BACKGROUND
numerous studies have demonstrated that organisms can be partitioned into sets of phenotypic traits or structures that show coordinated patterns of variation or evolution.
these sets of traits, termed phenotypic modules, can be defined as units composed of multiple traits that display high levels of covariation with other traits within that unit, but relatively weak covariation with traits outside of the unit.
the related concept of integration refers to the overall magnitude of covariation of phenotypic traits, and can refer to a single module, which would be expected to display relatively high within-module integration, or may span multiple modules or structures .
the integration of traits, and their organisation into discrete phenotypic modules, has been hypothesised to arise and/or evolve as a product of shared developmental origin or pathways, genetic pleiotropy, or common function  <cit> .
strong integration within modules, and reduced integration between modules, is further hypothesised to promote coordination among functionally-related traits, while allowing independence and differential specialization of distinct modules .
with its serial organisation and composition of vertebral units, distinguishable morphological differences among regions , and direct association of those regions with expression sites of genes in the hox family, the presacral axial skeleton would appear to encapsulate the concepts of regionalisation and modularity .
although regionalisation of the vertebral column can be observed in amniotes in general  <cit> , the mammalian axial skeleton shows the greatest differentiation in regional vertebral shape .
this increased divergence is accompanied by strict constraints in regional vertebral number, particularly in the cervical region with seven vertebrae present in almost all of the ~ <dig> mammalian species.
total presacral vertebral count is also highly conserved , although some variation does occur  <cit> .
this invariability with regards to vertebral count has been suggested to signal strong canalisation  and developmental stability in the axial skeleton, and is thought to have evolved early in mammalian history  <cit> .
additionally, rather than being the target of selection themselves, highly fixed vertebral numbers in mammals may reflect developmental constraints related to the muscularisation of the diaphragm and the advantages of involving the lumbar region in abdomen expansion during inspiration and in sagittal bending during locomotion  <cit> .
in addition to the almost universally fixed count of seven vertebrae in the cervical region in mammals, species of the order carnivora also show little variation in thoracolumbar count, generally between  <dig> and  <dig> vertebrae  <cit> .
moreover, some families, such as felidae , display absolutely no variation in vertebral numbers between taxa: all felid species present  <dig> presacral vertebrae which are traditionally divided into the three main vertebral column regions  by clear morphological differences .
in accordance with the observed trade-off between vertebral count invariability and high morphological disparity, both linear and landmark-based analyses of vertebral shape have shown evident functional regionalisation in the axial skeleton of felids.
these analyses revealed regions which differ in magnitude of phylogenetic and ecological signal  and both ontogenetic and evolutionary allometric scaling  <cit> .
specifically, the highest covariation between vertebral shape and prey size choice or locomotory mode  were found in the posterior region of the vertebral column, composed of the vertebrae caudal to the posterior attachment of the diaphragm, from t <dig> to l <dig>  conversely, vertebrae in the cervical region displayed high phylogenetic signal and little significant ecological signal  <cit> .
these examples of conspicuous morphological and functional regionalisation are strong indicators of modularity in the vertebral column, and not surprisingly, modularity has indeed already been described, or at least suggested, at different levels within the mammalian axial skeleton .
one example of a hypothesised vertebral module is composed of the mid-cervicals c <dig> to c <dig>  these vertebrae, whose somites have migratory muscle precursor cells which are committed to diaphragm transformation, have been suggested to be involved in the muscularisation of the septum and consequent fixed cervical number across almost all mammals  <cit> .
a larger hypothesised module stems from the relatively fixed count of total thoracolumbar vertebrae and has been suggested to arise from close association of these two regions, with any changes in regional vertebral number being counteracted by the inverse change in the opposite series, and thus no change to the total count   <cit> .
our previous studies of vertebral shape evolution in felids have already suggested some hypotheses of modularity specific to this study system.
the observation of regionalised patterns of allometric scaling in a linear morphometric study both supported the mid-cervical vertebral module and suggested the presence of three additional modules: an anterior cervicothoracic module, a lumbar module, and a functional ‘anticlinality module’ composed of the t10-t <dig> vertebrae  <cit> .
