An integrative insight into the synsacral canal of fossil and extant Antarctic penguins

The lumbosacral-canal system in birds most likely operates as a sense organ involved in the control of balanced walking and perching, but our knowledge of it is superﬁcial. Penguins constitute interesting objects for the study of this system due to their upright walking, but only the Humboldt penguin, Spheniscus humboldti , and some incomplete fossil penguin synsacra have been studied in this respect. Here, we give an integrative comparative insight into the synsacral canal of extant Emperor penguin, Aptenodytes forsteri , Adelie penguin, Pygoscelis adeliae , and Eocene giant Anthropornis and/or Palaeeudyptes Antarctic penguins, using computed tomography imaging and associated data-extraction methodologies, complemented by analytical approaches ranging from geometric morphometrics to modularity, curvature, and wavelet analyses. We document that the variability in the number of synsacro-lumbar vertebrae is evolutionarily conserved, and all studied synsacra possess osteological correlates of the lumbosacral-canal system. We also found that Eocene and extant Antarctic penguins were separable on the basis of the main direction of the shape-related (size-independent) variability within said system, and A. forsteri was unique in the entire studied set in terms of the relative cranial shift of this compound structure. Moreover, we suggest that the evolutionary processes, shaping both the terrestrial posture and gait, were responsible, in extant penguins, for the increased simplicity and stability of the synsacral canal cross-sectional periodic patterns, as well as pave the way for the lumbosacral-canal system modularity characterized by reduced atomization/complexity.


INTRODUCTION
The axial skeleton in vertebrate animals comprises the vertebral or spinal column, which in most amniotes, including birds, is usually divided into cervical, dorsal Correspondence: Thomas Mörs, Department of Palaeobiology, Swedish Museum of Natural History, P.O.Box 50007, SE 10405 Stockholm, Sweden.Email: thomas.moers@nrm.se(thoracic), lumbar, sacral, and caudal regions (e.g.Bui & Larsson 2021).In mature birds, all but cervical series can contribute to the synsacrum, a rigid segment consisting of fused vertebrae.However, the bulk of this bone is formed by the lumbar and sacral elements (Baumel & Witmer 1993).The total number of vertebrae involved varies between 10 and 23 (Lovette & Fitzpatrick 2016;Morrison et al. 2018); it is often species specific and also age dependent (Baumel & Witmer 1993;Kaiser 2007;Jadwiszczak & Mörs 2011).The synsacrum is either ankylosed or firmly attached to the pelvic girdle, constituting the median part of the pelvis (Baumel & Witmer 1993).Hence, it supports the body weight, is crucial for transmitting power from the hind limbs to the rest of the body (Nickel et al. 2004), and stabilizes the trunk during flight (Morrison et al. 2018).The synsacrum also encloses the spinal cord and participates in the protection of kidneys and some important blood vessels.These functions become apparent upon even a cursory examination of textbooks on avian anatomy (e.g.Nickel et al. 2004, to name one).However, the bearing of this composite bone on bird biology may go much further, involving sensory abilities.Kaiser (2007, p. 74) termed the broadly construed sacral portion of the spine as "the centre of pedestrian locomotion in birds," and it appears to be true in more ways than one usually assumes.The synsacral canal shows, along its enlarged lumbar and sacral portions, segmentally arranged canal-like bony structures (lumbosacral canals of Necker (1999)).These transversely running semicircular indentations of the main canal wall are bilaterally paired and represent the dorsolateral zones of fusion between the respective vertebrae.The immense selection of the relevant longitudinal sections was documented by Jelgersma (1951).Importantly, also the length of the spinal cord passing through the lumbar and sacral segments of the synsacral canal has its peculiarities.The cord is enlarged there and its dorsal surface shows an elongated cleft (lumbosacral or rhomboid sinus) accommodating a unique ovaloid gelatinous object, the so-called glycogen body.Its role remains not well understood (Scanes & Dridi 2022).The aforementioned lumbosacral canals protect and shape the "true" canals (Necker 2006), which are created by meninges.The latter open up above the accessory lobes of the spinal cord (structures with mechanoreceptive capability), enabling the flow of the cerebrospinal fluid within the enlarged subarachnoid space (Necker 2005, fig. 3).A craniocaudal fluid flow is also possible, and the whole system was hypothesized to function as a sense organ involved in the control of balanced walking (Necker 2005(Necker , 2006)).The oldest hard-tissue correlate of such an anatomical specialization was reported in some Cretaceous birds (O'Connor & Forster 2010).This idea has been already acknowledged, among others, in highly influential textbooks (Morrison et al. 2018;Scanes & Dridi 2022), and further explored and refined in a number of papers (e.g.Urbina-Meléndez et al. 2018;Stanchak et al. 2020).The results reported in said publications suggest that it would be legitimate to describe the structure in question using more general terminology, for example, as an extralabyrinthine sense organ of equilibrium, so that perching is also covered.Actually, as advocated by Urbina-Meléndez et al. (2018): "[in birds] hip-localized balance sense is likely relevant to all hindlimb-mediated behaviors." Considering penguins (Aves: Sphenisciformes), due to their exclusively amphibious locomotion, the terrestrial component of which constitutes "a prominent feature of their reproductive success" (Kurz et al. 2008, p. 273), they constitute interesting objects to study the lumbosacral system or its osteological correlates, especially, taking into account the dominant, scientifically grounded based on anatomical and neurophysiological evidence, view that aforesaid system functions as an actual organ in birds, and its components have also been described in Sphenisciformes.According to our knowledge, the only presentday species included in such analyses was the Humboldt penguin, Spheniscus humboldti Meyen, 1834 (see Necker 2006;Stanchak et al. 2020).Its breeding range is mostly limited to the western coast of South America, and it is also commonly kept in zoological gardens.Necker (2006) described the lumbosacral canals in S. humboldti as shallow, just like in cormorants and swifts.The only research on the lumbosacral system in fossil penguins was carried out by Jadwiszczak (2014).This very limited and purely visual study was based on 2 substantially damaged, hence showing some relevant internal features, specimens from the Eocene (56.0-33.9Ma) of Seymour Island (Antarctic Peninsula).Jadwiszczak (2014, p. 37) concluded that the "alleged" lumbosacral organ "gained its current penguin configuration by the late Eocene."The assemblage of early Sphenisciformes from Seymour Island comprises a single Paleocene (66.0-56.0Ma) and at least 11 Eocene species (e.g.Acosta Hospitaleche et al. 2019;Jadwiszczak et al. 2021).The vast majority of specimens is represented by single, isolated, and incomplete bones; synsacra are very rare.Most of these bones are assignable to the skeletons of large to very large-sized penguins, and 4 Eocene species were termed "giant" (for a review, see Acosta Hospitaleche et al. 2019, and references therein).
The objective of our study is to give an integrative comparative insight into the synsacral canal of Eocene and extant Antarctic penguins, with special emphasis on its lumbosacral segment.To achieve our goal in a nondestructive way, we took advantage of the computed tomography (CT) imaging and associated preprocessing and data-extraction methodologies.These were complemented by an array of analytical approaches ranging from the relatively widely known geometric morphometrics (GMM) to the more exotic, at least for most biologists, wavelet analysis.

