The influence of fossils in macroevolutionary analyses of 3D geometric morphometric data: A case study of galloanseran quadrates

In birds and other reptiles, the quadrate acts as a hinge between the lower jaw and the skull and plays an important role in avian cranial kinesis. Though previous studies have qualitatively described substantial variation in quadrate morphology among birds, none have attempted to quantify evolutionary changes in quadrate shape. Here, we investigate geometric evolution of the quadrate in Galloanserae, a major clade of extant birds uniting chicken‐like (Galliformes) and duck‐like (Anseriformes) fowl. We quantified morphological variation in the quadrate across 50 extant galloanseran species covering all major extant subclades using three‐dimensional geometric morphometrics, and performed ancestral shape reconstructions in the context of an up‐to‐date neornithine phylogeny. We find that our results based only on extant quadrates may overlook plesiomorphic features captured by fossil taxa, resulting in an ancestral state reconstruction for Galloanserae that is seemingly an approximation of the average shape of the extant data set. By contrast, analyses incorporating early fossil galloanseran quadrates (from taxa such as Asteriornis, Presbyornis, and Conflicto) result in ancestral geometric reconstructions more similar to the morphology of extant galliforms, indicating that the quadrate of the last common ancestor of galloanserans may have been more morphologically and functionally similar to those of extant galliforms than to extant anseriforms. These results generally corroborate previous inferences of galloanseran quadrate plesiomorphies and identify several additional plesiomorphic features of the galloanseran quadrate for the first time. Our results illustrate the importance of incorporating fossil taxa into ancestral shape reconstructions and help elucidate important aspects of the morphology and function of the avian feeding apparatus early in crown bird evolutionary history.


| INTRODUCTION
In birds, the skull comprises four major individual elements: the upper jaw, the braincase, the jugal bar and its suspension system, and the lower jaw ( Figure 1). The quadrate plays a key role in connecting the lower jaw and cranium in birds and other reptiles (Bühler, 1981;Palci et al., 2020). It also connects the bony palate (via the pterygoid) and jugal bars (through the quadratojugal) to the rest of the skull, playing a key role in avian cranial kinesis (Bailleul et al., 2017;Bock, 1964;Bühler, 1981;Dawson et al., 2011). The quadrate drives elevation of the upper jaw when it is pulled rostrally by the pterygoideus musculature, by transferring forces through two sets of pushrods (the pterygoid-palatine complex and the jugal bars) to the rostrum (Kaiser, 2010). Furthermore, the quadrate provides sites of attachment for key muscles involved in movement of both the upper and lower jawbones (Bühler, 1981). Avian quadrates exhibit complex morphological variation, and although this variation has been systematically investigated at a broad level (Samejima & Otsuka, 1987), it has been overlooked for several decades and has never been explored quantitatively.
The quadrates of galloanseran birds (Neognathae: Galloanserae) -the major neornithine subclade uniting Galliformes (chicken-like birds) and Anseriformes (duck-like birds)-have been examined in several previous studies. For example, Livezey and Zusi (2007) compiled 54 discrete quadrate characters for a broad-scale analysis of avian phylogeny, and listed two apomorphic galloanseran features: a caudolaterally positioned quadratojugal cotyle relative to the lateral condyle, and a pedunculate otic capitulum. Elzanowski and Stidham (2010) identified several additional features, such as the shape of certain muscle attachments, the presence of caudomedial pneumatic foramina, and the shape of the mandibular process, as synapomorphies of Galloanserae, Galliformes, or Anseriformes. For instance, all galloanseran quadrates exhibit an orbital crest and a subcapitular tubercle that serve as muscle attachments, a compact and bicondylar mandibular process, and a wide orbitocondylar angle.
Galliform quadrates exhibit a linear orbital crest, an obtuse orbital angle, and a wide intercondylar sulcus on the mandibular process.
Anseriform quadrates exhibit a U-or V-shaped orbital crest and a distinct caudomedial foramen. However, despite the detailed galloanseran quadrate descriptions and novel quadrate characters identified in that study, a number of notable continuous characters of galloanseran quadrates have yet to be investigated, such as the shape of muscle attachments and articulations with neighboring bones, suggesting that additional insights into macroevolutionary changes in galloanseran quadrate morphology remain to be discovered. Moreover, the recent discovery of exceptional new Late Cretaceous pangalloanseran fossils, such as Asteriornis maastrichtensis and Conflicto antarcticus, affords an unprecedented opportunity to investigate the plesiomorphic condition of galloanseran cranial morphology. In its original description, the skull of A. maastrichtensis was found to share several features with extant galliforms and anseriforms, including features of its quadrate, which is almost compete and threedimensionally preserved (Figure 2; Field et al., 2020). In light of its hypothesized phylogenetic position close to the divergence between total-clade Galliformes and total-clade Anseriformes, Asteriornis has exceptional potential to illuminate the ancestral morphology of the galloanseran quadrate and clarify questions surrounding character polarity arising from previous comparative investigations of the avian quadrate.
We provide a landmark scheme for quantifying interspecific morphological variation of the galloanseran quadrate, enabling the first three-dimensional quantitative analysis of avian quadrate F I G U R E 1 The skull of Alectura lathami (NHMUK S 2010.1.31) in lateral (a) and ventral view (b), and its quadrate in rostral, lateral dorsal, caudal, medial, and ventral view (c). Quadrate is highlighted in light blue in (a) and (b). Scale bar in (a) and (b): 5 mm, and in (c): 2.5 mm. morphology. We investigate the three-dimensional evolution of the galloanseran quadrate in light of an up-to-date understanding of avian phylogeny, and use ancestral state methods to infer quadrate morphology of the last common ancestor of Galloanserae. This approach enables comparisons with geometric morphometric data from the quadrates of Late Cretaceous crownward stem birds such as Ichthyornis, and early fossil representatives of total-clade Galloanserae such as Asteriornis (Field et al., 2020), Presbyornis (Elzanowski & Stidham, 2010), and Conflicto (Tambussi et al., 2019), yielding novel insight into the ancestral condition of the crown bird quadrate.

