sides are bowed laterally. The surrounding vertebral arch has ventrolaterally facing postzygapophyses (the left is not preserved) but lacks prezygapophyses. The arch has a prominent spine that extends across its entire anteroposterior. The neural spine is broken, thus its height is unclear. The second or third cervical vertebra is represented only by its centrum, the right transverse process, and both pedicles (Extended Fig. 3j). The centrum has a small yet distinct hypophysis. The transverse process is oriented ventrolaterally, and its dorsal side also faces slightly anteriorly whereas its ventral side also faces slightly posteriorly. The left pedicle has a thin ventrolaterally-projecting strut, which indicates a very large transverse foramen. The borders of the foramen are not entirely preserved, thus it is unclear if the foramen was completely encircled. The probable C6 is identified to vertebral position based on the hypertrophied transverse process (Extended Fig. 3k). The transverse process is similarly enlarged in basilosaurids 37 and at least some stem mysticetes 38. The long transverse process projects ventrolaterally, and its posterior side bears a distinct ridge. A narrow strut extends dorsally from the transverse process indicating that there was an enormous transverse foramen; however, it is unclear whether that foramen was entirely encircled because not all parts of the lateral border of the foramen are preserved. The neural canal is ovoid and much wider than tall. The surrounding neural arch has dorsomedially facing prezygapophyses and ventrolaterally facing postzygapophyses. The spinous process is rudimentary and just forms a sagittal anteroposteriorly-oriented ridge. There are portions of at least 7 ribs; two are interpreted to be right ribs and five are thought to be left (Extended Fig. 3a-g). The sides of the ribs (i.e. left or right) were determined based on the orientation of the tuberculum. Two of the left ribs are anterior ones as indicated by WWW.NATURE.COM/NATURE 16

deep shaft and large span between tubercle and head. The remaining ribs have two articular facets, although on the posteriormost preserved left rib, the facets have nearly merged. WWW.NATURE.COM/NATURE 17

Part II. Table of Measurements of holotype of Cotylocara macei (CCNHM-101) in mm. ant, anterior; boc, basioccipital; btwn, between; cerv, cervical; exoc, exoccipital; fen, fenestra; for, foramen; H, height; jug, jugal; L, length; lat, lateral; lac, lacrimal; lvl, level of; max, maximum; min, minimum; mx, maxilla; n, # of mandibular teeth; N, # of maxillary teeth; na, nasal; oc, occipital; pal, palatine; pet, petrosal; post, posterior; proc, process; px, premaxilla; squa, squamosal; vent, ventral; W, width; *, as preserved. Measurements in italics have no side Measurement Right Left Measurement Right Left Skull L. w/o px. 526* External bony nares, W. 28.2 Skull W. at antorbital notch 106.8 Ant. edge of na., depth 19 14 Skull W. at postorbital proc. 240.4 Ant. edge of na., W. 9.4 7.7 Skull W. at zygomatic proc. of squa. 269.6 Max. W. across nasals 26.4 Rostrum L. 348* Max. L. of nasal 69.0 72.5 Mx. on rostrum, L. 326 - W. across post. ends of nasals 25.5 Depth of palate at mx./pal. suture 5 - H. of nasals relative to edge of rostrum 133 Rostrum, max. H. 54.6 - Min. dorsal W. btwn. temporal fossae 38.8 Gap btwn. premaxillae ant. to nares 7.9 Depth of squa. fossa 33 31 W. of premaxillae at antorbital notch 35.1 Point above to dorsal edge of zygoma, W. 16 18 In lat. view, angle btwn. px. and rostrum edge 27 - Postglenoid proc. to apex of zygomatic proc. 83 85.8 N maxillary tooth, L. of crown 10.9 11.1 Glenoid fossa of squa., W. 38 32 N maxillary tooth, H. of crown 8.7 8.6 In vent. view, angle btwn. boc. crests 50 N-1 maxillary tooth, L. of crown - 11.3 Tympanic bulla, L. - 49.7 N-1 maxillary tooth, H. of crown - 8.7 Tympanic bulla, W. at lvl. sigmoid proc. - 31 N-2 maxillary tooth, L. of crown - 11.1 Promontorium of pet., W. 10.5 10.5 N-2 maxillary tooth, H. of crown - 10.3 Promontorium of pet., L. 15.7 15.9 N-3 maxillary tooth, L. of crown 11.1 11.3 Ant. proc. of pet., W. at midlength 8.3 7.5 N-3 maxillary tooth, H. of crown 10.4 10.3 Ant. process of pet., H. at midlength 13.7 14 N-4 maxillary tooth, L. of crown 10.0 10.2 Perilymphatic for. to fen. rotunda, min. 4.5 4.6 N-4 maxillary tooth, H. of crown - 10.7 Endolymphatic for. to fen. rotunda, min. D. 5.1 5.9 N-5 maxillary tooth, L. of crown - 8.7 Fen. ovalis to fen. rotunda, min. 4.1 4.7 N-5 maxillary tooth, H. of crown - 8.0 Superior proc. H., lvl. internal acoustic meatus 2.7 2.4 Mandible, H. max. 129 128.5 Superior proc. H., lvl. endolymphatic for. 1.1 1.9 Mandible depth, lvl. of last tooth 33.7 34.7 Post. proc. of pet., L. along long axis 6.4 7.5 Mandibular condyle, max. W. 26.4 - In ventrolateral view, angle of post. proc. 145 145 n-1 mandibular tooth, L. of crown 12.6 - W. of squa. lat. to exoc. 58 52 n-1 mandibular tooth, H. of crown 9.3 - W. from median plane to lat. margin exoc. 90 86 WWW.NATURE.COM/NATURE 18