Study subjects
All fossil material studied in this paper (5 synsacra; Fig. 1c-g) derives from late Eocene (Priabonian) shallow marine, coastal deposits, exposed on Seymour Island east off the Antarctic Peninsula.NRM-PZ A9 ("sacrum no. 3" in Wiman 1905;?Palaeeudyptes sp. in Jadwiszczak & Mörs 2011) had been collected by the Swedish South Polar Expedition in 1901-1903 at the Swedish locality no.11 (Acosta Hospitaleche et al. 2017).From the same fossiliferous horizon that is very rich in penguin bones, exposed on a plateau below and southeast of the Argentinian Marambio Base, NRM-PZ A1006 and NRM-PZ A1008 have been collected by Thomas Mörs at the "Whale Site" and at the "Site at the Lake" (Jadwiszczak & Mörs 2019) wiszczak & Mörs 2016wiszczak & Mörs , 2021)), situated in the steep slope southeast of the Marambio Base, above the beforementioned plateau.Nevertheless, all sites expose the middle part of the Submeseta Formation (Submeseta II = level 38; Montes et al. 2013), or Telm 7 of Sadler (1988).All specimens are housed in the paleozoological collections of the Naturhistoriska riksmuseet (Stockholm, Sweden).

CT data acquisition and processing
All studied specimens were subjected to CT scanning at the Karolinska University Hospital, Huddinge (Sweden), using Siemens Somatom Definition Flash (Siemens Healthcare, Forchheim, Germany).Resulting tomograms, 2D images representing slices through 3D objects, were processed by means of 3D Slicer (www.slicer.org;Fedorov et al. 2012).This procedure was fo-cused on the synsacral canal and comprised segmentation (isolation), cross-sectional area calculation, and digital endocast creation (Fig. 2a-c).To prepare 3D renders of whole bones (Fig. 1), the Pixologic ZBrush 3D sculpting software (pixologic.com; a licensed copy) was utilized.For more details, see Supporting Information.

Analysis of the cross-sectional area variation in the synsacral canal
Since the synsacral canal is by no means a uniformly developed structure, the analysis of its transverse area variation (the signal) has a potential to reveal the general patterns and, what is even more important, to detect possible localized features.The canal is inherently modular, so the most obvious pattern would be likely related to periodicity.Our approach was to treat each series of the calculated cross-sectional areas as a time series, time being substituted by a spatial dimension (location along the main axis; Fig. 2c), and to employ the continuous wavelet transform (CWT) for the periodicity-focused investigations.We decided upon a commonly used Morlet wavelet-a sinusoid modulated by a Gaussian envelope or window, very useful in the analyses of transient signals (e.g.Shyu & Sun 2002).
The analysis is basically a pattern-matching exercise, where one aims at determining the similarity between a studied noisy signal, endowed with wave-like properties, and a wavelet (a "small wave").One can also say that the signal is filtered by the wavelet.The area oscillation-like changes along the canal length (our signal) make up a fixed pattern, whereas the wavelet undergoes continuous modifications-it is translated (shifted along the signal) and dilated (stretched or compressed).However, during a single pass along the signal, the wavelet maintains a constant dilation.As a result, the transform will capture information about the signal in terms of both the location along the studied structure and frequency of cross-sectional area change (Fig. 2c).We recommend an excellent animation of the process available at the Wikimedia Commons (Bertolotti 2022).
The output from the above pattern matching can be presented in a graphical form, as a function of the spatial dimension and period (1/frequency).Interpretations of power-spectrum patterns are provided in Fig. S1, Supporting Information (upper left inset).The Morlet wavelet transform (MWT) was obtained using R environment (version 4.1.1,R Core Team 2021), with 2 additional libraries, "WaveletComp" (Roesch &  Schmidbauer 2018) and "EMD" (Kim & Oh 2009).For computational details, see Supporting Information.For an approachable introduction to CWT, see works by Addison (2017Addison ( , 2018)), and Torrence and Compo (1998).