| Landmarks & curve semilandmarks
Nine point-landmarks, 10 series of curve semilandmarks and 6 patches of surface semilandmarks (Supporting Information: Figure S1) were used to quantify quadrate shape variation using (1) articulations between neighboring bones; (2) the positions of muscle attachments; and (3) the overall shape of the bone. Details of our landmarking scheme and character descriptions are available in F I G U R E 2 Right quadrate of Asteriornis maastrichtensis (NHMM 2013 008) in rostral, rostrolateral, lateral, caudal, medial, dorsal, and ventral views.
Supporting Information material. All landmarking was performed in Avizo. Curve semilandmark series were initially placed with arbitrary numbers of points on each specimen, and then resampled to equal counts of evenly-spaced points before analysis using the digit.curves function of Geomorph 4.04, in R 4.0.3 (see Bjarnason & Benson, 2021).
Some characters, such as the orbital process and the surface of the subcapitular tubercle, were excluded from our analyses of fossil taxa due to incompleteness of the fossil material.

| Surface semilandmarks
For positioning surface semilandmarks, we followed the scheme of Schlager (2019) and Bardua et al. (2019). We manually placed surface semilandmarks on the surfaces of interest of a Smew (Mergellus albellus, UMZC 210.B) in Avizo. These semilandmarks were then used as a template to project surface semilandmarks onto other specimens in R. UMZC 210.B was selected using the "findMeanSpec" function in the Geomorph package (Adams et al., 2022) using our matrix of landmarks and curve semilandmarks to identify the specimen in our sample closest to the average geometric shape of all specimens in our sample. Surface semilandmarks and the mesh (in.ply file format) were imported into R, and landmarks were placed on the model using the "createAtlas" function in the Morpho package (Schlager, 2017) to create an atlas to patch (or project) each surface semilandmark onto each specimen in our data set for the next step.
There are two ways to create an atlas for patching: one way is to use the neighboring curve semilandmarks to fix surface semilandmarks during patching on other specimens; the other is to use all landmarks to fasten the position of surface semilandmarks with other specimens during the projection. Initially, we projected every surface semilandmark using the first method on different specimens using the "placePatch" function in the Morpho package, and the value for the parameter "inflate" was set to 0. If the projected semilandmarks on the target specimen were randomly scattered or misaligned with the curve semilandmarks, we adjusted the "inflate" parameter by increasing or decreasing its value until all semilandmarks were placed on the target surface. For bones with thin walls, like bird quadrates, projected surface semilandmarks may often be placed underneath the bone's surface because the projection algorithm can misidentify the surface of internal bone structure as being the external surface of the bone. To prevent this, we digitally filled the empty cavities within each quadrate in Avizo to properly patch semilandmarks on the targeted specimens. In instances where projected surface semilandmarks remained oddly positioned or misaligned, we generated an atlas using the second method described above, and then projected surface semilandmarks into their optimal positions. Before performing generalized procrustes analysis, we ran the "slider3d" function in the package Morpho to slide all surface semilandmarks to their biologically or structurally optimal positions (Bardua et al., 2019;Schlager, 2019).
Our landmark configurations (9 landmarks, 445 curve semilandmarks in 10 series, and 592 surface semilandmarks in 6 patches) were incorporated into our generalized procrustes analysis using the "gpagen" function, and the covariance matrix of Procrustes coordinates was subjected to principal component analysis (PCA) using the "plotTangentSpace" function in the Geomorph R package to visualize geometric variation within our sample. All series of curve semilandmarks and all patches of surface semilandmarks in our generalized procrustes analysis were slid using minimum bending energy as our optimality criterion.