Table 1 cont. n-4 mandibular tooth, L. of crown - 10.3 W. across oc. condyles 72.8 n-4 mandibular tooth, H. of crown - 8.2 Max. width across exoccipitals 172.2 n-5 mandibular tooth, L. of crown 9.3 - Axis vertebra, max. W 78.1 n-5 mandibular tooth, H. of crown 8.4 - Axis vertebra, max. H. 83.6 n alveolus, L 18.2 Middle cerv. vertebra, ant. W. centrum 38.9 n-3 alveolus, L 18.3 16 Middle cerv. vertebra, ant. H. centrum 38.1 n-6 alveolus, L - 12 Middle cerv. vertebra, max. L. of centrum 20 W. across middle of orbits 214 Post. cerv. vertebra, max. W 113* H. of orbit relative to edge of rostrum 42 - Post. cerv. vertebra, max. H. 90* Lvl. antorbital notch, L. of lac. + jug. 24.5 Post. cerv. vertebra, ant. W. of centrum 39.4, L. to postorbital ridge 48.7 - Post. cerv. vertebra, ant. H. of centrum 37.2 Angle of ant. edge of supraorbital proc. 70 - Post. cerv. vertebra, max. L. of centrum 26.8 WWW.NATURE.COM/NATURE 19

Part III. Supplementary Discussion Evolution of Echolocation Based on Osteological Characters Cranial characters that are associated with, and maybe indicative of, echolocation can be divided into three groups: 1) characters that indicate a single origin for echolocation, 2) characters indicating some aspects of echolocation evolved twice, and 3) characters suggesting that xenorophid echolocation was unique. The first group of characters includes a fossa for the premaxillary air sinus and an expansion of the maxilla over the frontals (Extended Fig. 7e,f). We find the expansion of the maxilla to be most convincing indicator of echolocating abilities; as described in the main text, the ascending process of the maxilla serves as an attachment site for large facial muscles that insert on and around the soft tissue nasal passages and air sinuses 9,13. An expanded ascending process is developed to some degree in all fossil odontocetes and is clearly absent in basilosaurids and all mysticetes 14,27. The occurrence of a premaxillary sinus is a little more problematic, and although there is strong osteological evidence for a premaxillary air sinus in xenorophids, the evidence is much weaker in some other Oligocene odontocetes. All xenorophids have a well-defined fossa on the premaxilla that likely housed the premaxillary air sinus, and we interpret the adjacent rostral basin as receiving a ventrolateral expansion of this air sinus. In contrast, Simocetus and Agorophius, which branch off of the odontocete stem after xenorophids, lack a clear fossa. Instead they have a gently convex and smooth portion of bone that is bordered anteriorly by the premaxillary foramen, anterolaterally by the posterolateral sulcus, medially by the mesorostral gutter, and posteriorly by the external bony nares. Based on comparisons with extant taxa and WWW.NATURE.COM/NATURE 20

also on the conserved anatomical relationships among the premaxillary foramen, posterolateral sulcus, and premaxillary air sinus, Fordyce 10,39 interpreted the smooth medial portion of the premaxilla as a premaxillary sac fossa. Although we think his interpretation is correct, there is an important, but subtle, distinction between a bony fossa and a smooth area of convex bone; the former can be taken as evidence of an air sinus whereas the latter should not. A more nuanced delineation of character states could help resolve this problem, but it is complicated by continuous variation between Simocetus, where the fossa is convex transversely, and the morphology in Waipatia 29 and many extant taxa 27, where a clear bony fossa is present. Based mainly on the well-developed premaxillary sac fossa and rostral basin in xenorophids, we suggest that a small premaxillary air sinus was present in the most recent common ancestor of xenorophids and extant odontocetes, and that a true fossa developed on the stem leading to extant odontocetes when the air sinus enlarged. The possible presence of the air sinus in the absence of an osteological fossa is supported by the observation that the premaxillary air sinus in porpoises (i.e. Phocoenidae) does not lie in a bony fossa but instead rests on an elevation of the premaxilla 13. Two skeletal characters indicate that some of the soft-tissue features associated with echolocation underwent convergent evolution, and a third can be interpreted that way. In extant odontocetes the temporal fossa, for the temporalis muscle, is highly compressed as compared to stem cetaceans (e.g. Georgiacetus and Pakicetus) 26. Several changes in skull shape contributed to this reduction. For example, in all extant odontocetes the supraorbital process of the frontal encroaches into the space formerly occupied by the temporal fossa and roofs over that fossa 27. Our phylogeny indicates that this evolved twice; once in the clade that includes Xenorophus and Cotylocara and a second time in the clade that includes Agorophius and extant odontocetes but WWW.NATURE.COM/NATURE 21