Analysis of shape variation of the lumbosacral canal system
The nouns shape and form are used interchangeably on a daily basis, but they are not considered synonyms in GMM.This distinction is essential for our analyses.Within the GMM, shape is defined as the geometric information about a landmark configuration (or outline of an object) remaining after location, scale, and rotational effects are rooted out (Zelditch et al. 2012;Dryden & Mardia 2016), which is in the spirit of Kendall's (1977) influential "interim report."In GMM, relevant shapepreserving transformations are usually accomplished via the Generalized Procrustes Analysis (GPA).
In order to study the shape variation of the lumbosacral-canal system, we decided to use a landmarkbased approach.Forty three-dimensional landmarks, one set per each synsacral-canal endocast (6 of them were complete enough), were manually placed on the surface model and digitized using 3D Slicer functionality.Their locations were chosen to provide parsimonious (by extension, robust), though adequate, and consistent coverage of the morphology of the investigated structure (Fig. 2d).
The landmark coordinates were imported to R environment and the "geomorph" library (Baken et al. 2021) was utilized for succedent data processing via GPA as well as further computations and visualizations.Since we were here interested in "pure" shape variation, we had to account for both the isometric (obtainable via "full" GPA) and allometric scaling.The latter can be achieved by means of several approaches (for a review, see Klingenberg 2016) and we decided to use 2 of them, in parallel.
The first way was based on supplementing (or augmenting) Procrustes shape variables with another variable-a natural logarithm of the centroid size (lnCS; Mitteroecker et al. 2004Mitteroecker et al. , 2013; Klingenberg 2016)effectively changing our perspective into that involving the size-shape (form or Procrustes form) space (Mitteroecker et al. 2013;Klingenberg 2016).This was followed by the principal component analysis (PCA) on the augmented dataset.PCA score plots were enriched with thin plate spline (TPS) deformations (their location and extent) between a mean shape (as a reference shape) and shapes predicted for extremes of computed principal components.A highly readable account of TPS is that by MacLeod (2010).Shape deformations were also visualized directly between extremes of computed principal components-predicted landmarks of both the target (max) and the reference (min) were superposed.
The second approach (Sidlauskas et al. 2011;Klingenberg 2016) involved a (multivariate) regression of shape on size (lnCS).This procedure is in line with a view that allometry is the covariation of shape with size.Isometry has been already removed during GPA.The regression was followed by PCA on residuals.For more explanations and computational details, see Supporting Information.

Curvature analysis of lumbosacral canals
The curvatures for the 4 central pairs of the lumbosacral canals were calculated as Menger curvatures of triples of points in Euclidean space (Menger 1930;Léger 1999), and averaged for each pair.Both, the raw and Procrustes-fitted 3D landmark coordinates were utilized.Such computations, accomplished via simple arithmetic in R, involved the area and side lengths of the triangle formed on the Euclidean plane spanned by the relevant landmarks.This is equivalent to the reciprocal of the radius (1/R) of the circumcircle through these 3 points (Fig. 2d).

Overall visual morphological assessment
All 5 fossil synsacra included into our study are clearly more massive, than those assignable to the present-day penguins (Fig. 1).Both modern bones comprise 13 fused vertebrae, whereas the counts for their Eocene counterparts differ.The most complete specimens from the latter group have 13 (NRM-PZ A1005) and 14 (NRM-PZ A1008) vertebrae.All but one (NRM-PZ A1006) bones studied possess preserved synsacrolumbar and sacral segments.The former comprises either 2 (NRM-PZ A1005) or 3 (A.forsteri, P. adeliae, NRM-PZ A9, and NRM-PZ A1008; most likely also NRM-PZ A632) vertebrae.Expectedly, sacral series in our specimens assignable to A. forsteri and P. adeliae consists of 2 vertebrae.Considering fossil synsacra, NRM-PZ A1005 and NRM-PZ A1008 definitely have 2 sacral vertebrae; this is most probably also true for NRM-PZ A632.NRM-PZ A9 lacks the portion caudal to the second sacral vertebra, and NRM-PZ A1006 is even more incomplete.
The main synsacral canals have, as evidenced by their endocasts, noticeable systems of the lumbosacral transverse canals (Fig. 1).They are especially pronounced within the length of the central enlargement.Two approximately midmost pairs of such canals are clearly distinguished by a strongly marked (between their levels) axial dorsal ridge of the endocast.In A. forsteri, P. adeliae, NRM-PZ A9, and NRM-PZ A1008, this length of the ridge is not only high, but also conspicuously wide.In all but one studied specimens, the boundary between the synsacro-lumbar and sacral series appears to coincide with the pair immediately caudal to the aforementioned midmost ones (Fig. 1).The exception hinted above is A. forsteri, with the above-mentioned border shifted caudally by one vertebral unit.

Analysis of the cross-sectional area variation in the synsacral canal
All power spectra resulting from the wavelet transform turned out to possess bands of statistically significant (at α = 0.05) levels, as compared to both the white and red noise, with marked power ridges or local maxima (Fig. S1, Supporting Information).A distribution of such regions in individual plots is not perfectly consistent within the studied set of specimens.Nevertheless, there is a conspicuous tendency of said distinct patches (especially their main power ridges) to be centered at the span of CT-scan locations corresponding to the enlargement of the synsacral canal (Fig. S1, Supporting Information; compare area fluctuations and corresponding power spectra).On the other hand, counts of ridges differ among specimens-there is a single one in present-day specimens (Fig. S1c,e, Supporting Information), and 2 or more in fossil specimens (Fig. S1b,d,f-h, Supporting Information).The ridges in the latter group extensively superpose one another (horizontally), within significance boundaries, in NRM-PZ A1008 (Fig. S1f, Supporting Information) and NRM-PZ A632 (Fig. S1h, Supporting Information).They only partially overlap in NRM-PZ A1005, and at least partially overlap in the incomplete NRM-PZ A1006.In the case of NRM-PZ A9, the main statistically significant ridge overlaps another, which is either within significance boundaries (white-noise context) or outside such boundaries (red-noise context) (Fig. S1g, Supporting Information).Considering the synsacral enlargement scope, the most stable power ridges (small variability, no apparent trend) are those in the 2 presentday specimens (Fig. S1c,e, Supporting Information).