| Phylogeny and ancestral shape reconstruction
To visualize the evolution of galloanseran quadrate geometry, we extracted the Galliformes tree from Kimball et al. (2021) and linked it with the Anseriformes tree of Liu et al. (2014) to generate a phylogenetic backbone. We adjusted the timescale of the tree in R using the package paleotree (Bapst, 2012), using divergence times based on published molecular clock studies and the ages of key fossils (Buchheim et al., 2011;Elzanowski & Stidham, 2010;Field et al., 2020;Prum et al., 2015;Tambussi et al., 2019). Any remaining uncalibrated nodes were adjusted with the "timePaleoPhy" function in paleotree (Bapst, 2012), using the "equal" time-scaling method.
When fossil taxa were added into our data set, four alternative phylogenetic scenarios were tested for Asteriornis and Presbyornis: Asteriornis as either the sister group of all Galloanserae or the sister group of all extant Galliformes (Field et al., 2020), and Presbyornis as either the sister group of all Anseriformes or the sister group of all extant Anatidae (Clarke et al., 2005;Elzanowski, 2013;Elzanowski & Stidham, 2010;Ericson, 1997;Field et al., 2020;Tambussi et al., 2019).
In our ancestral state reconstruction using fossils, Asteriornis was placed as the sister group of crown Galloanserae, and Presbyornis as the sister group of crown Anseriformes.
We used the "gm.prcomp" function in Geomorph to plot a phylomophospace, allowing us to visually illustrate reconstructed ancestral states in morphospace. To build a three-dimensional reconstruction of the ancestral galloanseran quadrate, we calculated the Procrustes distance (PD) from the estimated ancestral state to our samples, and the quadrate of the Maleo (M. maleo, UMZC 14/ Meg/5/a/3) and the Orange-footed Scrubfowl (Megapodius reinwardt, UMZC 14/Meg/6/h/2) were chosen as starting points due to their proximity to our estimates of the galloanseran ancestral condition excluding and including fossils, respectively (Supporting Information: Table S2). We warped these two quadrate models into the mean shape of our data set using the "warpRefMesh" function, and then used this average mesh as a starting point for reconstructing the ancestral galloanseran quadrate using the "plotRefToTarget" function. This three-dimensional reconstruction was compared with extant and extinct galloanseran quadrates, including the recently published early anseriforms Anachronornis anhimops and Danielsavis nazensis (Houde et al., 2023), two previously published specimens of putative stem galloanseran quadrates (Elzanowski & Boles, 2012;Elzanowski & Stidham, 2011), the pelagornithid Dasornis toliapica (see   Figure S11A-B), and all additional PC axes each explained less than 5% of the total variance in our data set. The shape variance described by our first four PC axes was visualized by warping quadrate models to 95% of the maximum and minimum values of each axis using the "shape.predictor" function in Geomorpho 4.04 (Supporting Information: Figure S13; Fabre et al., 2020).