not xenorophids (Fig. 3 and Extended Fig. 7i). An expanded supraorbital process allows for a larger ascending process of the maxilla, which serves as the origin for a suite of facial muscles that insert on the soft tissue nasal passages and air sinuses (see paragraph above and main text). Another character, the position of the posteriormost end of the ascending process of the maxilla (Extended Fig. 7a), is often, but not always (e.g. mysticetes), correlated with expansion of the ascending process of the maxilla. Here too there is convergence; within Xenorophidae and again along the stem to crown Odontoceti the maxilla shifted to the level of the ear (character state 5; Extended Fig. 7g,i). This interpretation is supported by the occurrence of fossil species with intermediate morphologies (states 3, 4) within both clades (i.e. Archaeodelphis, ChM PV4746, Agorophius, Simocetus). A third character, posterolateral expansion of the ascending process of the maxilla, may also exhibit convergent evolution. We have shown one most parsimonious reconstruction for this character (Extended Fig. 7f), but it is equally parsimonious for the common ancestor of all odontocetes to have had partial expansion (shown in purple), and then for complete expansion (in blue) to have evolved twice: once in all xenorophids except for Archaeodelphis and again in the clade including all odontocetes except xenorophids. The functional anatomy of xenorophid echolocation was likely distinct, as indicated by facial features restricted to that family of odontocetes. The rostral basin evolved within the group (Archaeodelphis and ChM PV4746 lack it), and we suggest that this basin was excavated by an expansion of the premaxillary air sinus (Extended Fig. 7d). This differs from extant odontocetes in which the premaxillary air sinus is confined to the premaxilla 9,15. Although it is possible that the rostral basin was excavated by a neomorphic air sinus, it is more parsimonious to infer that a known and adjacent air sinus (i.e., premaxillary) was expanded. The postnarial fossa is absent in all non-xenorophid odontocetes, and is clearly a neomorph, although its corresponding air sinus WWW.NATURE.COM/NATURE 22

was likely an extension of the inferior vestibule, an air sinus that is widely distributed among extant odontocetes 15. The postnarial fossa first appears as a shallow fossa in an undescribed species (GSM 1098), and then evolves into a deep cavity with a median septum of interparietal in Cotylocara (Extended Fig. 7h). Stages in the Development of Echolocation Below we lay out stages for the evolution of echolocation in odontocetes. These stages represent grades of evolution that are reconstructed from parsimony optimization of skeletal and soft tissues features on internal branches of our most parsimonious tree. The boundaries between stages are somewhat arbitrary and were chosen to highlight the evolution of this complex anatomical system. For each stage, at least one fossil taxon is listed as a representative. Stages 2 and 3 evolved twice, and separate iterations are described as stage 2 or 2 and stage 3 or 3. In those cases where there are no osteological correlates for a soft tissue structure, we have developed a hypothesis that is consistent with available evidence. For example, although there are no osteological correlates for a hypertrophied melon; however, parsimony indicates that this feature evolved somewhere along the stem leading to the odontocete crown group 26. The reconstruction of the melon at any particular node along the stem is consistent with available evidence but is not directly supported. The evolution of a neomorph, such as those associated with echolocation, is particularly challenging to reconstruct when much of the relevant anatomy involves soft tissues and few intermediate morphologies occur in extant species. The main methodology for reconstructing soft tissue structures in fossils is the phylogenetic bracket, which relies on the soft-tissue feature WWW.NATURE.COM/NATURE 23

