Sphenodontian phylogeny and the impact of model choice in Bayesian morphological clock estimates of divergence times and evolutionary rates

Background The vast majority of all life that ever existed on earth is now extinct and several aspects of their evolutionary history can only be assessed by using morphological data from the fossil record. Sphenodontian reptiles are a classic example, having an evolutionary history of at least 230 million years, but currently represented by a single living species (Sphenodon punctatus). Hence, it is imperative to improve the development and implementation of probabilistic models to estimate evolutionary trees from morphological data (e.g., morphological clocks), which has direct benefits to understanding relationships and evolutionary patterns for both fossil and living species. However, the impact of model choice on morphology-only datasets has been poorly explored. Results Here, we investigate the impact of a wide array of model choices on the inference of evolutionary trees and macroevolutionary parameters (divergence times and evolutionary rates) using a new data matrix on sphenodontian reptiles. Specifically, we tested different clock models, clock partitioning, taxon sampling strategies, sampling for ancestors, and variations on the fossilized birth-death (FBD) tree model parameters through time. We find a strong impact on divergence times and background evolutionary rates when applying widely utilized approaches, such as allowing for ancestors in the tree and the inappropriate assumption of diversification parameters being constant through time. We compare those results with previous studies on the impact of model choice to molecular data analysis and provide suggestions for improving the implementation of morphological clocks. Optimal model combinations find the radiation of most major lineages of sphenodontians to be in the Triassic and a gradual but continuous drop in morphological rates of evolution across distinct regions of the phenotype throughout the history of the group. Conclusions We provide a new hypothesis of sphenodontian classification, along with detailed macroevolutionary patterns in the evolutionary history of the group. Importantly, we provide suggestions to avoid overestimated divergence times and biased parameter estimates using morphological clocks. Partitioning relaxed clocks offers methodological limitations, but those can be at least partially circumvented to reveal a detailed assessment of rates of evolution across the phenotype and tests of evolutionary mosaicism.

11. Jugal, posteroventral process, orientation: directed posteriorly (0); directed laterally (1) (NEW). Remarks: The posteroventral process of the jugal forms the majority or all of the lower temporal bar in rhynchocephalians. Whereas in some taxa this process is directed posteriorly and relatively straight as compared to the maxilla, in other taxa (e.g. Sphenodon) it is directed laterally, creating the larger lower temporal fenestra and more space for the adductor chamber. This character can only be assessed on articulated specimens. 12. Prefrontal crest: absent (0)/ present (1) (G12, Ch. 130).
19. Postfrontals, medial margin, position, relative to parietal: ventral (0)/ dorsal (1)/ lateral (2)/ anterior (3) (G12, Ch. 65-modified). Remarks: The conservative relationship of the contact between the parietal and postfrontal across a wide range of clades and sampled taxa justifies the codification of the position of the postfrontal using the parietal as a landmark. 20. Squamosals, anterior process, lateral surface, facet for postorbital: absent (0)/ parabolic (1)/ half-parabolic (S18, Ch. 61-modified). Remarks: Absent refers to a smooth lateral surface of the squamosal. A parabolic shape facet for the postorbital creates an elongate lateral concavity into which the posterior process of the postorbital inserts. When both the squamosal and postorbital are in articulation in state "1", it creates the impression that the anterior process of the squamosal is anteriorly bifid. In state "2", the facet has a half-parabolic shape for the posterior process of the postorbital, located on the dorsolateral margin of the anterior process of the squamosal, as seen in Clevosaurus hudsoni.
25. Quadratojugals, anterior extension: present (0)/ absent (1) (G88a, Ch. 9) Remarks: In lepidosaurs, when the quadratojugal is present, the main body of the quadratojugal contacts the quadrate, but its anterior extension (such as the one observed in many archosauriforms) is absent.