additionally, we have previously demonstrated that presacral vertebral shape in felids is driven by the developmental origins of vertebral components, with two morphological modules found in adult vertebral shape: the ‘centrum’ and the ‘neural spine-related’ modules .
interestingly, this model of modularity, although widespread through most the presacral column, was not supported in vertebrae that are positioned immediately at or adjacent to the borders of morphological vertebral column regions: specifically, c <dig>  t <dig>  t <dig>  l <dig> and l <dig>  this observation led to the suggestion of a disruption of developmental modularity – or a functional overprint – in order to maintain the larger modular organisation of the vertebral column  <cit> .
although there have been recent additions to the literature on the morphological, biomechanical and developmental changes to the vertebral column in mammals or across vertebrates in general , much is yet unknown on its evolution and how patterns of trait integration or modularity may affect its response to selection  <cit> .
here we analyse patterns of shape covariation across the presacral vertebral column in order to quantify the modular organisation of the axial skeleton in felids.
specifically, we use three-dimensional geometric morphometrics to describe presacral vertebral shape and quantify intervertebral integration with pairwise comparisons of presacral vertebrae using phylogenetic two-block partial least square analysis .
the results of the pairwise pls analyses were used to test whether specific sets of vertebrae show higher magnitude of shape integration  within the set than with vertebral units outside of the set, therefore forming a ‘module’ .
the hypothesised intervertebral modules assessed with pairwise pls results were drawn from the literature and are as follows : 1) the ‘traditional regions’ hypothesis: traditional regional boundaries  in the felid vertebral column form discrete morphological modules  <cit> ; 2) the ‘cervicothoracic and lumbar modules’ hypothesis: two modules composed of multiple vertebrae that share a common allometric pattern  <cit>  can be found in the presacral axial skeleton: an anterior cervicothoracic module  and a lumbar module   <cit> ; 3) the ‘thoracolumbar’ hypothesis: thoracic and lumbar vertebrae show high covariation  <cit> ; 4) the ‘anticlinality’ hypothesis: vertebrae t <dig> to t <dig> compose an ‘anticlinality module’  <cit> ; and 5) the ‘developmental model disruption’ hypothesis: boundaries of modular organisation of the vertebral column match vertebral positions where the intravertebral developmental two-module  model is not supported, specifically at the edges of the c <dig> – c <dig> cervical module, between cervicals and thoracics , the division of the vertebral column into pre- and postdiaphragmatic regions at t <dig>  and at the last two presacral vertebrae l <dig> and l <dig>  <cit> .fig.
<dig> illustration of the five hypotheses of intervertebral phenotypic modularity tested here.
black rectangles illustrate sets of vertebrae which are hypothesized to show high integration among themselves and, therefore, to represent a module.
see text for detailed description of hypotheses.
hypothesis 1: traditional regions.
hypothesis 2: cervicothoracic and lumbar modules.
hypothesis 3: thoracolumbar module.
hypothesis 4: anticlinality model composed of vertebrae t <dig>  t <dig> and t <dig>  hypothesis 5: developmental model disruption.
c, t, and l stand for cervicals , thoracics , and lumbars , respectively.
filled circles describe landmarked vertebrae
we further conducted separate analyses of intervertebral integration for the two intravertebral developmental modules .
specifically, the same pairwise phylogenetic pls analyses were conducted across the presacral vertebral column, but traits were limited to those from either the neural spine or the centrum  <cit> .
following from our previous results showing the widespread developmental two-module model of intravertebral covariation, this latter analysis allows us to assess if the patter of intervertebral covariation across the vertebral column is the same for the whole vertebral morphology and for when only trait units regarding each of these modules are considered .
RESULTS
vertebral shape covariation
phylogenetic pls analysis demonstrated that  <dig> out of the total  <dig> pairwise analyses were not significant , suggesting extensive modularity of the presacral vertebral column.
the remaining  <dig> significant pairwise analyses allowed for identification of sets of vertebrae which presented particularly strong within-group covariation .
according to these results, six sets of highly covarying vertebrae were identified as follows: 1) c <dig> to t1; 2) c <dig> to t2; 3) t <dig> to t8; 4) t <dig> to t11; 5) t <dig> to l7; and 6) a set showing covariation between c <dig> to c <dig>  and t <dig> to l <dig>  with the exception of the pairwise comparisons between c <dig> and the lumbars l <dig> and l <dig>  and c <dig> and l <dig> table  <dig> results of phylogenetic partial least squares analysis of all landmarks.
