Modularity and integration of the neural arch and vertebral centrum in primates

Abstract

The vertebral column consists of multiple homologous elements that have specialized within and between taxa and serve important functions in positional support and as protection for the central nervous system. The study of modularity and integration provides new insights into the evolution of complex structures such as the vertebral column. Patterns of modularity and integration may reflect underlying genetic-developmental patterns and facilitate evolution. Previous studies have identified mixed patterns of modularity within and between elements across mammals generally, within primates, and within carnivorans. Here, we assess modularity within and between elements in the complete post-axial vertebral column in four catarrhine taxa: Macaca (n =96), Hylobates (n =77), Pan (n =92), and Homo (n =151). We use the Covariance Ratio (CR) and estimate r² and the standardized variance of eigenvalues (SVE) for comparative purposes. Our results show that there is general, widespread integration within the catarrhine vertebral column, both within and between elements. Hominoids tend to display greater modularity than do macaques, but these estimates are rarely significant. Clusters of modularity in the mid-cervical and upper thoracic region may relate to special nervous system structures in these areas, and locomotor behaviors in general may influence patterns of modularity in primates. In particular, we find that size is a pervasive factor affecting integration among vertebral elements, though its effects on specific structures are variable. Our results generally do not agree with those found across mammals or within carnivorans, and future studies should focus on genus-level assessments across a variety of taxa.

Introduction

The vertebral column is a defining feature of the Vertebrata and fulfills multiple important functions. These functions include protection of the central nervous system, serving as a muscle attachment site for both axial and limb muscles, and serving as an axis for locomotion. Adaptation in the vertebral column is thus an important component of vertebrate adaptations in general, and the vertebral column is both highly conserved across taxa and also highly variable in its specific morphology (McShea, 1993; Boszczyk et al., 2001; Narita & Kuratani, 2005; Hautier et al., 2010; Asher et al., 2011; Fleming et al., 2015; Jones, Benitez, et al., 2018; Bui & Larsson, 2021; Maxwell et al., 2021; Hauswirth et al., 2022). As a result, it is important to understand how the vertebral column develops and evolves, and investigators have approached these questions using a variety of approaches.

The evolution of the vertebral column has been broadly characterized using both comparative and paleontological methods, with special interest devoted to regionalization of the vertebral column and the fixed cervical count among mammals, as well as to functional specializations within taxonomic groups (McShea, 1993; Graf, Waele, et al., 1995; Galis, 1999; Moon, 1999; Boszczyk et al., 2001; Narita & Kuratani, 2005; Hautier et al., 2010; Asher et al., 2011; Fleming et al., 2015; Nalley & Grider‐Potter, 2015; Nalley & Grider-Potter, 2017; Jones, Benitez, et al., 2018; Jones, Angielczyk, et al., 2018; Bui & Larsson, 2021; Maxwell et al., 2021; Hauswirth et al., 2022). Generally, it is thought that the chordates, which gave rise to the Vertebrata, appeared by 500 Ma, and early specimens display the rudiments of future vertebrae (Chen et al., 1999; Shu et al., 1999; Shu, 2003; Shu et al., 2003), which are also found in hagfish (Ota et al., 2011, 2013). The vertebral column is unique in that it consists of a series of complex elements, each one formed by the vertebral centrum, neural arch, and, in some taxa, the haemal arch, and with a series of variable accessory processes including articular, spinous, and transverse processes. Notably, vertebrae did not evolve as complete elements; rather, vertebral arches first appeared in the fossil record in the Vertebrata, while vertebral centra appeared in the gnathostomes (Fleming et al., 2015), though these latter structures may have appeared separately in various lineages (Arratia et al., 2001).

The form of specific vertebral elements and the column itself varies within and among taxa, particularly among mammals with distinctly regionalized vertebrae (Jenkins, 1970; A. B. Ward & Mehta, 2014; Jones, Benitez, et al., 2018). In mammals, the pre-sacral vertebral column is divided into cervical, thoracic and lumbar regions. Regionalization may be tied to the transition into mammal-like locomotor and respiratory function in complex ways and may have resulted from increased locomotor specialization in the forelimb (Jones, Angielczyk, et al., 2018; Jones, Benitez, et al., 2018; Jones et al., 2021). Interspecific variation in vertebral form among mammalian taxa has been attributed to body size (Arnold et al., 2017), head carriage (Nalley & Grider-Potter, 2017; Nalley & Grider‐Potter, 2015), and other aspects of positional behavior (Russo, 2015; Russo & Williams, 2015), including positional behaviors associated with dietary ecology (Randau et al., 2017; Antón et al., 2020) and locomotion (L. J. Shapiro, 1993; Boszczyk et al., 2001; Jones, Benitez, et al., 2018), as well as to phylogenetic history (Jones, Benitez, et al., 2018). Both regionalization generally and interspecific specialization are characterized by distinct morphological changes in the vertebral centrum and structures of the neural arch. The mammalian cervical elements are characterized broadly by the presence of a transverse foramen in the transverse process, which transmits the vertebral artery to the brain, the thoracic elements are characterized by their articulation with the ribs, and the lumbar elements are characterized by the lack of either of those specializations. Functional specializations also involve changes in the size, shape, and orientation of the articular, spinous, and transverse processes, and the size and shape of the vertebral body (Boszczyk et al., 2001; Nalley & Grider‐Potter, 2015; Nalley & Grider-Potter, 2017; Russo & Williams, 2015; Randau et al., 2017; Meyer et al., 2018; Antón et al., 2020). While the function of the cervical elements, which interact with the hard and soft tissues of the head directly, and of the thoracic elements, which assist in maintaining ribcage structure and supporting the upper limb, are broadly similar across mammals (Vidal et al., 1986; Graf, Waele, et al., 1995, 1995; Liebsch & Wilke, 2018; Jones et al., 2019), the lumbar elements are typically involved in highly specialized locomotor functions, with highly specialized anatomies that vary across taxa, such as the wide postzygapophyseal distance in the ultimate lumbar of humans (Boszczyk et al., 2001).

The development of the tetrapod vertebral column has also been generally well-characterized from both a genetic and embryological perspective through the use of model organisms such as chickens and mice. The embryo develops a series of mesodermal somites corresponding to body segments and corresponding roughly to the final length of the body and the number of vertebrae in that taxon (Richardson et al., 1998; Gomez & Pourquié, 2009). Elongation by the addition of somites occurs principally towards the caudal end of the embryo, with some caudal somites later disappearing (Gomez & Pourquié, 2009; Bénazéraf & Pourquié, 2013). Parts of the process of segment addition appear to be directed by the specific expression or co-expression of Hox genes, which also later contribute to determining segment identity and morphology (Burke et al., 1995; Wellik & Capecchi, 2003; Wellik, 2007; Mallo et al., 2010; Bénazéraf & Pourquié, 2013; Böhmer et al., 2015; Böhmer, 2017). These somites undergo a process of resegmentation in which each somite divides into rostral and caudal segments, which join adjacent somites rostrally and caudally, respectively (Bagnall et al., 1988; Huang et al., 2000; L. Ward et al., 2017). These new condensations then give rise to the vertebrae, so that each vertebra consists of two somites, roughly divided into rostral and caudal segments across both the vertebral centrum and neural arch (Bagnall et al., 1988; Aoyama & Asamoto, 2000; Huang et al., 2000; L. Ward et al., 2017). The caudal somite segment may contribute more to the pedicles and the lamina of the neural arch, while pre- and post-zygapophyses are derived from caudal and rostral somites, respectively (Bagnall et al., 1988; Goldstein & Kalcheim, 1992; Aoyama & Asamoto, 2000), and there may be differences between vertebral regions in the particular contribution of each somitic segment (L. Ward et al., 2017). This process of resegmentation appears to be present across gnathostomes and is partially directed by Tx15/18/22 and Uncx4.1 (Criswell & Gillis, 2020), Mesp2 (Saga, 2012), and a variety of signaling pathways including Wnt, Notch, and FGF that induce somite polarization to determine the rostro-caudal axis (Kuan et al., 2004; Gomez & Pourquié, 2009; Saga, 2012). Some hypotheses suggest the resegmentation process evolved due to the need for muscles of the vertebral column to cross segments in order to generate movement, but these hypotheses have yet to be directly tested (Fleming et al., 2015; Criswell & Gillis, 2020). In addition, the sclerotome that gives rise to each vertebra will divide into three principal compartments, which give rise to the laminae and pedicles laterally, the spinous processes dorsally, and the vertebral centra ventrally (Christ et al., 2000). Once these vertebral precursors are formed, they begin to ossify in the embryo. The neural arches and vertebral centra ossify separately, and ossification proceeds in different order and directions in these two structures (Skórzewska et al., 2013; Skawiński et al., 2022).

Given the complex, multi-element nature of the vertebral column, and the sparse nature of the fossil record, it can be difficult to clarify the evolutionary processes shaping this region. In addition, although we understand the general genetic and developmental processes shaping the vertebral column across vertebrates, it can be difficult to assess differences in these processes at interspecific levels. As a result, our understanding of evolutionary processes at shorter taxonomic scales is sometimes limited. One approach to clarify these processes is that of phenotypic integration, which assess covariation among traits that results from shared genetic, developmental, and functional processes (Olson & Miller, 1958; Klingenberg, 2004; Armbruster et al., 2014; Rolian, 2014). Phenotypic integration itself evolves and can shape evolution in turn by creating paths of least resistance that can facilitate or hamper the response to selection (Schluter, 1996; Wagner et al., 1997; Goswami et al., 2014). Integration among traits is thought to evolve in response to shared function (Cheverud, 1996), and traits that are highly integrated with each other to the exclusion of other traits are said to form modules, which will evolve together (Wagner, 1996; Zelditch & Goswami, 2021). Importantly, although phenotypic integration reflects genetic-developmental and functional processes, it can be measured from the adult phenotype, which is relatively easily accessible.