28. Parietals, fusion to each other: separated (0)/ fused (1) (B85, Ch. Y1). 34. Quadrates, quadrate conch: absent (0)/ present (1) (B85, Ch. Y11). Remarks: The tympanic membrane attachment to the quadratojugal (or the quadrate when the quadratojugal is lost) creates a reinforced attachment site (the tympanic crest) that always occurs in conjunction with a thinner and medially projecting bony flange that forms by the quadrate conch. Therefore, the absence/presence of a quadrate conch, and the absence/presence of a tympanic crest, are dependent characters among the studied taxa herein, and the quadrate conch is scored in this dataset to avoid redundancy. Another important consideration is that the tympanic crest of most squamates is positioned on the lateral margin of the quadrate, whereas in most rhynchocephalians this crest actually belongs to the fused quadratojugal. This topological difference seems to be a consequence of the loss of the quadratojugal in squamates, transferring the attachment site of the tympanum from the quadratojugal to the quadrate. Therefore, this topological difference regarding the composition of the tympanic crest is dependent upon the loss of the quadratojugal itself (already considered under character 24), and thus it is not a separate and independent character. Accordingly, we do not treat the composition of the tympanic crest as a distinct character in order to avoid redundancy.
49. Dentary symphysis, symphysial spur: absent (0); present (1) (AN03, A14, Ch. 36-modified herein). Remarks: The symphysial spur is an edentulous anteriorly directed projection of the dentary (Apesteguía 2008). This character has been transformed to code for the absence and presence of the symphysial spur by combining the states that tried to account for the length of the spur into the present state. Without direct measurements to account for variations in length and the continuous nature of the spur length, the scoring of the spur length becomes subjective and arbitrary. The spur length is also quite prone to ontogenetic variation. 50. Dentary, symphysis, shape: circular (0); eliptical (1) (B85, Re96, AN03-re-phrased herein) 51. Dentaries, anterior end, symphysial articulatory facet, position: on dorsal margin only (0)/ on dorsal and ventral margins (1)/ on ventral margin only (2) (Lo12, Ch. 612).
54. Dentaries, dorsal margin, contact, with ventral margin in medial view: absent (0)/ present (1) (E88, Ch. 55-modified). Remarks: The degree of contact between both margins along the length of the dentary is a variable with a continuous range of variation that we do not attempt to code herein. Only the absence/presence of that contact is considered for this character. Because the contact between both margins results mostly from a ventral expansion of the subdental crest of the dentary in all of the observed taxa, we consider this feature to be primarily homologous among the sampled species.
70. Palatine teeth, longitudinal fusion into a single dentigerous element: unfused (0)/ fused (1) (NEW). Remarks: In some taxa, all palatine teeth within a single row become fused into a single dentigerous longitudinally elongate structure, such as observed in Kallimodon.
76. Marginal dentition, alternating teeth series: absent (0)/ present (1) (S18, Ch. 218). Remarks: In Sphenodon there are five generations of teeth, the first three occurring in the embryo. The fourth and fifth generations occur after hatching and are termed successional teeth (or replacement teeth). Each of these successional teeth replace two or more of the teeth from the preceding generation (Harrison 1901). Some of the hatchling dentition is retained with the larger successional teeth on the maxilla, creating a pattern of alternating teeth anteriorly. This alternating tooth pattern is also observed in adults of most fossil sphenodontians. This character is inapplicable when hatchling teeth are absent.
78. Marginal dentition, posterior teeth series, position, placement relative to jaw bone apical margin (= crista dorsalis): lingually (0); apicolingually (1); apically (2) (S18, Ch. 210-rephrased). Remarks: The classical categories of "tooth attachment", such as acrodonty, pleurodonty and thecodonty usually mix a combination of distinct features, such as tooth position on the jaws, ankylosis, and mode of replacement. However, tooth ankylosis to its surrounding tissue of attachment may occur in reptiles in combination with different kinds of tooth topologies and replacement modes. For instance, teeth set in four-sided sockets may or may not be ankylosed to alveolar bone, suggesting both are independent characters. Therefore, here we divide the classical tooth attachment classifications into its different properties that seem to vary independently in at least part of the sampled taxa: tooth position on the jaw bone (relative to the jaws labial wall apical margins), tooth ankylosis, tooth delimitation (e.g. three-sided vs foursided sockets), and presence or absence of replacement. In the present character, tooth position can be defined as: lingual to the dentary/maxillary labial wall; apically on the labial wall (sitting entirely on the crest forming the apex of the labial wall of the tooth bearing bones), such as in chamaeleonids, some priscagamids (e.g. Mimeosaurus crassus), and most sphenodontians (e.g. Kallimodon, Pleurosaurus and Sphenodon); or apicolingually, in which part of the tooth base lies apically to the dorsal crest, but they also extend lingually to it, such as in many agamids and priscagamids (Borsuk-Białynicka & Moody 1984;Borsuk-Białynicka 1996;Evans et al. 2002;Simões et al. 2015), a condition previously described as "pleuroacrodonty" (Evans et al. 2002;Simões et al. 2015). See more in Bertin et al. (2018).