above diagonal cells show the pairwise covariation values  between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction.
results in bold and in grey shaded cells show significant covariations and suggested modules, while results in italics and with white shaded cells are not significant
after benjamini-hochberg correction , the number of covariation tests that were not significant increased to  <dig>  leaving  <dig> significant results.
those tests that were rendered not significant after this correction were concentrated between the first cervicals  and c <dig> and t <dig>  c <dig> and the end-thoracics and lumbars, and some of the covariation results between the pre-diaphragmatic thoracics .
thus, the overall pattern of intervertebral modularity was similar after correction for multiple comparisons.
covariation across centrum versus neural spine modules throughout the vertebral column
centrum: results from the phylogenetic pls on centrum-only landmarks supported modules largely similar to those found when whole vertebral morphology was analysed: 1) c <dig> – t <dig>  with three exceptions in pairwise comparisons between c <dig> and t <dig>  c <dig> and c <dig>  and c <dig> and t <dig>  formed a cervical and first thoracics set; and 2) t <dig> to l <dig> composed a set with very strong within module covariation .
however, other vertebral combinations were also apparent: 3) t <dig> - l <dig> vertebrae; 4) between c <dig> – c <dig> and t <dig> – l <dig>  with the exception of t <dig>  which only presented significant shape covariation with c <dig> and c <dig> among the cervicals; and 5) c <dig> and every other vertebra included in this analyses, with the exception of c <dig> table  <dig> results of phylogenetic partial least squares analysis of landmarks concerning the ‘centrum’ module.
above diagonal cells show the pairwise covariation values  between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction.
results in bold and in grey shaded cells show significant correlations and suggested modules, while results in italics and with white shaded cells are not significant
correction of this analysis’ significance level with the benjamini-hochberg procedure reduced and rendered non-significant most pairwise comparisons between c <dig> – c <dig> and t <dig> – l <dig>  but had little effect on most other modules .
neural spine
there were fewer significant pairwise covariation results from the phylogenetic pls on neural spine-only landmarks than from the centrum-only analysis .
the significant pairwise tests on neural spine-only landmarks displayed four distinct modules: 1) between c <dig> and c <dig>  with the exception of c4; 2) between t <dig> and t11; 3) between vertebrae in the t <dig> – l <dig> region; and 4) between the cervicals c <dig> – c <dig>  with the exception of c <dig>  and t <dig> – l <dig>  benjamini-hochberg correction did not change these patterns and mainly reduced the covariations between the cervicals and the vertebrae in the t <dig> – l <dig> region and other vertebral pairs in the thoracic region .table  <dig> results of phylogenetic partial least squares analysis of landmarks concerning the ‘neural spine’ module.
above diagonal cells show the pairwise covariation values  between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction.
results in bold and in grey shaded cells show significant covariations and suggested modules, while results in italics and with white shaded cells are not significant
discussion
the results presented here provide new information on the structural organisation of the vertebral column in felids, and potentially mammals in general.
in light of the results presented here, the ‘traditional regions’ hypothesis  and the ‘cervicothoracic and lumbar modules’ hypothesis  could be rejected or considered insufficiently explanatory.
although high covariation was found between vertebrae within each of these regions, those either did not include all or most vertebrae which compose the regions or, more commonly, sets of highly covarying vertebral shapes were inclusive of vertebrae beyond the traditional boundaries.
specifically, in all of the analyses performed, with the exception of the phylogenetic pls of the neural-spine landmarks, covariation in the anterior portion of the axial skeleton included high pairwise covariation between cervicals and the first thoracics.
additionally, all cervicals analysed here, with the exception of c <dig> displayed high covariation with the last thoracics and lumbar vertebrae.
a distinct module composed of vertebrae in the cervicothoracic boundary  was found.
a developmental covariation had already been suggested for these units based on the migration of cells from somites bound to the forelimbs, which may additionally have been involved in the first evolutionary steps that contributed to the muscularisation of the diaphragm  <cit> .