Analysis of shape variation of the lumbosacral canal system
The size-shape PCA has expectedly revealed that size (lnCS) of the lumbosacral-canal system overwhelmingly dominated the main direction of variance (PC1) within a data set (Fig. 3a).Its contribution to PC1 amounts to 94%, and PC1 itself explains ∼97% of total variance.The studied system is clearly smaller in P. adeliae than its counterparts in other studied specimens (Fig. 3a,b).It is the largest in A632, closely followed by that in A1005.The ordinations along other PCs are effectively size independent (Fig. 3a).
Considering PC2, which explains ∼48% of shaperelated variance (or 1.3% of total variance), there are several patterns of shape change observable when moving from negative to positive values (Fig. 3c; Figs S2a,S3, Supporting Information).The one with the greatest reach is a relative lateral widening of the lumbosacral system touching the caudal two-thirds of its units.In the case of the second-caudalmost pair of lumbosacral canals, the outward expansion touches all its parts, also including a dorsal midline area (i.e. the whole unit).The midline area is also elevated in the third-caudalmost unit.Two caudalmost units incline toward each other, effectively reducing distance between their dorsal parts.The cranialmost unit is subject to forward rotation (up to ∼20 degrees).Two consecutive units become shallower, the first of them also inclined cranially.In terms of individual contributions to PC2, they are dominated by A. forsteri, whereas P. adeliae is the least influential one.The overall ordination along this axis highlights the contrast between A1008 + A9 and A. forsteri, leaving remaining specimens clustered close to the mean-shape position (i.e.zero value) (Fig. 3c).
In regard to PC3, it describes (among others; Fig. 3c,d; Fig. S2b, Supporting Information) the overall lateral narrowing of the system.This trend, caudally to the secondcranialmost unit, becomes conspicuous and progressive.In the case of the third-cranialmost unit, the contraction is not selective, but touches all its parts.Two consecutive (located more caudally) units become inclined cranially.However, this inclination was obtained in 2 ways: either via shifting a dorsal or ventral section of the cranial and caudal unit, respectively.In both the cranial-and caudalmost units of the lumbosacral system, the lateral contraction shifts the canals dorsally.The cranialmost unit, as a whole, becomes contracted dorsoventrally.PC3 explains ∼28% of all shape-related or 0.8% of total variance.The largest contribution to the component is that of A1008; the smallest input comes from P. adeliae.The overall ordination along this axis contrasts A1008 with A1005 and A9, whereas other specimens are clustered around the mean-shape position (Fig. 3c,d).
The pattern of shape change along PC4 mainly represents the transition from the lumbosacral system with its third-caudalmost unit being inclined cranially to that with the third-caudalmost unit being inclined caudally, apparently via rotation (Fig. 3d; Fig. S2c, Supporting Information).This deformation together with displacements in the more cranial unit leads to cranio-caudal expansion of the dorsal area between these 2 central units.There is also a trend in the second-caudalmost unit to rotate cranially.A pronounced deformation observed within the cranial end (Fig. 3d) appears to be exaggerated by the bilateral asymmetry of the cranialmost pair of lumbosacral canals in the most influential specimen (A632).PC4 explains ∼14% of shape-related and 0.4% of total variance.The largest contribution to the component is that of A632; the least influential is P. adeliae.The overall ordination along this axis accentuate the contrast between a cluster of 4 specimens (A1008, A1005, A. forsteri, and A9) and A632, with P. adeliae located in between them (Fig. 3d).
Results of the residual-based PCA coincide very closely with those from the size-shape PCA. (Fig. 3c,d).However, it should be noted that, because of different approaches, PC1 in the former corresponds to PC2 in the latter, and so on (up to residual-based PC4).Both, the first 3 principal components from the residual-based PCA and the first 3 size-independent components from the sizeshape PCA explain ∼90% of the shape-related variance in data.

Analysis of modularity within the lumbosacral canal system
Considering all studied combinations of specimen subsets and modular hypotheses, with and without the midline landmarks (Fig. 4), the strongest (standardized) modularity signal is associated with the model assuming 2 equal modules in all specimens.For a subset devoid of P. adeliae, said model remains favored, and the signal, though weaker, is relatively strong.As for the presentday specimens only, the signal is strongest (though much weaker than that in both previous cases) in respect to the scenario assuming 3 equal modules.For 2 remaining sub-sets of specimens (i.e. one without A. forsteri and another comprising fossils), the greatest degrees of modular signal are similar to that above, and mainly associated with the 6-module model.All the aforementioned favored models are statistically significant at α = 0.05 (Fig. 4).

Curvature analysis of lumbosacral canals
The study on the Menger curvature of 4 central lumbosacral canals, using raw landmark coordinates, has unveiled that respective values of 3 cranialmost canals in P. adeliae have the most pronounced curvature relative to their counterparts in other specimens, whereas 3 caudalmost ones in A. forsteri are the least curved in respect to their counterparts from the analyzed set (Fig. 5a).Considering the intra-individual patterns, the most conspicuous is the difference between the curvature of the cranial-and caudalmost canals in all studied fossil bones.The latter values are clearly higher.In the case of A. forsteri, the difference is small, whereas in P. adeliae, the cranialmost canals are distinctly more curved than the others.
The intra-individual patterns expectedly remain unchanged after the Procrustes superimposition, but this is not the case for some inter-specimen contrasts.While most of the changes within the latter patterns are minor, noteworthy alteration concerns P. adeliae (Fig. 5b).Although its cranialmost canal curvature remains the most pronounced, it is only slightly larger than that in A632.The curvature values for its other canals decreased markedly relative to the other specimens, and turned out to be either the second-lowest (2 pairs of centermost canals) or the lowest (caudalmost canals).The overall range of curvature values is the smallest for the cranialmost and the greatest for the caudalmost canals.