79. Marginal dentition, posterior teeth series, ankylosis to crista dorsalis (apex of labial wall) of dentary: absent (0)/ present (1) (S18, Ch. 211-re-phrased) 80. Marginal dentition, posterior teeth series, delimitation by tooth bearing bone: by a labial wall only (0)/ by a three-sided socket (1)/ by a four-sided socket (2)/ by a lingual and labial wall only (3) (S18, Ch. 212-re-phrased). Remarks: See comments above for character #78 The three-sided socket condition occurs when interdental ridges are present connecting to the labial wall of the jaws. The four-sided socket condition occurs when the teeth are fully enclosed inside a socket or alveolus on the jaws. When teeth are at the apex of the labial wall, instead of medially to it, this character is scored as inapplicable.
86. Dentary teeth, posterior teeth series, shape of basal cross section: circular (0)/ labiolingually compressed (1)/ mesiodistally compressed (2)/ quadrangular (3) (NEW). Remarks: Early rhynchocephalians possessed conic (peglike) marginal dentitions with a circular basal cross section. Later forms, such as clevosauruids, Kallimodon, Saphaeosaurus and pleurosaurids possessed labiolingually compressed teeth, and other forms, such as opisthodontids, possessed mesiodistally compressed teeth. Sphenodon possesses a quadrangular basal cross section of the posterior tooth series (clearly defined four sides), which is also observed in Kawasphenodon and Opisthias (Throckmorton et al. 1981;Apesteguía et al. 2014). In the latter state (quadrangular bases), whereas some of the teeth have equal sided quadrangular bases, some of the teeth in the posterior series may be slightly compressed labiolingually or mesiodistally. However, even in such instances, four clearly distinct sides are still discernible and form the perimeter of the tooth bases, which is considered here a qualitative difference to the features scored under state 1 (with narrow and curved mesial and distal borders) and state 2 (with narrow and curved lingual and labial borders) 87. Dentary teeth, posterior teeth series, concave anteriorly: absent (0)/ present (1) (S18, Ch. 209). Remarks: This character is the result of the development of laterally projecting ridges, both lingually and labially, sometimes termed "anteromedial" and "anterolateral" ridges or flanges (Throckmorton et al. 1981;Apesteguia & Carballido 2014;Apesteguía et al. 2014;Jones et al. 2018). The development of those ridges, which are usually as thick as the central cusp [as they composed of extremely thick enamel (Throckmorton et al. 1981;Jones et al. 2018)], gives the posterior tooth series an anteriorly concave appearance when observed in lateral view, or in occlusal view (if there is some degree of apical tooth wear)-see also Fig. 4 in Throckmorton et al. (1981). This character is applicable only when teeth are mesiodistally compressed or has a quadrangular base, as it is logically impossible on teeth that are conical or labiolingually compressed. Observed in several Mesozoic taxa occurring in South and North America, such as Toxolophosaurus and Eilenodon. Remarks: The present character considers variations on the orientation of the anterior flange, as defined in character #88 only. Such an anterior flange may be oriented anteriorly (as in Kallimodon, Homeosaurus and pleurosaurids), or anterolaterally, in which the posteriormost portion of each tooth is hidden in lateral view by the anterior tip of the flange from each posteriorly succeeding tooth (as in clevosaurids and Cynosphenodon). An anteromedial orientation of the anterior flange has not been observed on the taxa sampled for this data set, but we provide it as third possible state for this character for potential future findings and analyses. Importantly, this character is conditional on the presence of an anteriorly directed flange (i.e. lying on the longitudinal median axis of the tooth row), and it is therefore not homologous to the "anterolateral" and "anteromedial" crests-laterally oriented and more robust dental projections composed of extremely thick enamel of taxa like Opisthias, Toxolophosaurus and Eilenodon (Throckmorton et al. 1981;Jones et al. 2018)-which confer the anteriorly concave aspect of the posterior additional teeth of those taxa.