Previous researchers have characterized integration within or across vertebrae primarily in mammals, with some studies focused on birds or salamanders (Arlegi et al., 2020, 2022; Jung et al., 2021; Jung & Von Cramon-Taubadel, 2022; Martín-Serra et al., 2021; Powell et al., 2018; Randau & Goswami, 2017a, 2018; Villamil, 2018; Terray et al., 2020; Urošević et al., 2020, 2023; Villamil & Middleton, 2024a). These studies have identified a variety of shared and derived patterns of integration and modularity, including generally conserved cervical modules among mammals (Arnold et al., 2016; Arlegi et al., 2018, 2020; Villamil, 2018; Martín-Serra et al., 2021) and among birds (Terray et al., 2020), signals of high integration in the rib-bearing thoracic region (Jones, Benitez, et al., 2018; Arlegi et al., 2020; Martín-Serra et al., 2021; Villamil & Middleton, 2024a), and signals of behavioral selection in the thoracolumbar regions (Randau & Goswami, 2017a; Martín-Serra et al., 2021; Villamil & Middleton, 2024a). In general, these studies support both developmental and functional hypotheses for vertebral evolution and form. However, only a handful of these studies have considered modularity within vertebral elements that may result from the divergent evolutionary and developmental origins of different parts of each vertebra, such as the neural arch and centrum (Arnold et al., 2016; Randau & Goswami, 2017a, 2017b; Villamil, 2018; Figueirido et al., 2023), or have otherwise explicitly tested modularity (Jones, Benitez, et al., 2018; Arlegi et al., 2020; Jung & Von Cramon-Taubadel, 2022). Understanding the relationship of these structures within and between vertebrae may clarify the evolution of functional specializations across taxa.

The aim of this study is to assess the integration and modularity of vertebrae and their parts, both within individual elements and across adjacent elements, in a primate sample. This study expands the number of taxa for which we have this kind of information, which will further inform us about whether previously-identified patterns are shared among mammals and, if not, how those patterns differ. Ultimately, this will clarify processes of evolution in mammalian vertebrae. We apply the covariance ratio (CR) (Adams, 2016) to test for the presence or absence of modular structure. In particular, we test the following hypotheses:

1. Whole vertebrae will be integrated with adjacent or nearby vertebrae and will display modularity with vertebrae that are further away. A pattern showing less independence among adjacent or nearby vertebrae was identified by previous researchers in a broad sample of mammals (Jones, Benitez, et al., 2018). We predict this effect, with modularity between distant elements, will be more marked in hominoids, who have been argued to display increased modularity relative to other primates (Arlegi et al., 2020; Jung & Von Cramon-Taubadel, 2022). We also predict a cluster of integrated cervical elements, which is highly conserved in mammals (Arnold et al., 2016, 2017; Randau & Goswami, 2017b, 2018; Arlegi et al., 2018; Villamil, 2018; Martín-Serra et al., 2021), and a cluster of integrated elements in the thoracic region across taxa, which has been identified generally in mammals (Jones, Benitez, et al., 2018), and is likely related to the special respiratory and rib-supporting functions of this region (Arlegi et al., 2020; Villamil & Middleton, 2024a).

2. Individual vertebrae will display modularity between the neural arch and vertebral body. The neural arch has a separate embryologic origin to the vertebral centrum (Bagnall et al., 1988; Aoyama & Asamoto, 2000; Christ et al., 2000; Huang et al., 2000; L. Ward et al., 2017) and ossifies in a different manner (Skórzewska et al., 2013; Skawiński et al., 2022). Further, the neural arch and centrum appeared separately in vertebrate evolution (Arratia et al., 2001; Fleming et al., 2015) and thus may be formed via different mechanisms. Finally, the two structures respond to separate functional pressures (Pal & Routal, 1986, 1987, 1996; Machida & Inoue, 1994; Graf, Waele, et al., 1995; Boszczyk et al., 2001; Smit, 2002; Kozanek et al., 2009; Jaumard et al., 2011), although direct functional assessments of vertebral anatomy in mammals are largely limited to human samples so the extent of those differences among other taxa is not known.

3. The neural arches will be integrated across vertebral elements due to shared developmental origins and functional demands. Similarly, the vertebral bodies will be integrated across vertebral elements.

Methods

Our sample consists of all postaxial vertebral elements (third cervical [C3] through last lumbar) of four catarrhine taxa: Macaca, Hylobates, Pan, and Homo (Table 1). These four taxa were chosen to represent varied locomotor behaviors and body sizes. Macaca is largely a terrestrial quadruped with occasional climbing and leaping (Wells & Turnquist, 2001), Hylobates is a high-speed brachiator (Hollihn, 1984; Chang et al., 2000), Pan moves using a mixed quadrupedal and suspensory set of behaviors (Doran, 1997; Hunt, 1992), and Homo is an obligate biped. Previous researchers have hypothesized that modularity has either facilitated locomotor diversity among hominoids, or resulted from the wide variety of locomotor adaptations in that taxon (Young, 2004; Rolian, 2009; Young et al., 2010; Grabowski et al., 2011; Arlegi et al., 2020; Jung et al., 2021; Jung & Von Cramon-Taubadel, 2022), which makes them a useful taxon in which to study the evolution of integration and modularity. All individuals were skeletally mature, as assessed by dental eruption and skeletal fusion in the skull and postcranial elements, as available. The non-human primates come from either wild (Hylobates, Pan) or free-ranging (Macaca from Cayo Santiago, Puerto Rico) contexts.

Table 1.

Sample characteristics.

Taxon	Groups	Total (N)a	Average Mass (kg)b	Positional behavior	Modal vertebral formula	Institution(s)c
Macaca mulatta	Cayo Santiago	96	7.8	Pronograde quadrupedd	7C:12T:7L	CPRC
Hylobates lar	Doi Inthanon Chieng Dao	77	5.3–5.7	Orthograde high-speed brachiatore	7C:13T:5L	MCZ
Pan troglodytes	P. t. schweinfurthii P. t. troglodytes P. t. verus	92	33.2–60.0	Orthograde quadrupedf	7C:13T:4L	AMNH, CMNH, NMNH, PC, RMCA
Homo sapiens	North Africa South Africa East Africa	151	57.2–71.9	Orthograde biped	7C:12T:5L	BM, MC, UW

^aTotal sample size refers to the total number of individuals in the sample. However, sample sizes for individual elements or element pairs vary widely. These specific sample sizes are provided in results tables 5, 8, and 9.

^b(Stephan et al., 1981; Kappelman, 1996)

^cAMNH =American Museum of Natural History, New York, USA; BM =British Museum, London, UK; CMNH =Cleveland Museum of Natural History, Ohio, USA; CPRC =Caribbean Primate Research Center, Puerto Rico, USA; MCZ =Harvard Museum of Comparative Zoology, Massachusetts, USA; MC =Makerere University College of Health Sciences, Kampala, Uganda; NMNH =Smithsonian National Museum of Natural History, Washington, DC, USA; PC =Powell-Cotton Museum, Birchington-on-Sea, UK; RMCA =Royal Museum of Central Africa, Tervuren, Belgium; UW =University of Witwatersrand, Johannesburg, South Africa

^d(Wells & Turnquist, 2001)

^e(Hollihn, 1984; Chang et al., 2000)

^f(Hunt, 1992; Doran, 1997)

Variable vertebral formulae were addressed as in Villamil and Middleton (2024a) by removing T7 in individuals with an extra thoracic vertebra, or L3 (Hylobates) or L4 (Macaca) in individuals with an extra lumbar vertebra, and moving the remaining vertebrae up in the sequence; by treating T7 as missing in individuals with fewer than modal thoracic elements, or by treating L2 (Pan) as missing in individuals with fewer than the modal number of lumbar segments, and moving the remaining vertebrae down in the sequence. Individuals with two or more deviations from the modal condition were excluded. As noted in Villamil and Middleton (2024a), this strategy does not result in significantly different parameters for any vertebral level.

We used Mitutoyo digital calipers accurate to 0.02 mm to collect a total of eight measurements on each vertebra, attributed to either a ‘Body’ or ‘Neural Arch’ module (Figure 1, Supplementary Table 1). These measurements include the dataset described in Villamil and Middleton (2024a, 2024b), and an additional measurement of pedicle breadth (Supplementary Table 1). The transverse processes were excluded due to their variable embryological origins across regions (O’Rahilly et al., 1990). Intraobserver error ranged from 1.06% to 1.52% and was not significant when assessed using a two-tailed paired t-Test (p =0.11, T =−1.19, D.F. =90 for ERM; p =0.42, T =−0.21, D.F. =40 for CIV) (Villamil & Middleton, 2024a).

Figure 1. Measurements collected on each vertebra, shown on a macaque thoracic element in cranial (a), caudal (b), and lateral (c) views.

Measurements and the modules to which they belong are described in Supplementary Table 1 and follow the protocol of Villamil & Middleton (2024a, 2024b). Dorsoventral body width, transverse body width, and craniocaudal body height are included in the “body” hypothesized module. All other measurements are included in the “neural arch” hypothesized module.

Prior to any further analyses, data were adjusted for sex-related differences by using residuals from a Multiple Analysis of Variance (MANOVA) performed using the mnv function in R.

Absolute body size may play an integrating role in organismal anatomy but may also obscure other relationships, which has implications for organismal adaptation and particularly for understanding integration and modularity (Porto et al., 2009, 2013; Marroig & Cheverud, 2010; Machado et al., 2019). Because of this, analyses were performed on both size-corrected and full-sized data. Size correction was performed by dividing individual measurements by the geometric mean of its corresponding vertebral element. The geometric mean was calculated using the geomean function from the EnvStats package in R (Millard, 2013). Analyses were performed only on full-sized data for whole vertebra pairs, to keep in consideration size differences between cranial and caudal elements.

We estimated the covariance ratio (CR) (Adams, 2016) between linear measurements of each whole vertebra and all other individual vertebrae, within a vertebra (the neural arch and its corresponding body or centrum), between adjacent neural arches, and between adjacent vertebral centra using the geomorph package v.4.0.5.999 (Adams & Otárola-Castillo, 2013; Adams et al., 2020) in R v.4.3.1 (R Core Team, 2023). We also calculated the coefficient of determination (r²) and the standardized variance of eigenvalues (SVE) (Cheverud et al., 1989; Pavlicev et al., 2009; Porto et al., 2009) for each pair of measurements as alternate estimates of covariation magnitude and for purposes of comparison to other studies; however, these variables do not explicitly test modularity and are discussed in a more limited manner. In addition, these two variables are affected by sample size (Pavlicev et al., 2009; Grabowski & Porto, 2017), which varies considerably by element and element-pair in our sample. Element and element-pair sample sizes are presented in the corresponding results tables. For this reason, we discuss only general patterns in r² and SVE and not specific point estimates. Analyses were carried out independently for each taxon.