DISCUSSION
All fossil synsacra presented here, judging from their overall size (Fig. 1), can be unequivocally assigned to the so-called giant penguins (Simpson 1946;Myrcha et al. 2002;Jadwiszczak & Mörs 2011).That implies that they most probably represent either the genus Anthropornis Wiman 1905, or Palaeeudyptes Huxley, 1859 (or both).Specimen A9 (Fig. 1c) has been already tentatively assessed as a non-Anthropornis penguin, supposedly representing Palaeeudyptes (Simpson 1971;Jadwiszczak & Mörs 2011).Two other bones, A1006 and A1008 (Fig. 1f,g), possess a pronounced cranial swelling of the consolidated vertebral bodies, a structure also observable in Paleocene Waimanu manneringi Jones, Ando et Fordyce, 2006 (Mayr et al. 2017, fig. 7y) from New Zealand as well as in an Eocene Antarctic synsacrum suggested to represent Anthropornis (Jadwiszczak & Mörs 2011, fig. 3) and Oligocene Kairuku waewaeroa Giovanardi, Ksepka et Thomas 2021 (Giovanardi et al. 2021).In our opinion, such a swelling is probably a remainder of the vertebral fusion.However, if retained throughout ontogeny, it could have served as a supportive structure (Jadwiszczak & Mörs 2011).Considering the total numbers of vertebrae incorporated into the analyzed Eocene synsacra, they are consistent with "13 ( 14)" reported for modern Sphenisciformes by Stephan (1979: p. 54).As a matter of fact, there were occasionally noted contemporary individuals having less than 13 synsacral vertebrae (supposedly younger birds), but also possessing as much as 15 such bones (e.g.Boas 1933;Simpson 1946).The numbers of synsacro-lumbar vertebrae correspond exactly to counts observable in extant penguins, which are either 2 or 3 (Stephan 1979).A majority of the fossil specimens studied here have 3 such bones and it is also the most common condition in modern penguins (authors' personal observation).One of the earliest penguins, W. manneringi, has 3 synsacro-lumbar vertebrae (e.g.Mayr et al. 2017, fig. 7y).That can be a plesiomorphic character state, apparently an evolutionarily persistent one, and common at both ends of the considered length of the geologic time line.One of the possible factors might be the very morphology of the lumbar vertebrae, which are devoid of the costal processes hence theoretically more structurally flexible, favorable for the functioning of the internal sense organ.This is supported by the observation that the best-developed part of the system of transverse canals is housed predominantly within the synsacro-lumbar section.The counts we presented above also show that both synsacra of extant species described in the present paper (Fig. 1a,b) are consistent with earlier counts for these species.Guinard and Marchand (2010) reported, based on their studies of cervical modularity in extant and fossil penguins, modification of the (modular) identity of a vertebra into another.The authors attribute it to the complete natural homeotic transformations resulting in variability that supposedly did not undergo prominent changes in the course of penguin evolution.There is a possibility that such a process could also have taken place at the junction of the synsacro-thoraco-lumbar and synsacro-lumbar segments.Apart from the above, the variability in the number of lumbar vertebrae is evolutionarily conserved as well.
Moving on to the discussion of internal features, we emphasize at the outset that, to our knowledge, the wavelet-based analysis thus far has not been used in the broadly construed ornithology for study of osteological structures.The overall interpretation of the results from the periodicity-focused investigations touching the crosssectional area changes within the main synsacral canal is straightforward.In all specimens, the canal is largely a structure with the periodic property.This quality is best pronounced along its enlargement (Fig. S1, Supporting Information), which is not that surprising given its concurrency with the explicitly segmental lumbosacral-canal system (Figs 1,2; see also Necker 2005Necker , 2006)).However, other important sources of periodicity also need to be acknowledged.One of them is a repetitive enlargement of endocasts due to passages for the bilateral spinal nerves (Fig. 2; see also Boas 1933, fig. 10.6); another represents the recurring deepening (and widening) of the marginal ventral grooves along the midmost part of the synsacral canal (Fig. 2a; Jadwiszczak 2014, fig. 2d).Actually, we can observe (Fig. S1, Supporting Information) the combined effect of all these factors on the cross-sectional area, and it is informative.
Namely, when the spatial mismatch between the aforementioned sources is relatively small, as in the present-day synsacra we studied, the wavelet power spectra are quite simple, with a single power ridge (Fig. S1c,e, Supporting Information).In the case of fossil specimens, the appearance of additional shorter, higher-frequency, and overlapping ridge within the levels of the canal enlargement, or in its proximity (Fig. S1b,d,f-h, Supporting Information), reflects the locally increased mismatch.This is a consequence of a more pronounced separation, via increased phase difference, of at least 2 sources of periodicity.In A1008, the picture is even more complex by involving an additional vast area of lower-frequency periodic changes, with a marked ridge (Fig. S1f, Supporting Information).It is significantly above the white and red-noise levels and deserves particular attention.What can be deduced, based on simple pattern matching, is that the cranially sloping power ridge covers the length of 7 complete vertebrae (Fig. 1g; Fig. S1f, Supporting Information).Six of them correspond to 2 full wavelengths, measured from through to through, of the area-value oscillation detected by the MWT for Fourier periods covered by that ridge (Fig. S1f, Supporting Information).Interestingly, the midpoint of the middle trough coincides with the boundary between the synsacro-lumbar and sacral segments (Fig. 1g).
Such a symmetry is intriguing.There is a perfect match between the range of the synsacro-lumbar segment of A1008 (3 vertebrae) and wavelength.However, the synsacro-sacral segment is (anatomically) by one vertebra shorter than wavelength.In our opinion, this may indicate that, functionally, it is 3-unit long, the third (supplementary) vertebra coming from the synsacro-caudal section (Fig 2b).Actually, this would be by no means unique.For example, dinosaurs from all major lineages increased, in the course of their evolution, the number of the sacral vertebrae by incorporation of thoracic and/or caudal ones (the original count was 2; Moro et al. 2021).Three sacral vertebrae are also typical of present-day ostriches (e.g.Kaiser 2007).