Ribs
105. Presacral ribs, uncinate processes, anterior dorsals: absent (0)/ present (1) (G88b, Ch. L17). Remarks: Neomorph cartilages that calcify in Sphenodon and crocodiles, and ossify in birds (Gauthier et al. 1988b), as well as within some marine reptiles.  (Etheridge 1965)). Remarks: Also termed postxiphisternal ribs, these are present posterior to the last presternal ribs and connected distally to the dorsal ribs in many instances. Alternatively, inscriptional ribs may occurs as "free" ribs, when not attaching to the dorsal ribs, such as in Chalarodon (Etheridge 1965). The latter condition is observed in many squamates and within rhynchocephalians (e.g. Sphenodon punctatus and Kallimodon pulchellus), but absent in observed specimens of pleurosaurs and Clevosaurus hudsoni) We only scored for mineralized inscriptional ribs, since cartilaginous ones may be incorrectly scored as absent in fossils.

Girdles
110. Scapula, posterior emargination: absent (0)/ present (1) (S18, Ch. 307) 111. Scapula, anterior emargination: absent (0)/ present (1) (E88, Ch. 111) Remarks: In squamates, the anterior margin is not truly emarginated. In most squamates the anterior margin is relatively straight or convex. Iguanians may bear a scapular ray (see above), but the margin to which it connects to is also straight. Some rhynchocephalians have a true emargination, with the anterior margin being concave anteriorly and is not homologous to the scapular "emargination" or fenestra to which the scapular ray contributes in some squamates.
119. Humeri, entepicondyle foramen: absent (0)/ opening dorsally only (1)/ opening ventrally only (2)/ fully open ventrally and dorsally (3) (S18, Ch. 341). Remarks: Most reptiles with an entepicondylar foramen display it on the dorsal surface of the distal end of the humerus, state "1". However, some sphenodontians develop this foramen ventrally only, and in sauropterygians and early reptiles there is a full opening connecting the dorsal and ventral sides of the humerus. The character states herein do not occur in conjunction, thus being mutually exclusive and being better coded as different character states within a single character instead of split into contingently coded characters. 120. Humeri, expanded radial condyle (= capitelum): present (0)/ absent (1) (S18, Ch. 344).
122. Radia, distal epiphysis, styloid process: absent (0)/ present (1) (G88a, Ch. 99; Fig. 9 in G88a). Remarks: Observable in ventral and medial aspect in articulation with the radiale. This feature may not be seen in fossil taxa with the epiphyses not preserved (in which case they are scored as missing data).
123. Ulnae, distal epiphysis, expansion: absent (0)/ present (1) (B85, Ch. X3; Fig. 9 in G88a). Remarks: A distally expanded or "ball-like" distal epiphysis of the ulna is observed within squamates. The presence of a proximal concavity on the ulnare of lizards is dependent upon the presence of a distal ball-like distal epiphysis of the ulna and the formation of a ball-socket articulation. Therefore, a character on the proximal concavity on the ulnare is not included in the present dataset.
125. Distal carpal 1: present (0)/ absent (1) (G88a, Ch. 103; Fig. 4c and d in G88a). Remarks: The element that partially occupies the position of the first distal carpal in lizards represents the medial centrale (Russell & Bauer 2008) [lateral central sensu (Romer 1956)], resulting from the fusion of the first carpal to the first metacarpal, and a slight shift in position of the medial centrale (Carroll 1977;Gauthier et al. 1988a). This fusion usually results in an enlarged epiphysis of the first metacarpal (which also occupies part of the position of the first carpal) followed by a reduced number of anterior carpal elements. Because the underlying developmental process of fusion, this cannot be assessed in the vast majority of sampled taxa, the wording of the present character reflects the absence of DC1 only. Nevertheless, among all taxa studied herein the absence of a distinct DC1 always seemed to reflect the fusion of the latter to the first metacarpal (by possessing an expanded proximal epiphysis on MC I) Therefore, all taxa scored with the absent condition herein are primarily homologous based on similarity, likely all due to the fusion of the DC1 to the first metacarpal.
128. Distal tarsal 4, proximal peg: present (0)/ absent (1) (Ev88, Ch. J1; Fig. 1.20 (Russell & Bauer 2008)) . Remarks: This proximal peg is better observed in ventral aspect on the tarsus of lizards in articulation with the astragalocalcaneum. The proximal peg is responsible for the mesotarsal articulation in lizards and is also observed in other reptilian groups. The presence of a distomesial articulatory surface on the astragalocalcaneum that articulates with this proximal peg is dependent upon this character, and therefore it is not included as a character here to avoid redundancy.