and its osteological correlate being present in an extinct taxon s closest extant relative and the nearest extant outgroup to the clade they form 40. When the nearest outgroup lacks the correlate and soft-tissue feature, as often happens in the evolution of neomorphs, then some other approach is needed. Here we use the concept of one-way positive osteological correlates to reconstruct some aspects of echolocation and its associated anatomy 41. Such correlates always co-occur with their corresponding soft-tissue structure, but the soft-tissue structure may occur without its corresponding osteological correlate. One example of a one-way positive correlate is a small canal between the petrous part of the temporal bone and the occipital bone in some humans that transmits the glossopharyngeal nerve 42-44. This canal is an osteological correlate of the glossopharyngeal nerve, but the latter occurs even when the canal is absent. In fact, that is the most prevalent condition, and in such cases the glossopharyngeal nerve exits the cranium with several other structures (i.e., vagus and spinal accessory nerves, internal jugular vein) through the jugular foramen 43. The distribution of one-way osteological correlates in the fossil record can underestimate the distribution of its corresponding soft-tissue feature, and as a consequence, a literal reading of the fossil record could lead one to infer that a soft-tissue structure evolved later than it actually did 41. Parsimony can be used to develop better estimates for a when a soft-tissue neomorph evolved by coding fossils that have the one-way positive correlate as having the softtissue feature and then coding other fossils that lack the correlate as ambiguous (i.e., present or absent). Stage 1: Represented by Archaeodelphis and ChM PV4746. Stage 1 spans the portion of the phylogeny that starts with the most recent common ancestor of all known odontocetes (both extant and extinct) and includes the basal portion of the Xenorophidae, up to the most recent WWW.NATURE.COM/NATURE 24

common ancestor of ChM PV4746 and Xenorophus sloani. ChM PV4746 is an undescribed fossil cetacean skull in the Charleston Museum vertebrate paleontology collections (Charleston, SC) that was collected from nearby exposures of the Rupelian Ashley Formation 27. Its elongate rostrum and simplified dentition, among many other features, indicate that this specimen represents an unnamed species of early odontocete, and it is clearly a xenorophid based on the presence of a well-developed ascending process of the lacrimal, premaxilla wedged between supraorbital process of frontal and maxilla, and a pointed ventrolateral tuberosity of the petrosal. Archaeodelphis patrius is only known from its holotype skull in the Museum of Comparative Zoology (Harvard), and the provenance of the specimen has been lost. However, dinoflagellates from matrix inside the braincase support an Oligocene age 45. Both Archaeodelphis and ChM PV4746 are inferred to have had a premaxillary air sinus and enlarged facial muscles (i.e., derivatives of the maxillonasolabialis); the former based on a premaxillary sac fossa and the latter on an expanded ascending process of the maxilla. Stage 1 includes the most recent common ancestor of all known extant and extinct odontocetes, and parsimony optimization supports these osteological correlates as being present on this internal branch (Extended Fig. 7e,f); however, optimization of their corresponding soft-tissue feature yields mixed results. Enlargement and elaboration of facial muscles is optimized to have evolved on the stem to the odontocete crown group and is thus consistent with its osteological correlate. By contrast, the premaxillary air sinus is optimized to have evolved later in the stem to Synrhina because the most basal extant odontocetes (i.e., Physeteroidea, sperm whales) lack this sinus 15. If we code Oligocene odontocetes, like Archaeodelphis, that have a premaxillary sac fossa as having the sinus and code taxa without the fossa as ambiguous, then it is most parsimonious to infer that stage 1 odontocetes had a premaxillary air sinus and that it was later lost in WWW.NATURE.COM/NATURE 25

physeteroids. Such a scenario would not be surprising given the highly unusual and apomorphic facial anatomy of sperm whales 15. If stage 1 odontocetes had a melon, it was probably quite small. This inference is based on the position of their external bony nares on the rostrum, as seen in Archaeodelphis and ChM PV4746, which limited the space available for a large melon. Space would be further restricted if the narrow rostrum of Archaeodelphis and ChM PV4746 was typical of all stage 1 odontocetes. Other aspects of stage 1 odontocetes can be reconstructed using one-way osteological correlates that are present in Cotylocara. As described in the main text, there is strong evidence (e.g., dense and downturned rostrum, laterally expanded premaxilla adjacent to bony nares, facial asymmetry) that Cotylocara had phonic lips and could echolocate. Thus it is most parsimonious to assume that echolocation evolved in stage 1 odontocetes, and that echolocation occurred in the other stages as well (stages 2, 2, 3, 3 ). Similarly, the postnarial fossa in Cotylocara and GSM 1098 suggests that a rudimentary form of the proximal air sac/inferior vestibule was present in stage 1. An early evolution of the proximal sac is consistent with its occurrence in all extant odontocetes 15,26. In a cladistic analysis of extant odontocetes, Heyning 15 showed that the most recent common ancestor of crown Odontoceti did not have a blowhole ligament, thus it follows that stem odontocetes lacked it as well. Stage 2 and 2 : Represented by Simocetus rayi and Xenorophus. Stage 2 corresponds to the portion of odontocete phylogeny that begins with the most recent common ancestor of Agorophius pygmaeus and extant odontocetes and then ends with the most recent common ancestor of ChMPV2761and extant odontocetes. This stage is the second of three leading up to the odontocete crown group. Simocetus rayi, the representative of stage 2, is known only from WWW.NATURE.COM/NATURE 26