Admittedly, additional lower-frequency patches are also traceable in the spectra of A. forsteri, P. adeliae, and A1005 (Fig. S1c-e, Supporting Information).They are much smaller, incommensurately weaker in respect to power levels, and have no power ridges.Hence, they might be quite safely treated as red-noise artifacts.In our view, it would be premature to claim the supernumerary significant ridge, or local maximum, of lowerfrequency periodicity observed in A1008, as a likely taxonomically diagnostic character.On the other hand, this specimen is the only one within the studied set (except for A1006, which is incomplete) that possesses the characteristic cranial swelling, the feature considered in the context of Anthropornis (see above).Some representatives of the genus were extremely massive (e.g.Myrcha et al. 2002); therefore, a functionally longer "sacrum" could have been biomechanically beneficial.
All in all, present-day and fossil synsacra differ in regard to the analyzed periodicity patterns (simple vs. complex setting).The biological significance of said difference appears to be explainable in terms of an evolutionary process of gaining a more streamlined body form (penguins are wing-propelled divers).This change resulted in the backward shift of pelvic limbs, hence fully upward posture while not in water and unavoidable alterations to the pelvic girdle and associated structures (e.g.Jadwiszczak & Mörs 2019).Thus, a stability and simplicity of said patterns observed within the synsacral canal of living penguins can be simply a product of an osteological (and functional) adaptation of some synsacral vertebrae that made them better suited for the truly upright posture and its consequences.Such a process could have (potentially) influenced the course of the spinal-nerve roots through the intervertebral foramina, and was undoubtedly responsible for gait adaptations.
The only digital endocast of the lumbosacral-canal system of a present-day penguin published so far has been that of Spheniscus humboldti (Stanchak et al. 2020, fig. 4).The visual comparison with both endocasts of other extant species presented here (Fig. 1) reveals that its section corresponding to the canal enlargement is relatively more convex dorsally than that in the considerably larger A. forsteri.In this respect, S. humboldti much more resembles the approximately similarly sized P. adeliae.Nevertheless, the lumbosacral-canal system in S. humboldti differs from the other 2 extant species in orientation of the 2 midmost canals.In dorsal view, they are clearly deflected caudally (Stanchak et al. 2020, fig. 4), whereas their counterparts in A. forsteri and P. adeliae are quite perpendicular to the main synsacral axis (Fig. 1a,b).Some fossil specimens also show a deflection within said segment, but limited to a single (caudal) pair.This is demonstrable in A9 and A1005 (Fig. 1c,e) as well as in the only endocast of the lumbosacral-canal system of an Eocene penguin reported so far (Jadwiszczak 2014, fig. 4).The synthesis of the data reveals that individuals with 2 synsacro-lumbar vertebrae (A1005 and S. humboldti) possess at least 1 midmost pair deflected caudally, whereas those with 3 such vertebrae tend to have non-deflected midmost canals.Clearly, the tendency neither reflects a directional evolutionary change nor is size-dependent.The location of the boundary between the synsacro-lumbar and sacral series of vertebrae relative to the lumbosacral-canal system, an issue actually reducible to the contrast between A. forsteri and remaining specimens, appears not to be a factor here.
Perusing the main orthogonal axes of shape variation (i.e.PC2-PC4 in a context of the size-shape PCA; Fig. 3), we found the lumbosacral system of P. adeliae constantly located close to the mean-shape position.It is seemingly counter-intuitive that, along the spectrum represented by projections of data points on PC2, another present-day penguin (A.forsteri) is an obvious outlier.However, the ordination depicted by this "line-of-best-fit" (see Quin & Keough 2002) does also differentiate fossil (on the left) from modern (on the right) Sphenisciformes (Fig. 3b).This is not the case with PC3 and PC4, although incontestably, in their context, A. forsteri is never an outlier.There are 3 crucial characteristics that singularize the lumbosacral system of A. forsteri within the most important axis of shape variation, as is clearly demonstrated by the relevant variable (or coordinate) contributions, graphically summarized in Fig. S3, Supporting Information.Ap-parently, paramount is the pronounced relative lateral expansion spanning 4 caudalmost units, closely followed by a dorsal contraction between 2 caudalmost units.There is a noteworthy correspondence between the placement of the latter characteristic and the unique, within studied specimens, location of the synsacro-lumbar and sacral boundary relative to the studied lumbosacral-canal system (Fig. 1).It looks as if the relative cranial shift of the system, with respect to the boundary, have triggered some modifications, such as the aforesaid contraction, possibly also a conspicuous dorsal elevation of the midline area within the second-caudalmost unit (that pulled the adjoining canals with it).The accompanied pronounced lateral expansion could be of a compensatory value (see Fig. S3, Supporting Information).
The observed otherness of A. forsteri perhaps evolved due to the selection pressure related to extremely difficult conditions during the breeding season.The hind limbs of this largest of extant Sphenisciformes are used very intensively on land-during long trips to the breeding sites (and back to sea) as well as constant rotation of the place occupied within the colony, to maximize the protection of adults and eggs, incubated on their feet, against extremely harsh conditions typical of continental Antarctic winters.Considering the extralabyrinthine sense organ of equilibrium (e.g.Necker 2005Necker , 2006)), an increase in the distance between its central part and the sacral vertebrae can be beneficial for some reason (maybe related to the center of mass location).