The CR provides an estimate of covariation among blocks, standardized by the covariation structure within blocks, and is not affected by sample size or trait number (Adams, 2016). CR values between 0 and 1 can be interpreted as denoting greater integration within blocks than between them (modularity), with values closer to 1 representing greater integration between blocks within a modular structure, while CR values greater than 1 indicate greater integration between blocks than within them (integration) (Adams, 2016). Although CR can be used to assess degree of modularity or integration, it is applied here as a test of modular structure following Adams (2016), e.g. is there modularity or is there integration among blocks. The covariance ratio is calculated using the following equation:

$$\mathit{\text{CR}}=\sqrt{\frac{\mathit{\text{trace}}\left(S_{12}{S}_{21}\right)}{\sqrt{\mathit{\text{trace}}\left(S_{11}^{*}{S}_{11}^{*}\right)\mathit{\text{trace}}\left(S_{22}^{*}{S}_{22}^{*}\right)}}}$$

Here, $S_{11}^{*}$ and $S_{22}^{*}$ represent the covariance matrices of each of the blocks (e.g. the putative modules) being compared (M₁ and M₂), in which the diagonal elements have been replaced by zeroes (Adams, 2016). Meanwhile, $S_{12}$ and $S_{21}$ are the covariance matrices for the combined blocks (Adams, 2016). We ran the modularity.test function in the geomorph package with 999 iterations and a random seed to assess confidence intervals and p-values for each CR estimate (Adams et al., 2020). In this permutation procedure, variables are randomly assigned to modules, after which the CR value is recalculated and the proportion of permuted CR values less than the original CR estimate is treated as the p-value (Adams, 2016). In other words, a non-significant p-value indicates that there are other combinations of variables that form ‘better’, more distinct modules, although these may be fairly random combinations with no biological basis. We assessed significance at p ≤0.05.

The two additional estimates of covariation were calculated as follows. We constructed a variance covariance (VCV) matrix for each module set, which is then converted into a correlation matrix. The r² value is then calculated as the average coefficient of determination for each matrix (Cheverud et al., 1989; Porto et al., 2009). The SVE is calculated from the same correlation matrix using the following equation, in which λ_i is the eigenvalue, N is the number of traits, and N-1 is the maximum possible eigenvalue variance (Pavlicev et al., 2009):

$$\text{SVE}=\frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}{({\lambda }_{\mathrm{i}}-1)}^2}{\mathrm{N}(\mathrm{N}-1)}$$

We compared CR for our first hypothesis using Mantel tests for matrix comparisons due to the complexity of the data. We used the mantel function from the vegan package in R (Oksanen et al., 2024), with the Pearson product-moment correlation and 9,999 iterations. Since different taxa have different numbers of elements, we removed T7 from analyses for Hylobates and Pan, which have 13 thoracic elements, we removed L3 from analyses for Homo and Hylobates, which have 5 lumbar elements, and removed L3, L4, and L5 for Macaca, which has 7 lumbar elements, for inter-taxon comparisons. In each case, we removed the middle elements of the sequence. This was done to preserve as much structural and functional similarity as possible among the remaining elements. For example, Pan has four lumbar elements total, and so for the other taxa we preserved the upper two elements that form part of the thoracolumbar transitional sequence, and the lower two elements that form part of the lumbosacral sequence.

For all other hypotheses, we assessed normality using a Shapiro-Wilk test (S. S. Shapiro & Wilk, 1965) for each set of CR point estimates, and compared variances using a Levene’s Test (Levene, 1960). Based on these results (Supplementary Tables 2–4), we made the decision to use non-parametric Mann Whitney U (Mann & Whitney, 1947) or Kruskal-Wallis (Kruskal & Wallis, 1952) tests for two-group or multi-group comparisons, respectively. Kruskal-Wallis tests were combined with a pairwise Wilcoxon test with a Benjamini and Hochberg correction (Benjamini & Hochberg, 1995).

Results

Patterns among vertebrae

All four taxa display broadly similar patterns of integration and modularity, with strong integration among thoracic elements and among lumbar elements, and modularity between regions (Figure 2, Supplementary Tables 5–8). However, for most point estimates suggesting modularity (CR <1), the confidence interval cannot exclude integration (CR ≥1), and across taxa, only a few CR confidence intervals can do so (Figure 2, Supplementary Tables 5–8). There is general similarity in CR pattern among taxa, with the hominoids being on average more similar to each other than they are to Macaca (R =0.7224–0.7450 versus R =0.6278–0.7262, all p <0.001; Table 2).

Figure 2. Covariance ratios (CR) of whole vertebrae pairs.

Red indicates CR values >1, with deeper colors indicating a larger value, white is centered at CR =1, and blue indicates low CR values <1, with deeper colors indicating a smaller value. Pairs where the confidence interval includes the possibility of modularity (e.g. includes CR =1 and CR <1 in the confidence interval) are boxed within a black outline, and those where the confidence intervals excludes the possibility of integration (e.g. entire confidence interval is CR <1) are boxed within a darker outline and marked with an asterisk (Supplementary Tables 5–8). Dashed gray lines indicate that the vertebral element does not exist in that taxon.

Table 2. Mantel correlations for covariance ratio (CR) across taxa, for whole vertebra pairs.

The Mantel correlation (R) is shown below the diagonal and the corresponding P-value is shown above the diagonal.

	Macaca	Hylobates	Pan	Homo
Macaca	-	<0.001	<0.001	<0.001
Hylobates	0.7262	-	<0.001	<0.001
Pan	0.7036	0.7340	-	<0.001
Homo	0.6278	0.7450	0.7224	-

Across taxa, but most strongly in Homo and Pan, patterns of integration as estimated from CR broadly reflect magnitudes of integration in r² and SVE (R =0.6944–7732, all p <0.001 except for Hylobates CR to SVE at p =0.002; Table 3; Supplementary Tables 9–12). Although in general higher CR values correspond to higher values of r²and SVE, there are no specific values of r²or SVE that match CR thresholds of modularity versus integration or the confidence intervals that exclude either possibility (e.g. no values of r² or SVE are consistently equivalent to CR =1). Patterns of r² and SVE are generally highly similar within taxa (R =0.9519–0.9714, all p <0.001; Table 3), so only r² results are discussed in detail below.

Table 3. Mantel correlations for covariance ratio (CR), r², and the standardized variance of eigenvalues (SVE) across taxa, for whole vertebra pairs.

R is the Mantel correlation.

	Macaca		Hylobates
	R	P-value	R	P-value
r2 to SVE	0.9686	<0.001	0.9649	<0.001
CR to r2	0.5454	<0.001	0.4760	<0.001
CR to SVE	0.5276	<0.001	0.3569	0.002
	Pan		Homo
	R	P-value	R	P-value
r2 to SVE	0.9714	<0.001	0.9519	<0.001
CR to r2	0.7732	<0.001	0.7378	<0.001
CR to SVE	0.7557	<0.001	0.6944	<0.001

Comparing estimates of magnitudes of integration via r², Hylobates is least similar to all other taxa (R =0.4269–0.6480, all p <0.001 except for Pan comparison at p =0.002; Table 4), with Macaca, Pan, and Homo highly similar (R =0.7413– 0.8194, all p <0.001; Table 4). Patterns of r² and SVE suggest greater integration among thoracic elements across taxa, with an additional cluster of greater integration among lumbar elements in hominoids, possibly extending into a thoracolumbar cluster in Hylobates (Supplementary Tables 9–12). However, some of these differences in Hylobates may be related to sample size effects (Supplementary Table 13).

Table 4. Mantel correlations for r² across taxa, for whole vertebra pairs.

The Mantel correlation (R) is shown below the diagonal and the corresponding P-value is shown above the diagonal.

	Macaca	Hylobates	Pan	Homo
Macaca	-	<0.001	<0.001	<0.001
Hylobates	0.6480	-	0.002	<0.001
Pan	0.8194	0.4269	-	<0.001
Homo	0.7413	0.6032	0.8141	-

Patterns within vertebrae

Individual vertebral elements generally display integration between the neural arch and vertebral body (Table 5, Figure 3). The hominoids tend to have values indicating modularity (CR <1) for more individual elements than the macaque, at least for size-corrected data. Differences in CR estimates between full-sized and size-corrected data are significant for Macaca and Hylobates (Table 6). In Hylobates, full-sized data tend to display higher CR and the converse is true for Macaca. The majority of CR estimates are non-significant.

Table 5. Intravertebral covariance ratio estimates and 95% confidence intervals for individual vertebrae.

The covariance ratio(CR) value is followed by the confidence interval in parentheses. When the confidence interval includes CR =1 as a possible value, the result may or may not indicate modularity or integration. CR confidence interval estimates that include CR =1 are highlighted in bold. Only two intervals exclude the possibility of integration, and these are marked with an *.