| Phylomorphospace and ancestral state reconstruction
By inferring the most likely morphology of the ancestral galloanseran quadrate using our updated phylogeny (excluding any extinct galloanseran quadrates), we found that our estimate of the ancestral galloanseran quadrate is most similar to another representative of Megapodiidae (Macrocephalon maleo; PD from ancestral quadrate shape = 0.0995; Ancestral state 1 of Supporting Information:  F I G U R E 6 Three-dimensional reconstruction (a) and its landmark constellations (b) of the ancestral crown galloanseran quadrate generated from analyses incorporating three early fossil total-group galloanserans (Asteriornis, Conflicto, and Presbyornis) in rostral, rostrolateral, lateral, caudal, medial, dorsal, and ventral views. The above-mentioned morphological similarities between our reconstructed ancestral crown galloanseran quadrate (Model II), the previously published Lance and Tingamarra stem galloanseran quadrates, and the newly described stem anseriform quadrates of Anachronornis and Danielsavis help corroborate the reliability of Model II, even though these four stem galloanseran quadrates were not included in our geometric data set.
In addition to well-established total-clade galloanseran fossils (Asteriornis, Presbyornis, and Conflicto), we also investigated the quadrate of Dasornis toliapica, an early representative of the extinct clade Pelagornithidae, which has often been thought to be closely allied with, or positioned within, Galloanserae (Bourdon, 2005;Mayr, 2011), mostly on the basis of basicranial similarities. We found that the quadrate of Dasornis differs markedly from both of our ancestral models of galloanseran quadrate morphology, as well as the morphology of any known total-clade galloanserans. For example, the affinities . Alternatively, if pelagornithids are total-group galloanserans, their unique quadrate features may represent adaptations for a biomechanical function unobserved in any other known galloanserans, such as skim-feeding (Mayr & Rubilar-Rogers, 2010). Further research on pelagornithid anatomy and functional morphology will be required to delineate between these alternative hypotheses.
Beyond the extinct Galloanserae and bizarre Pelagornithidae, we also compared our reconstructed models with the quadrates of palaeognaths, the sister group to all other crown birds (Figure 7). For example, the intercapitular incisure (the groove between the two capitula on the otic process) is absent or underdeveloped in Palaeognathae, but it is obvious in both of our reconstructed models of the ancestral crown galloanseran quadrate (Figure 7, dorsal view).
However, the quadratojugal cotyle of the tinamou quadrate is similar to that in Phasianidae in that the ventral and dorsal margins of the quadratojugal cotyle vanish (Figure 7, lateral view; Supporting Information: Figure S21). Though the pterygoid condyle is rostrally blunt in most Palaeognathae, similar to that of Model II, it apparently has a greater range of morphological disparity than is seen in any

Regardless of the phylogenetic position of Asteriornis or
Presbyornis (see Section 2), the ancestral state of the galloanseran quadrate is inferred to be similar-both geometrically and in terms of discrete characters-to that of extant Galliformes (Figure 4b). For instance, the quadratojugal cotyle is rounded with a relatively deep fossa, similar to the condition observed in Megapodiidae (Supporting Information: Figure S17A). The pterygoid condyle in our ancestral quadrate reconstructions, which exhibits a triangular outline, is much like that of some Galliformes, such as many representatives of Phasianidae. The mandibular process on our reconstructed models has two condyles with relatively flat articular surfaces, especially the lateral condyle, similar to the condition in Megapodiidae (Galliformes), but unlike that of crown Anseriformes.
Finally, the subcapitular tubercle of our ancestral quadrate reconstructions is elliptical in shape, which is similar to the condition in most of Galliformes. On the basis of overall geometry and discrete characters, we infer that the quadrate of the last common ancestor of Galloanserae was generally morphologically and biomechanically similar to that of Galliformes, especially Megapodiidae.
The orbital process of galliform quadrates is relatively elongate and slender, with a rounded or pointed tip. The orbital crest is a linear ridge running ventral to the orbital process, the subcapitular tubercle retains a plesiomorphic mound-like shape, and the squamosal facet is diamond-or square-shaped, with a convex profile along the lateralmedial axis. Based on our geometric morphospace, galliform quadrate geometry can be separated into three distinct groups: Megapodiidae, Cracidae, and "other Galliformes" (uniting Numididae, Odontophoridae, and Phasianidae; Figure 3a,b and Supporting Information: Figure S12A-B). Each group has distinctive quadrate features; for instance, in Megapodiidae, the pterygoid condyle protrudes relatively far, and the medial condyle is unexpanded caudally (Supporting Information: Figure S18). In Cracidae, the orbital process has a flat tip and the submeatic prominence arises from the caudal side of the quadratojugal cotyle (Supporting Information: Figure S19).
This attachment can also be found in most Anseriformes (except for Anseranas, see in Supporting Information: Figure S27), but its shape differs from the condition in Cracidae. In other Galliformes, the dorsal and ventral margins of the quadratojugal cotyle vanish, making the quadratojugal cotyle saddle-like (except in at least some odontophorids such as Colinus and Odontophorus) (Supporting Information: Figure S21). In many galliforms, especially phasianids, the otic capitulum becomes relatively small, and it even disappears in some  Alternatively, if Presbyornis is a crown anseriform and the sister group of Anatidae, as hypothesized by previous studies (Clarke et al., 2005;Dyke, 2001;Ericson, 1997), its galliform-like quadrate must have evolved independently: once among stem galloanserans, with the plesiomorphic condition inherited by galliforms and the Paleocene stem anseriform Conflicto, and convergently in the early Eocene Presbyornis.
We view this latter scenario as doubtful, and believe quadrate morphology supports the hypothesis that Presbyornis is a stem anseriform.
The quadrate of crown anseriforms exhibits a unique suite of characters including the presence of a robust orbital process, a platform-like subcapitular tubercle, a submeatic prominence attached to the dorsocaudal side of the quadratojugal cotyle, and a bulging lateral condyle (Supporting Information: Figure S25). Additionally, the primary anseriform subclades (Anhimidae, Anseranas, and Anatidae) can be clearly distinguished on the basis of quadrate morphology: Anhimidae occupies the negative sides of PC1 and PC2 in our galloanseran quadrate morphospace, and the positive side of PC3, whereas Anatidae occupy the positive side of PC1 and are widely distributed across PC2 and PC3 (Figure 3a,b and Supporting Information: Figure S12A). Anseranas sits on the positive side of PC1 and the negative side of PC2 and PC3. In Anhimidae, several autapomorphies are evident, such as a medially facing otic capitulum, a relatively narrow quadrate body (compared with other Anseriformes), and a protruding submeatic prominence (Supporting Information: Figure S26). Anseranas, the sole extant representative of Anseranatidae, lies close to Anatidae in morphospace, yet its quadrate morphology differs from that of Anatidae in three clear ways (Supporting Information: Figure S27): the submeatic prominence, which is a folded structure attached to the dorsocaudal side of the quadratojugal cotyle in Anatidae, is absent in Anseranas. Also, the lateral condyle of Anseranas is situated more laterally than that of Anatidae, and the caudomedial pneumatic foramen faces caudally on the Anseranas quadrate, while in Anatidae, it generally faces medially (except in Malacorhynchus where it faces caudally, as in Anseranas; Supporting Information: Figure S28).