Considering the results of the modularity analysis (Fig. 4), it seems justified not to narrow our discussion to the calculated standardized effect sizes (Z CR ).Admittedly, they can be used for comparisons within and between datasets (Adams & Collyer 2019), but another piece of information, the observed covariance ratio (CR in Fig. 4), should also be taken into account.The ratio constitutes quite a useful complementary tool (Adams 2016), although insights are meaningful only within a given dataset (Adams & Collyer 2019).In our opinion, its utility is rather underestimated by Adams and Collyer (2019) in cases when CR exceeds 1.The model with 2 equal modules in all specimens achieved by far the highest score (in terms of Z CR ) amid all model-subset combinations; however, the corresponding CR values were undeniably close to 1. Since the covariation within modules is always placed in the denominator of the formula (Adams 2016), the latter suggests that the modular signal (the denominator) is not that much above the noise level (represented by covariances between modules; the numerator).Nevertheless, the fact of it being statistically significant indicates that the signal is most likely stronger than that expected by chance.
The step-wise inclusion and exclusion of specimens in our considerations, performed in line with the arrow of geologic time, allowed for a better understanding of the underlying patterns.Regarding the fossil group, the most supported model of modularity within their lumbosacral-canal system is that with 6 modules.The minimum addition that leads to the all-specimen and overall dominant model of 2 symmetric modules is that of A. forsteri, forming the "all sans P. adeliae" subset.The consecutive inclusion of P. adeliae results in an increase of the majority of Z CR values, especially those for 3 suboptimal models ([1,2][3,4][5,6], [1,2][3,4,5,6], and [1,2,3,4][5,6]).The Z CR measure calculated for the symmetric 2-module model increases as well, though not as spectacularly as in the latter subset.Importantly, it retained the position of the overall most strongly supported scenario.
In the case of the other order of inclusion, after the addition of P. adeliae, the "fossil" type of modularity (though in canals only) is retained, but the resulting CR surpasses 1.Actually, after inspection of the relevant pairwise CRs matrix (not tabled here), all ratios exceeded 1.This signifies the signal jammed by random noise.Considering the subset of both present-day specimens alone, they appear to favor the model with 3 equal modules, though CR is above 1.Also in this case, after inspection of the pairwise CRs matrix (not tabled here), all ratios exceeded 1.The statistical significance is secondary here, because the involved randomization procedure is agnostic of the border value (i.e. 1) meaning.Hence messages from both issues discussed in this paragraph are rather obscure.
The revealed statistically significant modular signal in the studied lumbosacral-canal systems of large-sized Antarctic fossil penguins (Fig. 1) indicates greater independence among modules than can be expected from random reassignments of the variables among partitions.However, the favored model of modularity assumes the extreme atomization of the whole structure.In this respect, there is no conspicuous trace of a (structural) specialization in transverse canals reflecting 2, crucial for leg innervation, neural plexuses (lumbar and sacral; e.g.Dubbeldam 1993), stemming along the same length of the synsacral canal in modern birds.Both plexuses share a single (forked) nerve, they are often collectively termed as the lumbosacral plexus, but their branches leave the pelvis in different locations (cranial and caudal to the acetabulum, respectively; Dubbeldam 1993).One could hypothesize them to function as 2 modules rather than 6.Such an expectation is by no means unfounded, because inclusion of a present-day A. forsteri changes the current most supported model to that postulating 2 (equal) modules, as has been demonstrated above.It is quite likely that this reflects an evolutionary signal.Importantly, A. forsteri being the largest modern penguin is best suited for considerations involving large-sized (or even "giant") Sphenisciformes.P. adeliae is much smaller (Fig. 1), hence potentially vulnerable to allometric shape changes (i.e.those deviating from isometry), not correctable by the GPA alone.Moreover, much smaller species may just respond differently to selection pressures than their larger relatives.So far, the modularity in the penguin axial skeleton was investigated solely in the context of the cervical spine (Guinard & Marchand 2010;Sosa & Acosta Hospitaleche 2022).
The results from another analysis reported in the present work show that P. adeliae is in stark contrast to other studied specimens (especially fossils) in respect to curvature ratios within their central set of 4 pairs of lumbosacral canals (Fig. 5).One can only speculate why, in P. adeliae, the curvature of the cranialmost pair of the 4 midmost canals is, unlike in other studied penguins, developed much better than that of the caudalmost canals.Nonetheless, we have been able to determine its actual significance within main directions of variability in the lumbosacral-canal system.The Y coordinates of the 9th and 13th 3D landmarks (Fig. 2d), located at midpoints of the curvature of a discussed pair of canals, are among the most influential variables in a context of the main, size-dominated, axis of variation (PC1) revealed by the size-shape PCA (Fig. 3a).They are also, to some degree, correlated with size (lnCS).Thus, the link with the synsacrum assignable to P. adeliae is quite obvious-it is the smallest one (an actual outlier) and contributes most to PC1.Additional support comes from the TPS deformations estimated for the minimum value of PC1 reflecting the position of said specimen (Fig. 3b).
Present-day penguins, while on land, appear to be quite ungainly.This undeserved label comes obviously from their distinctive waddling gait.It is actually purposeful and constitutes a very efficient way for mechanical energy recovery.In short, it is by no means wasteful (Griffin & Kram 2000).Kurz et al. (2008) indicated that such a walking pattern is also very stable in the context of the frontal plane dynamics; the consistency in a step width surpassed that in a step length.Kurtz et al. (2008) have rightly pointed out that if maintaining stability during a waddling gait required additional control from the nervous system, and nevertheless was ineffective, such a method would be eliminated by the natural selection.
Since this has not happened, we can safely assume that the neural control is efficient enough and not too energetically expensive relative to the benefits obtained.The reasonable explanation, as pointed out below, may be sought in the synsacral-canal specializations.