	Macaca			Hylobates
Vertebra	N	Full-Sized	Size-Corrected	N	Full-Sized	Size-Corrected
C3	92	1.2625 (0.8382–1.7887)	1.1385 (0.6692–1.7207)	69	1.44 (1.0151–2.0401)	0.905 (0.5973–1.7717)
C4	92	1.0345 (0.7163–1.4792)	0.6611 (0.5255–1.2886)	71	1.6421 (0.988–2.8767)	0.7123 (0.5114–1.321)
C5	93	0.796 (0.5365–1.2046)	1.3539 (0.7278–2.0663)	70	1.1587 (0.7373–2.1536)	0.7116 (0.5529–1.262)
C6	94	0.6615 (0.4135–1.3718)	1.2192 (0.6615–2.5233)	67	1.4924 (1.1017–2.1522)	0.7443 (0.459–1.39)
C7	94	0.9372 (0.7188–1.3712)	1.1309 (0.7946–1.9032)	71	1.5795 (1.0437–2.9238)	1.3907 (0.9241–2.08)
T1	91	1.3704 (0.9915–2.0215)	0.747 (0.5462–1.532)	66	1.0901 (0.8264–1.5334)	0.6386 (0.4809–1.4278)
T2	91	1.0205 (0.7718–1.3603)	1.1487 (0.8295–1.7814)	60	1.4645 (1.0913–2.1049)	0.6318 (0.4906–1.29)
T3	90	1.245 (1.0059–1.693)	1.3492 (0.8208–2.4941)	59	1.2177 (0.8793–1.9861)	1.3106 (0.8545–1.9483)
T4	93	1.5513 (1.2547–1.9288)	0.7116 (0.5577–1.5715)	56	1.113 (0.7931–1.6794)	0.8576 (0.6013–1.8121)
T5	95	1.2486 (0.9919–1.5748)	1.1463 (0.7906–1.7713)	55	1.2217 (0.7731–2.2143)	0.9111 (0.5984–1.8312)
T6	96	1.1127 (0.9492–1.3529)	1.0113 (0.6497–2.0336)	47	0.9736 (0.7614–1.4514)	0.8328 (0.6214–1.4164)
T7	90	1.066 (0.8727–1.2739)	1.5684 (0.8101–2.5038)	52	0.7931 (0.6228–1.1904)	0.9419 (0.6505–1.8272)
T8	93	0.9235 (0.7407–1.1428)	1.6029 (0.9539–2.7195)	50	0.8537 (0.598–1.2773)	0.6421 (0.5193–1.3604)
T9	91	1.0193 (0.8326–1.2381)	1.8199 (0.9949–3.2037)	47	0.9288 (0.7125–1.3315)	1.0537 (0.6732–1.9155)
T10	94	1.3291 (1.1008–1.623)	2.0024 (1.1528–3.5167)	46	0.9104 (0.7201–1.2028)	0.9954 (0.6384–2.1312)
T11	94	1.233 (0.9718–1.5144)	1.5556 (0.9105–2.4244)	43	0.9651 (0.7619–1.2466)	0.902 (0.7054–1.4488)
T12	96	0.91 (0.7037–1.1605)	1.2374 (0.8693–1.7852)	38	0.8531 (0.5591–1.2958)	1.7087 (1.0174–2.7719)
T13	-	-	-	39	1.1926 (0.9728–1.461)	1.259 (0.8273–1.8747)
L1	95	0.9142 (0.7353–1.1706)	2.2103 (1.2378–3.0668)	30	1.2214 (0.9312–1.5987)	0.8401 (0.5873–1.3773)
L2	94	1.1027 (0.7982–1.6579)	1.1832 (0.9114–2.1413)	31	1.1602 (0.8948–1.472)	0.6823 (0.526–1.1268)
L3	95	0.9975 (0.7852–1.2887)	1.3406 (1.0129–1.8641)	32	1.2286 (1.0057–1.4385)	0.99 (0.707–1.6269)
L4	90	0.9995 (0.7948–1.2213)	1.247 (1.0076–1.6056)	34	1.1146 (0.9011–1.3566)	0.8392 (0.5687–1.6856)
L5	94	0.997 (0.7677–1.3151)	1.2607 (1.059–1.4947)	34	1.6032 (1.3556–1.9445)	1.2083 (0.6566–2.5506)
L6	96	1.0777 (0.8799–1.4503)	1.6778 (1.3028–2.2629)	-	-	-
L7	94	1.129 (0.8926–1.4163)	1.5424 (1.3426–1.8289)	-	-	-
	Pan			Homo
Vertebra	N	Full-Sized	Size-Corrected	N	Full-Sized	Size-Corrected
C3	72	1.0308 (0.6957–1.4515)	1.6383 (0.9149–2.8562)	93	1.0477 (0.8124–1.3465)	1.0549 (0.611–1.682)
C4	61	1.4594 (1.0378–2.1029)	0.8719 (0.5826–1.4184)	101	0.7728 (0.4295–1.244)	0.3015 (0.2419–1.1328)
C5	67	1.3872 (1.0111–1.6964)	0.7462 (0.4581–1.2114)	89	1.0445 (0.8405–1.4143)	0.6104 (0.4376–1.1069)
C6	62	1.2285 (0.9541–1.8319)	0.804 (0.5704–1.3464)	64	1.0128 (0.7483–1.4652)	0.7891 (0.5848–1.2522)
C7	66	1.2281 (0.9629–2.0702)	1.1734 (0.7239–1.8505)	62	0.9273 (0.6325–1.6767)	1.1221 (0.6654–2.083)
T1	78	1.0638 (0.7287–1.4438)	1.0144 (0.7271–1.8582)	131	1.7852 (0.8593–2.1926)	1.3813 (1.1161–2.559)
T2	73	1.2481 (0.9341–1.9089)	2.5142 (1.2588–3.2418)	120	1.1984 (0.9436–1.5512)	1.5679 (1.0245–2.6662)
T3	72	1.2606 (1.0018–1.5217)	1.1636 (0.7519–2.3503)	103	1.2579 (0.9961–1.6177)	1.0144 (0.7421–1.7167)
T4	73	1.2201 (1.0158–1.4339)	1.3041 (0.8457–2.3997)	106	1.417 (1.1774–1.7859)	1.5957 (1.0174–2.4045)
T5	72	1.1568 (0.9269–1.3519)	1.007 (0.7435–1.6096)	106	1.3532 (1.0022–1.7118)	1.6634 (0.8684–2.6626)
T6	71	1.1695 (0.8853–1.4487)	1.1259 (0.7127–2.3168)	105	1.2395 (0.9467–1.5917)	1.1484 (0.6869–2.0111)
T7	68	1.0908 (0.8411–1.3442)	0.9131 (0.6702–1.5083)	109	1.1708 (0.893–1.4463)	0.7094 (0.4831–1.4604)
T8	69	1.0092 (0.7107–1.2656)	0.9199 (0.7317–1.3725)	113	0.9876 (0.7566–1.2428)	0.8406 (0.6327–1.369)
T9	69	0.8325 (0.55–1.1543)	0.8015 (0.6672–1.193)	115	1.0757 (0.8947– 1.2489)	0.9439 (0.7006–1.4751)
T10	69	0.9453 (0.6765–1.2229)	0.6638 (0.5509–1.0106)	121	1.0054 (0.8326–1.1909)	0.9044 (0.757–1.364)
T11	74	0.9255 (0.7116–1.1854)	0.7517 (0.5957–1.1656)	121	1.3247 (1.1496–1.6143)	1.7891 (1.1519–3.0192)
T12	77	0.9206 (0.6779–1.2151)	0.8095 (0.5959–1.3776)	127	1.3735 (1.1301–1.6404)	1.087 (0.6784–2.0379)
T13	77	1.0523 (0.9369–1.6798)	1.6752 (0.7567–3.1266)	-	-	-
L1	45	1.0685 (0.8244–1.3816)	1.3637 (1.144–1.9165)	91	0.9002 (0.66–1.1982)	1.3076 (1.1657–1.5342)
L2	41	0.7141 (0.5429–1.1945)	1.3228 (1.0498–1.7997)	81	0.8272 (0.6182–1.1488)	1.1716 (0.9664–1.4242)
L3	43	0.8554 (0.6001–1.347)	1.2666 (0.9151–1.6306)	79	0.7069 (0.5045–1.0233)	1.1896 (1.0188–1.4075)
L4	63	1.1357 (0.8687–1.4163)	1.2159 (0.8503–2.0512)	46	0.6334 * (0.5054–0.9933)	1.2418 (1.0826–1.433)
L5	-	1.0308 (0.6957–1.4515)	1.6383 (0.9149–2.8562)	68	0.5707 * (0.4443–0.8956)	1.0961 (0.8472–1.4308)

Figure 3. Covariance ratio (CR) estimates for full-sized data and size-corrected data.

The red line indicates CR =1, and points below that line indicate modularity, although confidence intervals may include the possibility of integration (see Tables 5, 8–9). For adjacent neural arches and adjacent vertebral bodies, the dot is placed on the more cranial element (e.g., for C3-C4 adjacent elements, the dot is placed at C3). Graphs are scaled according to the maximum range found across taxa for comparative purposes, either within full-sized data (0 to 5) and within size-corrected data (0 to 10). Gaps indicate that the vertebral element does not exist in that taxon.

Table 6. Mann-Whitney U test comparisons of results for full-sized and size-corrected estimates of the covariance ratio (CR).

Significant differences are in bold. “D” indicates whether full-sized (FS) or size-corrected (SC) data display larger CR values generally for taxa with significant differences between estimates.

	Intravertebral			Adjacent Neural Arches			Adjacent Vertebral Bodies
	W	P	D	W	P	D	W	P	D
Macaca	427	0.004	SC	238	0.568	-	492	<0.001	SC
Hylobates	129	0.002	FS	221	0.634	-	344	0.016	SC
Pan	229	0.772	-	251	0.455	-	357	<0.001	SC
Homo	266	0.585	-	183	0.356	-	361	<0.001	SC

Differences between taxa are significant only for size-corrected data (Table 7) and consist of differences between Hylobates and Macaca (p =0.0029). Hylobates tends to have lower CR estimates than Macaca across regions. Although there are differences in CR estimates using full-sized and size-corrected data for individual vertebral elements, there is no specific pattern to these differences within or across taxa.

Table 7. Kruskal-Wallis test comparisons of differences in the covariance ratio (CR) between taxa.

Significant differences are in bold. “D” indicates which pairs are significantly different (M =Macaca, Ho =Homo, Hy =Hylobates, P =Pan), with further details provided in the text.

	Intravertebral			Adjacent Neural Arches			Adjacent Vertebral Bodies
	χ2	P	D	χ2	P	D	χ2	P	D
Full-sized data	2.074	0.557	-	7.828	0.050	P-Ma, P-Hy	12.89	0.005	Ma-Hy
Size-corrected data	13.70	0.003	Ma-Hy	4.499	0.212	-	3.948	0.267	-

In full-sized data, Macaca displays weak modularity among mid-cervical elements. Among the hominoids in full-sized data, two specific patterns emerge: weak modularity within elements in the lower thoracic column of Hylobates, and strong modularity within lumbar elements in Homo. Pan displays components of both patterns. However, these estimates are not significant (Supplementary Table 14) and, with the exception of Homo L4 (CR =0.6334, p =0.156) and L5 (CR=0.5707, p =0.113), have confidence intervals that cannot exclude CR ≥1 (Table 5). Only one CR estimate in the full-sized data was significant, for Macaca C6 (CR =0.6615, p =0.008; Supplementary Table 14).