| Limits to our ancestral state reconstructions and future work
We quantified morphological variation of the crown galloanseran quadrate and inferred the ancestral quadrate shape for this clade.
Nevertheless, current approaches to geometric morphometric analyses exhibit some shortcomings with respect to quantifying morpho- This issue will complicate homology assessments in future efforts to incorporate galloanserans as well as other crown birds into a unified geometric morphometric analysis, as features such as the orbital crest and subcapitular tubercle are thought to be autapomorphies of Galloanserae. As such, there will always remain a need to combine insights from geometric morphometric analyses with qualitative descriptive approaches when investigating morphological evolution across a broad and structurally disparate taxonomic group. Two anatomical structures of the quadrate that presented practical challenges with respect to inclusion in our geometric data set were the orbital crest and pneumatic foramina. Galliformes and Anseriformes exhibit divergent morphologies of the orbital crest: it is linear in Galliformes, while in Anseriformes, the orbital crest is V-or U-shaped. The orbital crest in Anseriformes might be homologous with that of Galliformes, but its dorsal portion is absent in all galliforms. Hence, we only quantified the ventral portion of this feature with two landmarks: the apex of the orbital crest and its dorsal-most point. Due to their variable position among galloanserans and their absence in some subclades (Supporting Information: preservation forced us to exclude some quadrate features from our geometric analyses with fossils, such as the orbital process and the surface of the subcapitular tubercle. These characters exhibit considerable morphological variation among Galloanserae, and as such their removal may influence our inferences of the ancestral galloanseran quadrate, although we expect this influence to be relatively minor.
In the future, it will be productive to apply a modified version of our landmark scheme across the avian crown group to draw justified inferences about the ancestral condition of the crown bird quadrate, and to trace evolutionary patterns in quadrate morphology throughout crown bird evolutionary history. The quadrate plays a key role in avian cranial kinesis; thus, clarifying its evolutionary history will also shed light on biomechanical evolution of the avian feeding apparatus.

AUTHOR CONTRIBUTIONS
Pei-Chen Kuo and Daniel J.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are openly available in MorphoSource at https://www.morphosource.org/projects/ 000508434, reference number 000508434. All data are presented in the Supplementary Information. 3D data will be made openly accessible from MorphoSource upon manuscript acceptance.