CONCLUSIONS
The Eocene and present-day Sphenisciformes are separated by more than 34 million years of evolution.As far as osteological traits and their functional interpretations are concerned, in some respects, penguins have changed considerably, and yet in others, they have remained virtually the same.As exemplified by the results of our study of synsacra, such a statement holds true in its entirety even when the scale is narrowed down to a single element of the skeleton.Importantly, the role of synsacrum goes beyond the purely mechanical context; it can also be considered as a structure housing and cocreating the extralabyrinthine sense organ of equilibrium.The relevant osteological correlates of the latter, the lumbosacral canals, are readily apparent in all the studied synsacra.
The analyzed Eocene synsacra resemble their presentday counterparts in regard to the scope of variability in both the total number of vertebrae and, even more so, the relevant figure for the synsacro-lumbar series.The fossil and contemporary penguin synsacra differ in regard to the complexity of detected periodicity patterns in the crosssectional area changes of the main (axial) canal-they are much simpler and more stable in the latter.They are also distinguishable or separable along the main orthogonal direction of the shape-related (size-independent) variability within the lumbosacral system, although A. forsteri is an obvious outlier (differences are lucidly depicted in Fig. S2b, Supporting Information).Additionally, we have premises to suggest that the observed contrast between the fossil and extant penguins manifested by the dissimilarity of the most strongly supported modularity models within the lumbosacral-canal system, atomization versus emergence of larger units, is a tendency of adaptive value.Despite some interpretational ambiguity (related to the unstandardized effect size), when considering extant penguins alone, the results for the combined set leave no doubt about the tendency.
Not all phylogeny-informed contrasts have yielded such clear results.The observed tendencies of deflections touching 2 midmost pairs of lumbosacral canals, the very middle of the sense organ of equilibrium, turned out to be neither consistent with phylogeny nor size dependent.The extant A. forsteri is unique in the entire studied set in terms of the relative cranial shift of the lumbosacral system.This may represent an adjustment relative to the center of mass, functionally advantageous for the breeding in the uniquely harsh conditions of the Antarctic winter (and adjacent periods of time), requiring the almost constant use of legs, even during incubation.Maintaining balance is especially important then as dropping the egg from the feet (a surrogate nest) onto the ice results in losing the brood.Anyway, the said change has been responsible for its aforementioned outlying location within the crucial gradient of shape-related variation.Another present-day synsacrum, the specimen assignable to P. adeliae, differs from the remaining bones in terms of the curvature of the cranial-and caudalmost of 4 midmost lumbosacral canals.The former is best pronounced, being the reversal of the state in other specimens, and it proved to be (at least partly) a size-dependent feature.
We are convinced that the anatomical and functional basis for the above considerations was mostly shaped by the evolution of the streamlined body shape in penguins and its prominent by-product, the formation of an upright posture on land.However, having short tarsometatarsi (thus legs), a feature gained by penguins in the process, translate in potentially unstable and energetically costly gait.In fact, as we noted in Discussion, the opposite is true-their characteristic side-to-side waddling proved to be surprisingly stable and energy conserving.In such a case, the most parsimonious explanation seems to be the involvement of some supplementary sensing organ located much closer to the legs than the long-recognized vestibular system, the sensory part of which can be found in the inner ear.The sense organ of equilibrium housed by the synsacrum is the most obvious candidate.The assumption that the differences in the former, revealed between the Eocene and extant penguins, reflect its directional adaptive change seems well grounded.Undoubtedly, the increasing degree of modularity of a series of the best-developed paired transverse canals would be evolutionarily beneficial.Simply, a better organized version of a structure is more likely to be simultaneously more efficient functionally and less demanding energetically.This dependence appears to scale up well in penguin synsacra, touching the changes of the cross-sectional area of the relevant length of their main canal, transverse canals being merely its "indentations."It is manifested by better spatial concurring of the sources of periodicity, represented largely by the transverse canals and the spinalnerve roots.
We hope that our findings will stimulate other (paleo)ornithologists and help to outline the avenues for future research on the lumbosacral-canal system and the lumbosacral organ in penguins as well as other birds.

Figure 2
Figure 2 Synsacrum of the Emperor penguin, Aptenodytes forsteri, in (a) lateral, (b) dorsal, and (c) oblique views, rendered semitransparent to present the shape and location of its spinal canal.These are supplemented by an endocast-surface model with a visualized landmark distribution and sources of data for the analyses described in text (c,d).The white star marks the reference point for the localization of the landmark configuration.

Figure 3
Figure 3 Results of the principal component analyses (a-d) and thin plate spline deformations (b-d) of the lumbosacral-canal system in the studied fossil and present-day penguins.The percentage of variance, that is explained by each of the selected components, is given at relevant axes for both the size-shape (in black) and residual-based (in orange; c,d) PCAs.The scatters of points in (c) and (d) reflect overlaid outputs from both PCAs.Additionally, the contribution of size (in a form of lnCS) to the first 4 principal components from the size-shape PCA, and its correlation with them are presented as well (a).The blue arrows (their projections on axes) in (a) account for contributions of the rest of 10 most influential variables (considering PC1 and PC2).

Figure 5
Figure 5 Curvatures of the 4 central pairs of the lumbosacral canals (averaged), for studied fossil and present-day penguins, based on (a) raw and (b) Procrustes-aligned configurations.