In size-corrected data for Macaca, there are no clear trends in modularity and the majority of vertebrae display intravertebral integration. Meanwhile, the hominoids tend to display modularity in the cervical and thoracic regions, with Hylobates displaying modularity throughout the thoracic region and Pan and Homo displaying modularity in the mid- to lower- thoracic regions. However, the majority of the associated confidence intervals cannot exclude integration (CR ≥1), and only nine estimates of CR were significant (Supplementary Table 14): Hylobates T1 (CR =0.6386, p =0.006), T2 (CR =0.6318, p =0.009), L1 (CR =0.8401, p =0.009), and L4 (CR =0.8392, p =0.032); Pan T10 (CR =0.6638, p =0.022) and T12 (CR =0.8095, p =0.029); and Homo C4 (CR =0.3015, p =0.050), L3 (CR =1.1896, p =0.043), and L5 (CR =1.0961, p =0.045).

Patterns among adjacent neural arches

Adjacent neural arches also display integration (Table 8, Figure 3). For all full-sized data, CR indicates integration (CR >1) and the majority of confidence intervals excluded modularity (CR ≤1). There are seven specific cases using size-corrected data where CR <1, though only two of these estimates are significant (Supplementary Table 14) and CR ≥1 cannot be excluded for any based on the confidence interval: Macaca C3 to C4 (CR =0.8946, p =0.200) and C4 to C5 (CR =0.8590, p =0.133); Pan T12 to T13 (CR =0.9804, p =0.129) and T13 to L1 (CR =0.7965, p =0.005); Homo C4 to C5 (CR =0.8219, p =0.043), C5 to C6 (CR =0.9138, p =0.095), and C7 to T1 (CR =0.9611, p =0.140).

Table 8. Covariance ratio estimates and 95% confidence intervals for adjacent neural arches.

The covariance ratio (CR) value is followed by the confidence interval in parentheses. When the confidence interval includes CR =1 as a possible value, the result may or may not indicate modularity or integration. CR confidence interval estimates that include CR =1 are highlighted in bold.

Macaca				Hylobates
Pair	N	Full-Sized	Size-Corrected	Pair	N	Full-Sized	Size-Corrected
C3-C4	90	1.1538 (0.844–1.6724)	0.8946 (0.4946–1.3027)	C3-C4	68	1.4477 (1.3129–1.6386)	1.4477 (1.3129–1.6386)
C4-C5	90	1.1448 (0.9054–1.6261)	0.859 (0.4501–1.2762)	C4-C5	70	1.4416 (1.2858–1.6494)	1.4416 (1.2858–1.6494)
C5-C6	92	1.5337 (1.3751–1.8862)	1.2541 (1.0703–1.5558)	C5-C6	66	1.6036 (1.4199–1.7792)	1.6036 (1.4199–1.7792)
C6-C7	93	1.4611 (1.3334–1.7624)	1.1579 (0.8944–1.5082)	C6-C7	67	1.5477 (1.3676–1.7488)	1.5477 (1.3676–1.7488)
C7-T1	90	1.6642 (1.4422–1.9507)	1.2157 (0.9682–1.5276)	C7-T1	65	1.8293 (1.5757–2.0486)	1.8293 (1.5757–2.0486)
T1-T2	88	1.9226 (1.5322–2.2825)	1.5343 (1.2124–1.8535)	T1-T2	60	1.623 (1.4276–1.8301)	1.623 (1.4276–1.8301)
T2-T3	86	1.7003 (1.3535–2.0586)	1.4907 (1.0577–1.9938)	T2-T3	56	1.6164 (1.3015–2.0285)	1.6164 (1.3015–2.0285)
T3-T4	88	1.6639 (1.4473–2.0131)	1.8013 (1.2144–2.3164)	T3-T4	53	1.8319 (1.4821–2.2281)	1.8319 (1.4821–2.2281)
T4-T5	93	1.5552 (1.4053–1.7552)	1.5023 (0.9773–1.9926)	T4-T5	51	1.6537 (1.3999–1.9308)	1.6537 (1.3999–1.9308)
T5-T6	95	1.5266 (1.3836–1.7279)	1.874 (1.494–2.2785)	T5-T6	46	1.85 (1.4039–2.4094)	1.85 (1.4039–2.4094)
T6-T7	90	1.4944 (1.3486–1.7307)	1.9934 (1.5417–2.4187)	T6-T7	46	1.8131 (1.4216–2.4332)	1.8131 (1.4216–2.4332)
T7-T8	88	1.4973 (1.3111–1.7663)	2.0717 (1.5859–2.4669)	T7-T8	49	1.6762 (1.3752–2.2867)	1.6762 (1.3752–2.2867)
T8-T9	89	1.6043 (1.3759–1.8991)	2.4852 (1.7448–2.9717)	T8-T9	46	1.7513 (1.3734–2.3379)	1.7513 (1.3734–2.3379)
T9-T10	90	1.7374 (1.4753–2.1153)	2.31 (1.6023–2.6251)	T9-T10	43	1.6396 (1.3634–2.1047)	1.6396 (1.3634–2.1047)
T10-T11	92	1.9151 (1.5731–2.3202)	2.0664 (1.6443–2.2797)	T10-T11	43	1.5452 (1.3432–1.8128)	1.5452 (1.3432–1.8128)
T11-T12	94	1.6663 (1.4736–1.8828)	1.4691 (1.3169–1.6231)	T11-T12	37	1.3705 (1.1405–1.66)	1.3705 (1.1405–1.66)
T12-L1	95	1.4904 (1.409–1.6003)	1.4934 (1.3909–1.6286)	T12-T13	36	1.6482 (1.2979–1.9288)	1.6482 (1.2979–1.9288)
-	-	-	-	T13-L1	28	1.5795 (1.3222–1.8588)	1.5795 (1.3222–1.8588)
L1-L2	93	1.4857 (1.4177–1.609)	1.2261 (0.9174–1.5168)	L1-L2	25	1.5242 (1.3814–1.6836)	1.5242 (1.3814–1.6836)
L2-L3	93	1.494 (1.4071–1.6128)	1.184 (0.9285–1.4627)	L2-L3	26	1.4032 (1.2599–1.5429)	1.4032 (1.2599–1.5429)
L3-L4	90	1.5935 (1.4397–1.7356)	1.471 (1.3031–1.6711)	L3-L4	28	1.4742 (1.3144–1.6584)	1.4742 (1.3144–1.6584)
L4-L5	89	1.5899 (1.4469–1.783)	1.5261 (1.3335–1.7358)	L4-L5	27	1.3059 (1.153–1.5187)	1.3059 (1.153–1.5187)
L5-L6	94	1.5441 (1.3967–1.7889)	1.5867 (1.3782–1.8244)	-	-	-	-
L6-L7	94	1.5847 (1.4287–1.7897)	1.6297 (1.4343–1.8418)	-	-	-	-
Pan				Homo
Pair	N	Full-Sized	Size-Corrected	Pair	N	Full-Sized	Size-Corrected
C3-C4	57	1.6533 (1.3444–2.1002)	1.4867 (1.2441–1.7747)	C3-C4	78	1.3372 (1.2417–1.447)	1.0371 (0.8903–1.1674)
C4-C5	57	1.6397 (1.3663–1.9567)	1.5643 (1.2804–1.9271)	C4-C5	78	1.3273 (1.2248–1.4069)	0.8219 (0.5179–1.0748)
C5-C6	56	1.745 (1.4672–2.0057)	1.3836 (1.185–1.6319)	C5-C6	54	1.3696 (1.2601–1.4604)	0.9138 (0.7557–1.079)
C6-C7	54	1.7395 (1.4768–2.0934)	1.5802 (1.3755–1.8386)	C6-C7	39	1.4447 (1.2744–1.6995)	1.2957 (1.1812–1.4475)
C7-T1	60	1.6615 (1.4353–2.014)	1.8104 (1.4672–2.1087)	C7-T1	59	1.0045 (0.5643–1.565)	0.9611 (0.5938–1.7226)
T1-T2	69	1.658 (1.4229–2.0001)	1.8977 (1.5418–2.2619)	T1-T2	113	1.3866 (0.8943–1.7076)	1.2876 (0.952–2.0725)
T2-T3	66	1.7154 (1.4352–2.0913)	1.8297 (1.4745–2.3126)	T2-T3	99	1.9026 (1.567–2.388)	2.2228 (1.7184–2.8153)
T3-T4	69	1.7483 (1.461–2.2078)	2.4309 (1.8132–3.1157)	T3-T4	91	2.206 (1.724–2.8277)	2.5329 (1.936–2.9599)
T4-T5	70	1.8162 (1.5116–2.4425)	3.2554 (2.1852–4.1086)	T4-T5	92	2.37 (1.8272–3.1491)	2.7096 (2.1386–3.2005)
T5-T6	69	1.9148 (1.5976–2.576)	2.9849 (2.0689–3.9259)	T5-T6	91	2.4601 (1.8984–2.9205)	2.4412 (2.0036–2.9255)
T6-T7	65	1.9455 (1.6024–2.5466)	2.6949 (1.9295–3.441)	T6-T7	94	2.1788 (1.7005–2.6945)	2.2208 (1.7932–2.7266)
T7-T8	63	1.8936 (1.5465–2.4704)	2.4613 (1.8077–3.2016)	T7-T8	99	1.9355 (1.6262–2.3468)	1.8808 (1.5765–2.2792)
T8-T9	65	1.7475 (1.4687–2.191)	2.411 (1.8127–3.1331)	T8-T9	101	1.7054 (1.4806–2.0221)	1.8416 (1.5509–2.2584)
T9-T10	64	1.7432 (1.4753–2.0795)	2.0489 (1.5602–2.8826)	T9-T10	103	1.5219 (1.3894–1.7357)	1.8914 (1.5756–2.2426)
T10-T11	67	1.7241 (1.4482–2.1566)	2.07 (1.5912–2.6705)	T10-T11	106	1.5391 (1.356–1.8289)	1.6475 (1.2753–1.9937)
T11-T12	72	1.8208 (1.4794–2.3762)	2.2007 (1.7115–2.6223)	T11-T12	112	1.8747 (1.5688–2.2454)	1.5915 (1.3394–1.8463)
T12-T13	72	1.1174 (0.7089–1.9297)	0.9804 (0.6028–1.8945)	T12-L1	88	1.9538 (1.6697–2.2)	1.5204 (1.3974–1.6371)
T13-L1	45	1.7724 (1.4625–1.954)	0.7965 (0.4621–1.6833)	-	-	-	-
L1-L2	29	1.5178 (1.3185–1.6384)	1.4687 (1.3071–1.6851)	L1-L2	69	1.4989 (1.3865–1.6527)	1.2103 (1.1143–1.3493)
L2-L3	31	1.5042 (1.3639–1.6384)	1.4819 (1.3573–1.663)	L2-L3	66	1.4701 (1.379–1.5621)	1.2563 (1.1757–1.3521)
L3-L4	39	1.8625 (1.4289–2.1154)	1.4717 (1.2794–1.647)	L3-L4	39	1.4077 (1.3161–1.4984)	1.1977 (1.1527–1.258)
-	-	-	-	L4-L5	35	1.4744 (1.2929–1.7902)	1.3287 (1.2454–1.4627)

When compared to full-sized CR estimates, size-corrected CR estimates tend to be lower in the cervical region across taxa, higher in the upper- to mid-thoracic region, and similar overall in the lumbar region, with no clear inter- or intra-specific patterns. There are no significant differences between full-sized and size-corrected CR estimates within taxa (Table 6). Differences between taxa are significant only in full-sized data, and only for Macaca versus Pan (p =0.012) and Hylobates versus Pan (p =0.033; Table 7). Pan tends to have higher CR estimates than both these taxa, particularly in the thoracic region.

Patterns among adjacent vertebral bodies

Adjacent vertebral bodies also display integration (Table 9, Figure 3). All CR estimates for these paired vertebrae indicate integration (CR >1) for both full-sized and size-corrected data, and no estimates are significant (Supplementary Table 14). With the exception of C3-C4 (CR =1.7823, p =0.653) and C7-T1 (CR =1.4912, p =0.571) in Homo full-sized data, and C7-T1 in Hylobates size-corrected data (CR =0.9054, p =0.648), all confidence intervals exclude the possibility of modularity (CR ≤1) for any vertebral body pairs. Differences between full-sized and size-corrected data are significant in all taxa (Table 6), and size-corrected CR estimates are always bigger. Differences between taxa are significant only for full-sized data, and they are significant only for Macaca and Hylobates (p =0.0045; Table 7).

Table 9. Covariance ratio estimates and 95% confidence intervals for adjacent vertebral bodies.

The covariance ratio (CR) value is followed by the confidence interval in parentheses. When the confidence interval includes CR =1 as a possible value, the result may or may not indicate modularity or integration. CR confidence interval estimates that include CR =1 are highlighted in bold.

Macaca				Hylobates
Pair	N	Full Sized	Size-Corrected	Pair	N	Full Sized	Size-Corrected
C3-C4	90	2.1578 (1.5938–3.1658)	2.1756 (1.3684–3.5772)	C3-C4	68	4.7771 (2.4821–7.5661)	2.8119 (1.8858–5.4111)
C4-C5	90	2.2381 (1.6101–3.091)	2.8494 (1.5233–5.5614)	C4-C5	70	4.2861 (2.1694–7.7134)	2.3904 (1.675–3.5837)
C5-C6	92	1.9063 (1.373–2.7079)	3.2968 (1.468–5.9102)	C5-C6	66	3.0559 (1.7523–5.558)	2.4263 (1.6714–3.7758)
C6-C7	93	1.7916 (1.1351–3.1768)	1.8336 (1.0082–3.8859)	C6-C7	67	3.4983 (2.0778–6.1835)	2.5793 (1.6608–4.0981)
C7-T1	90	1.932 (1.4374–3.1193)	2.6328 (1.5251–4.2148)	C7-T1	65	2.374 (1.5829–4.0925)	1.4774 (0.9054–2.6518)
T1-T2	88	1.8966 (1.4734–2.9451)	2.5184 (1.6815–3.9338)	T1-T2	60	2.3284 (1.7085–3.5041)	2.0874 (1.5522–3.8166)
T2-T3	86	1.9587 (1.5463–2.8756)	3.3591 (2.0676–4.986)	T2-T3	56	2.373 (1.6651–4.6508)	2.9221 (1.6155–4.3249)
T3-T4	88	2.5482 (1.868–3.6433)	3.6557 (2.149–6.3582)	T3-T4	53	2.3745 (1.6773–4.9607)	3.5503 (2.0233–5.0172)
T4-T5	93	2.5148 (1.8888–3.6538)	2.9314 (1.9258–5.2919)	T4-T5	51	2.9199 (1.7972–6.0561)	3.6692 (2.0666–6.5618)
T5-T6	95	2.0084 (1.6678–2.6696)	3.0506 (1.9129–4.7713)	T5-T6	46	2.5094 (1.7883–4.5616)	3.1567 (1.9914–5.4102)
T6-T7	90	1.7588 (1.5009–2.2854)	5.5365 (2.5307–7.6584)	T6-T7	46	1.9632 (1.5671–2.8227)	2.6331 (1.8974–4.2936)
T7-T8	88	1.6205 (1.4004–2.0007)	6.2806 (2.4857–9.0876)	T7-T8	49	1.9319 (1.586–2.7034)	2.6115 (1.757–4.8053)
T8-T9	89	1.5853 (1.3501–1.9804)	5.8391 (2.688–10.0657)	T8-T9	46	2.1072 (1.7004–3.1067)	2.8883 (1.8157–5.2682)
T9-T10	90	1.6404 (1.4537–2.0102)	5.7711 (2.8409–9.7538)	T9-T10	43	1.9902 (1.6066–2.8283)	3.1835 (1.9137–5.5024)
T10-T11	92	1.7552 (1.5581–2.1597)	4.3514 (2.3339–8.5152)	T10-T11	43	1.9064 (1.6024–2.4968)	2.6751 (1.8474–4.1509)
T11-T12	94	1.8434 (1.5919–2.3141)	3.8896 (2.1532–6.3644)	T11-T12	37	1.9526 (1.6479–2.4303)	2.7974 (1.7042–4.4333)
T12-L1	95	1.8696 (1.5576–2.6136)	5.5385 (2.8108–8.7741)	T12-T13	36	1.9768 (1.5839–2.6808)	3.6008 (1.6726–5.7438)
-	-	-	-	T13-L1	28	2.0721 (1.5723–3.1073)	2.8295 (1.6419–4.3931)
L1-L2	93	1.8873 (1.5794–2.6496)	5.1862 (2.6367–8.5655)	L1-L2	25	2.0222 (1.5483–3.0061)	2.0674 (1.6214–3.165)
L2-L3	93	1.8053 (1.5797–2.3463)	3.2196 (2.1345–5.9118)	L2-L3	26	1.8501 (1.5896–2.2627)	1.9625 (1.5266–2.8714)
L3-L4	90	1.6579 (1.4641–2.0358)	2.667 (1.9672–4.026)	L3-L4	28	1.7961 (1.5417–2.0336)	2.4089 (1.7694–3.832)
L4-L5	89	1.6232 (1.4453–1.9441)	1.873 (1.5238–2.5486)	L4-L5	27	1.4411 (1.2081–1.7445)	2.4999 (1.434–4.105)
L5-L6	94	1.7534 (1.5183–2.2612)	1.9192 (1.5655–2.6492)	-	-	-	-
L6-L7	94	1.4458 (1.2123–1.889)	2.0624 (1.629–2.8921)	-	-	-	-
Pan				Homo
Pair	N	Full Sized	Size-Corrected	Pair	N	Full Sized	Size-Corrected
C3-C4	57	3.4237 (2.054–6.3491)	3.1392 (1.8951–4.9346)	C3-C4	78	1.7823 (0.9466–3.1486)	2.4615 (1.1082–8.3932)
C4-C5	57	3.3035 (1.8026–6.3111)	2.4392 (1.6566–3.3003)	C4-C5	78	2.4388 (1.8316–4.4447)	3.2275 (1.9805–5.7303)
C5-C6	56	2.3808 (1.5274–4.5344)	1.7715 (1.1214–2.7534)	C5-C6	54	2.3566 (1.6903–3.7258)	3.5387 (2.1863–5.944)
C6-C7	54	2.5262 (1.5734–5.0706)	1.6425 (1.0206–2.7428)	C6-C7	39	2.707 (1.8194–4.4425)	4.3854 (2.7374–6.7326)
C7-T1	60	2.4214 (1.6827–4.9381)	2.9097 (1.8771–4.299)	C7-T1	59	1.4912 (0.7736–4.7896)	2.129 (1.0322–7.6899)
T1-T2	69	2.171 (1.641–4.3964)	5.5216 (2.3166–7.5573)	T1-T2	113	2.1778 (1.5124–3.0827)	2.1939 (1.4422–7.1588)
T2-T3	66	2.0843 (1.5747–3.823)	8.318 (2.8019–11.5186)	T2-T3	99	2.365 (1.8467–3.4067)	4.1875 (2.4187–6.5384)
T3-T4	69	1.8805 (1.5577–2.6787)	8.2428 (3.0057–12.0714)	T3-T4	91	2.4706 (1.8984–3.6407)	4.5236 (2.36–8.2419)
T4-T5	70	1.7581 (1.5296–2.2597)	4.6644 (2.4569–6.9748)	T4-T5	92	2.2525 (1.8445–3.026)	5.7956 (2.8464–9.6211)
T5-T6	69	1.6631 (1.4891–2.0496)	3.9796 (2.2–6.6446)	T5-T6	91	2.3174 (1.8358–3.505)	9.8459 (2.5624–11.7527)
T6-T7	65	1.7215 (1.5242–2.2618)	3.7748 (2.1568–6.5163)	T6-T7	94	1.9724 (1.7154–2.4196)	3.303 (1.961–7.0477)
T7-T8	63	1.6571 (1.4755–2.1208)	2.7747 (1.9816–4.3507)	T7-T8	99	1.8924 (1.6677–2.2699)	2.7052 (1.8761–6.3487)
T8-T9	65	1.6275 (1.4931–1.9128)	2.161 (1.752–2.9948)	T8-T9	101	1.7963 (1.5852–2.1007)	3.1065 (2.0796–5.2632)
T9-T10	64	1.5715 (1.4752–1.7189)	1.8353 (1.5621–2.442)	T9-T10	103	1.7226 (1.5533–2.0107)	2.9874 (2.0416–4.4462)
T10-T11	67	1.6446 (1.4999–1.8786)	2.0318 (1.7009–2.6077)	T10-T11	106	2.1943 (1.8085–2.9617)	5.6988 (2.9409–8.1062)
T11-T12	72	1.8667 (1.6061–2.402)	2.3648 (1.8324–3.9437)	T11-T12	112	2.3943 (1.8984–3.5389)	6.7727 (3.2215–10.6706)
T12-T13	72	1.8818 (1.5897–2.3239)	2.4599 (1.7967–3.9869)	T12-L1	88	2.1127 (1.7619–2.7576)	2.0424 (1.4125–3.8486)
T13-L1	45	1.8578 (1.5478–2.433)	2.2558 (1.6379–3.3208)	-		-	-
L1-L2	29	1.8105 (1.4072–2.7596)	2.6853 (1.8007–4.8469)	L1-L2	69	1.9393 (1.6497–2.5518)	1.8804 (1.5559–2.5957)
L2-L3	31	1.7689 (1.4516–2.3458)	2.4737 (1.7801–3.8791)	L2-L3	66	1.8801 (1.6036–2.4772)	2.1045 (1.7051–2.9471)
L3-L4	39	1.6498 (1.3262–2.2591)	2.6997 (1.6662–5.1817)	L3-L4	39	1.7656 (1.5495–2.2438)	1.8724 (1.5662–2.4289)
-	-	-	-	L4-L5	35	1.6519 (1.323–2.4374)	2.2707 (1.717–3.0996)

Overlaps among single elements, adjacent neural arches and adjacent vertebral bodies

We compared overlaps in CR confidence intervals for full-sized and size-corrected data (Supplementary Table 15). In general, CR confidence intervals of single elements overlap substantially with those of both adjacent neural arches and of adjacent vertebral bodies, particularly for size-corrected data. For full-sized data, all taxa display gaps in these overlaps in the thoracic and lumbar regions, but the location and extent of the overlap varies between taxa. These gaps are most extensive in Pan and Homo full-sized data. Homo also displays a gap across the mid-cervical region for full-sized data. In general, CR of single elements tends to be lower than that of adjacent neural arches. The gaps in these overlaps remain in a reduced form in the size-corrected data. In general, there are overlaps in the CR confidence intervals of adjacent neural arches and those of adjacent vertebral bodies. The main exceptions are in the size-corrected data, where there is a gap in the lower thoracic and upper lumbar region of Macaca, the cervical region in Hylobates and Homo, and the lumbar region across the hominoids. Notably, the cervical gap is present in the Homo full-sized data as well. In general, CR of adjacent vertebral bodies tends to be higher than that of adjacent neural arches.

Magnitude of covariation

There are some significant relationships of sample size to r² and standardized variance of eigenvalues (SVE), principally in Hylobates and in size-corrected data (Supplementary Table 13). Full-sized estimates for r² and SVE tend to be higher than size-corrected estimates, though absolute ranges do not vary much (Supplementary Tables 16–17). Within taxa, individual vertebrae tend to display the lowest r² and SVE values compared to adjacent neural arches or adjacent vertebral bodies. This effect is present across data types but most marked for full-sized data. When comparing taxa, all taxa display similar overall values of r² and SVE for intravertebral integration, and absolute values are somewhat lower for size-corrected data (Figure 4, only r² shown). For both adjacent neural arches and adjacent vertebral bodies, Pan tends to show the strongest integration for full-sized data, but this effect is reduced for size-corrected data, where the hominoids are largely similar (Figure 4, only r² shown). For adjacent neural arches, the mid-thoracic and lumbar regions tend to show somewhat higher integration, though in Macaca this effect is substantially reduced in size-corrected data (Figure 4, only r² shown). For adjacent vertebral bodies, the cervical region tends to show the weakest integration (Figure 4, only r² shown).

Figure 4. r² estimates for full-sized data and size-corrected data.

For adjacent neural arches and adjacent vertebral bodies, the dot is placed on the more cranial element (e.g., for C3-C4 adjacent elements, the dot is placed at C3). Graphs are scaled according to the absolute possible range for r² of 0 to 1. Point estimates are provided in the supplementary materials (Supplementary Table 16). Gaps indicate that the vertebral element does not exist in that taxon. SVE displays generally similar patterns and is not shown (Supplementary Table 17).

Discussion

Our first hypothesis, of integration among nearby vertebrae and modularity among distant vertebrae, was partially supported. Vertebrae are generally integrated with other adjacent or nearby vertebrae. Thoracic vertebrae in particular are definitively integrated with one another across taxa, although the extent of the thoracic cluster varies, with Hylobates and Pan displaying the most extensive versions of this cluster (Figure 2). The shared thoracic cluster likely reflects constraints related to the specific functions of the thoracic vertebrae, which support the ribcage and its role in respiration, and thus must maintain a balance between rigidity and flexibility (Liebsch & Wilke, 2018; Jones et al., 2019; Martín-Serra et al., 2021). In primates, these functions are supported by anatomical adaptations such as largely overlapping spinous processes and coronally-oriented post-zygapophyses that are embedded within the laminae, both of which serve to limit motion. Definite clusters of integrated cervical and lumbar vertebrae also exist, though again the extent of these clusters varies across taxa. In Pan and Homo, the lumbar clusters occur among sets of two or three nearby vertebrae, rather than among all lumbar vertebrae, and may not represent a lumbar cluster per se. In Macaca and particularly in Hylobates, the lumbar cluster is more extensive, extending to include the lower thoracic vertebrae. Previous studies have suggested that the lower thoracic and lumbar vertebrae may be variably recruited for locomotor function, resulting in divergent patterns of modularity and disparity across taxa (Jones, Benitez, et al., 2018), and our results are consistent with that suggestion. For example, the extensive degree of thoracolumbar integration in Hylobates, which has been identified consistently across studies, may be more specifically related to evolutionary changes related to the need for stability during high-speed brachiation (Jung et al., 2021; Villamil & Middleton, 2024a). Overall, the pattern of definitively integrated clusters (cervical, thoracic, lumbar) is consistent with patterns of regionalization in the mammalian column.

Distant whole vertebrae pairs (e.g. cervico-thoracic, cervico-lumbar, or thoraco-lumbar pairs) tend to display point estimates that indicate modularity. However, for the majority of vertebrae pairs, neither integration nor modularity can be ruled out. In other words, potentially all vertebrae are integrated with each other. General integration among vertebrae may reflect the shared processes of vertebral development, which rely on the expression and coexpression of Hox genes as well as a variety of shared signaling mechanisms (Wellik, 2007; Lewis et al., 2009; Mallo et al., 2010; Mallo, 2018; Diaz-Cuadros et al., 2021). If so, then rather than evolving integration as a response to shared function, as proposed by Cheverud (1996), generalized integration may be the default or ancestral state, with modularity among elements evolving in response to selection pressures, as potentially observed in the lumbar region of Homo in this study.

Our results are contrary to Jones, Benitez, et al.’s (2018) finding of widespread modularity in the mammalian vertebral column. This difference may be partially because of their sampling procedures, which included a subset of 5 vertebrae from 52 taxa, with one specimen per taxon representing each major group of mammals, which may obscure clade-specific patterns at lower levels (Jones, Benitez, et al., 2018). Our results are also incongruent with previous findings of generalized modularity in primates (Jung & Von Cramon-Taubadel, 2022), and again this difference may be due in part to Jung and Von Cramon-Taubadel’s (2022) sampling procedures, which include the use of multiple species per genus for some genera, and to their much lower sample sizes (as low as 8 for some genera). Further, although other authors found that hominoids display greater modularity than macaques (Arlegi et al., 2020; Jung & Von Cramon-Taubadel, 2022), that finding is not well supported here based on our confidence intervals. Increasing the number of measurements and representation of vertebral morphology may narrow our confidence intervals and clarify this point. However, our result is generally in agreement with that of Martín-Serra et al. (2021), who found that the vertebral column of carnivorans is largely integrated.

Finally, the pattern of integration and modularity identified here is broadly similar to that identified by Villamil and Middleton (2024a) using Hansen and Houle’s (2008) integration statistics on the same dataset, suggesting broad correspondence between different measures of integration and modularity.

Our second hypothesis, of modularity within vertebrae, was generally not supported. The majority of vertebral elements display intravertebral integration of the neural arch and vertebral body. Some vertebrae may display modularity, but with two exceptions (Homo L4 and L5) confidence intervals cannot rule out integration. However, although individual vertebrae tend to be integrated, the magnitude of integration within these individual vertebrae, as measured by r² and the standardized variance of eigenvalues (SVE), tends to be lower than the magnitude of integration among adjacent neural arches or adjacent bodies. In addition, although hominoids tend to display more point estimates indicating intravertebral modularity, confidence intervals cannot rule out integration. Again, our results are inconsistent with those of other authors regarding differences between hominoids and other taxa (Arlegi et al., 2020; Jung & Von Cramon-Taubadel, 2022), potentially due to their reliance on point estimates rather than confidence intervals for comparisons.

The only well-supported modular vertebrae were L4 and L5 in Homo. These two elements contribute directly to lumbar lordosis and the lumbosacral angle in humans (Been et al., 2010), which facilitate our adaptation to upright posture and bipedalism (Lovejoy, 2005). Increased intravertebral modularity may thus be linked to the evolution of divergent morphologies in the neural arches and vertebral bodies of these elements compared to other primates.

Considering only point estimates of modularity, we identified several potential modular clusters. We identified a potential mid-cervical cluster of intravertebral modularity, variably present across taxa in full-sized and size-corrected data. A mid-cervical pattern could be associated with nervous system structures such as the phrenic nerve or brachial plexus, as has been hypothesized in previous studies assessing cervical integration or evolution (Buchholtz et al., 2012; Villamil & Middleton, 2024a). Intravertebral modularity in this region may thus facilitate adaptation to the divergent needs of structural support for the head (via the vertebral bodies) and space and structural support for the nerves (via structures of the neural arch). Differences between full-sized and size-corrected estimates of modularity may reflect species-specific differences related to size and position of the head, or to nerve structure as it relates to the respiratory system or upper limb. For example, hominoids display high rates of evolution in the brachial plexus, likely linked to locomotor evolution (Shearer, 2019). This process may have resulted in a breakdown of vertebral integration at the developmental level, since peripheral nerves originate in the somites of their corresponding vertebrae (Goethe, 1790; Onai et al., 2015). A mid-cervical pattern could also be associated with the specific biomechanical requirements of cervical lordosis, which is found across mammals (Graf, de Waele, et al., 1995, 1995; Vidal et al., 1986). In addition, we identified a potential lower thoracic cluster of intravertebral modularity in the hominoids, again variably present in full-sized and size-corrected data. This region of intravertebral modularity is potentially associated with the presence of the thoracolumbar transitional region and the diaphragmatic vertebra. The diaphragmatic vertebra marks the transition between thoracic-like and lumbar-like anatomies, with thoracic-like pre-zygapophyses and lumbar-like post-zygapophyses, and consequently marks a shift in the functional characteristics of the column (Filler, 1986; Williams, 2012; Jones et al., 2020). Typically, the thoracic column displays greater rotation and reduced sagittal flexion-extension when compared to the lumbar column (Williams, 2012; Kinoshita et al., 2023; Belyaev et al., 2024). The thoracolumbar transition is also associated with the location of expression of HoxPG10 during development (Wellik & Capecchi, 2003; Wellik, 2007). Intravertebral modularity in this region may be associated with one or more of these factors. Although we reiterate that our confidence intervals cannot exclude integration, our finding of potential intravertebral modularity in this thoracolumbar transitional region is consistent with Martín-Serra et al.’s (2021) finding that the diaphragmatic vertebra is the least integrated vertebra in the carnivoran vertebral column.

Our results disagree with those of Randau and Goswami (2017b) and Figueirido et al. (2023), who found that the presacral vertebrae of carnivorans display two distinct modules for the vertebral body and neural arch (i.e. intravertebral modularity). It may be that primates, having more diverse patterns of locomotion and positional behavior compared to other mammals (Hunt et al., 1996; Fleagle & Lieberman, 2015; Granatosky, 2020), have undergone selection for different patterns of integration and modularity than other mammals. Alternately, it may be that a pattern of modularity is only present in carnivorans and has specifically evolved in that lineage. However, although our module hypotheses were broadly similar, these previous studies used 3D landmark data rather than linear data, which may have influenced these different results (Randau & Goswami, 2017b; Machado et al., 2019; Figueirido et al., 2023). Nonetheless, even though Randau and Goswami’s (2017b) CR estimates point to modularity within vertebrae, point estimates are relatively high (0.727–0.983) and confidence intervals may have included CR ≥1. Figueirido et al.’s (2023) estimates appear to be within similar ranges, although they do not report numeric CR values or their intervals.

Our third hypothesis, of broad integration among adjacent neural arches and adjacent vertebral bodies, was supported using both size-corrected and full-sized data, with all or almost all CR >1, and the majority of confidence intervals excluding the possibility of modularity. Estimates of r² and SVE also broadly support this hypothesis. Unlike Martín-Serra et al. (2021) and Randau and Goswami (2017a, 2017b), who found distinct patterns of modularity in the thoracolumbar transitional regions of the canid and felid vertebral columns, respectively, we found no such pattern here in primates. However, we did identify a pattern of particularly low magnitude of integration in this transitional region for individual vertebrae and adjacent neural arches, even if CR values could not confirm modularity. As noted above in our discussion of our second hypothesis, intravertebral modularity in the thoracolumbar region, and weak integration overall, may reflect the effects of the expression pattern of HoxPG10, which suppresses rib formation (Wellik & Capecchi, 2003; Carapuço et al., 2005; Mallo et al., 2010), among other factors.

Taken together, our combined results suggest that it is likely we are capturing a similar phenomenon as previous authors, but it may be reflecting differently in our dataset as a result of methodological differences or real biological differences between taxa. It is possible, for example, that all mammals experience selective pressures that favor modularity in the thoracolumbar transitional region because of its unique functional characteristics, but these occur via different processes in different taxa—shifts in intravertebral modularity in primates, and shifts in intervertebral modularity in carnivorans. Further study in additional taxa may clarify this point.

Our results highlight the overall development and function of the vertebral column as a single structure and suggest that vertebrae need to be considered in sequence rather than as individual elements, as intervertebral covariation interactions may be as important as or even more important than intravertebral ones. In general, our findings reflect the broadly similar genetic-developmental patterns that drive the formation of the vertebral column. However, it may be that this result is limited to primates and future studies should focus on other taxa, so that we may parse the differences between primates and carnivorans.

Although we were not explicitly testing the effects of size, our results confirm that size is a pervasive factor affecting integration among elements, in particular vertebral elements. A similar effect was found by Jones, Benitez, et al. (2018). However, although others have suggested that the inclusion of size inflates estimates of integration (Goswami & Polly, 2010; Machado et al., 2019), our results suggest that while the inclusion of size may lead to higher estimates of the magnitude of integration, it does not necessarily result in assessments of more integration (less modularity) among structures, as measured by the covariance ratio (CR). This difference may be in part a result of the mathematical aspects of calculating the CR, as size-correction alters the variances and covariances of each trait, which will affect the numerator and denominator differently in the calculation of this variable. In comparison, size correction in variables such as r² and SVE removes the greatest component of variation and covariation overall. Alternately, the inclusion of size may have variable effects on integration in different anatomical regions, which would be consistent with findings in the mammalian skull (Marroig et al., 2009; Villamil, 2021). Regardless, our results support the assertion that size is an important component of organismal adaptation (Calder, 1984; Bookstein, 2009), as also suggested in the case of the vertebral column by previous findings that size is the most heritable component of vertebral form (Villamil et al., 2024), and should not be indiscriminately removed from analyses. For example, full-sized data point to distinct patterns of modularity in the vertebral columns of Hylobates and Homo, with Hylobates potentially displaying some weak modularity within vertebrae in the mid- to lower-thoracic region, and Homo potentially displaying modularity in the lumbar region, though most of these modularity estimates are not significant. However, these two taxa have unique locomotor behaviors even for the behaviorally diverse primates, which highlights how functional demands regarding weight-bearing and muscle attachment areas may be particularly affected by body size. Broad developmental patterns, on the other hand, are likely to be more uniformly affected by body size changes (Mitteroecker & Bookstein, 2009). These results suggest that size should be included or excluded from analyses of modularity and integration on a case by case basis, according to the specific hypotheses to be tested, as was suggested by Machado et al. (2019). For example, hypotheses focused on identifying developmental patterns may be better tested with size-corrected data, in order to account for the global effects of size changes, while hypotheses focused on functional questions, where body size may have a significant effect on function, may be better tested with full-sized data.

Limitations of our study include the use of a limited number of linear measurements. We used linear data in order to maximize our sample depth and scope, which included approximately 10,300 individual vertebral elements. It is possible that having dense landmark sampling would provide stronger support for our preliminary findings of modularity in specific regions, or that it would point to different modularity and integration patterns altogether (Machado et al., 2019). Future studies should address the distinctions between linear and non-linear estimates of modularity and integration in the vertebral column so that we can better understand and interpret vertebral modularity.

Conclusions

Our findings indicate that vertebrae are broadly integrated in catarrhine primates. Whole vertebrae are integrated across the column, with a definite cluster of intervertebral integration in the thoracic region. Our findings do not support the assertion that there is a generalized mammalian pattern of intravertebral modularity (modularity between the neural arch and its corresponding vertebral body) or of modularity among vertebral elements. Instead, we find that structures within individual vertebrae are generally integrated, and that there is generalized integration between adjacent vertebral elements, particularly among adjacent neural arches and adjacent vertebral bodies. Whether these are unique primate patterns, or represent broader mammalian patterns, is not clear. Although Jones, Benitez, et al. (2018) included primates in their broad mammalian sample, more studies at the species or genus level of both primate and non-primate taxa will help address the question or whether integration is a derived condition within primates.

Overall, our results find both shared and divergent patterns of integration and modularity in the catarrhine vertebral column, though most specific estimates of modularity are weakly supported. There are trends towards intravertebral modularity in the mid-cervical region, which may be associated with the phrenic nerve or brachial plexus, important nervous system structures that emerge in this region. However, there is no indication that hominoids have overall greater modularity between elements compared to Macaca, whether vertebrae are considered as a whole or whether only specific vertebral structures are considered. Hominoids do tend to display more point estimates of intravertebral modularity than Macaca, although these are not supported by the confidence intervals. There are also trends towards intravertebral modularity in the lower thoracic region among hominoids, perhaps reflecting the unique functions of this transitional region in spinal mobility and the transition away from the ribcage. Homo in particular definitely displays modularity within the lower lumbar elements. Increased modularity within these elements may be linked to adaptation in the hominoid vertebral column, particularly as it relates to orthograde posture and unique locomotor behaviors such as brachiation and bipedality (Fleagle & Lieberman, 2015), as has been suggested for other postcranial regions (Young et al., 2010; Grabowski et al., 2011). Modularity may also be linked to the wide variation in thoracolumbar counts in these taxa (Williams et al., 2016), perhaps reflecting fewer constraints.

Data availability:

The data used for this study are available at https://doi.org/10.5061/dryad.v6wwpzh17 Human data are only partially available according to the policies of the institutions where these data were collected.