due to the lack of vertebrae c <dig> and c <dig> in our dataset, it was not possible to test for higher covariation between those and c <dig>  composing the suggested c <dig> – c <dig> developmental module in mammals  <cit> .
nevertheless, c <dig> presented very high covariation with both c <dig> and c <dig>  indicating that a c <dig> – c <dig> set would likely not be distinguishable as a separate morphological module in the analyses presented here.
high covariation was found between the two last thoracics, t <dig> and t <dig>  and the lumbars.
these two last thoracic vertebrae indeed have morphological characteristics that resemble lumbar shape more than they do the rest of the thoracics, such as a larger centrum, a cranially oriented neural spine and the presence of accessory processes  <cit> .
this result thus supports the ‘thoracolumbar’ modularity hypothesis , although only with regards to these last thoracics.
additionally, when considering mammals in general, this t <dig> – l <dig> modularity could facilitate, or be driven by, the homeotic changes between the thoracic and lumbar regions which can promote vertebral column variation without changes in overall vertebral count  <cit> .
we found strong support for the ‘anticlinality’ hypothesis  <cit> , although this was only composed of vertebrae t <dig> and t <dig>  and not t <dig>  this group comprises a biomechanically important region of the axial skeleton for two main reasons.
firstly, t <dig> is the diaphragmatic vertebra, which marks the dorsocaudal attachment of this septum and is also the first of the thoracic vertebrae to present ribs which are vertebrochondral, commonly named ‘false’ or ‘floating’, instead of vertebrosternal ribs   <cit> .
this release from the physical constraint of direct attachment allows for greater sagittal bending towards the posterior end of the vertebral column, particularly in the rib-less lumbar region  <cit> .
secondly, t <dig> is the anticlinal vertebra, with a much reduced and usually perpendicular neural spine, marking the change in neural spine orientation from a caudally inclined process prior to this vertebra to the cranially orientated process present in vertebrae t <dig> through l <dig> .
this change in neural spine orientation is especially well defined in carnivorans  and, along with the observed increase in centrum length, promotes greater motion and sagittal bending of the posterior region of the axial skeleton  <cit> .
finally, the boundaries of the modules found here mostly supported the ‘developmental model disruption’ hypothesis, in which it was proposed that boundaries of intervertebral modules would reflect the positions of vertebrae that did not show significant intravertebral modularity  <cit> .
the intravertebral developmental modularity model of two modules was not supported in vertebrae c <dig>  t <dig>  t <dig>  l <dig> and l <dig>  <cit> , and the results presented here show that most of the intervertebral modules follow the hypothesized boundaries or have vertebral boundaries that only slightly differ from those by one vertebra .
this result is best displayed in the mid-posterior region.
anterior to the suggested boundary at t <dig> between the prediaphragmatic and postdiaphragmatic vertebrae, the t1-t <dig>  or mid-thoracics t <dig> – t <dig> composed a distinct set; while the postdiaphragmatic vertebrae were divided into two modules  with very high within-module covariation.
as discussed above, these postdiaphragmatic vertebrae undergo more pronounced bending due to the release from the physical constraints of the ribs and diaphragm  <cit> .
accordingly, previous studies have shown that the t10-l <dig> region shows higher ecological signal in felids and that measurements from this region are best at separating species in a vertebral morphospace  <cit> .
furthermore, our previous study has shown that these vertebrae also displayed the greatest overall intravertebral integration and morphological variance, an observation which supports the hypothesis of high integration being able to facilitate increased levels of disparity, and therefore promoting morphological evolution on those preferred axes of variation   <cit> .
taken together, these results indicate that the postdiaphragmatic vertebrae t <dig> –l <dig> compose an evolutionarily highly responsive region which is organised into two strongly covarying modules.
this modularity may therefore be responsible for maintaining the organisation and relative independence of this region, while the high integration both within each module and within individual vertebrae may contribute to higher levels of shape disparification  while retaining functionality.fig.
<dig> schematics of vertebral column modules based on pairwise covariation between vertebrae.
a
vertical dashed lines are hypothesized regional boundaries based on vertebrae showing disruption of the two-module model for intravertebral shape covariation .
b
rectangular boxes showing suggested vertebral column modules.
dashed boxes and connecting line describe covariation between the cervicals and the t <dig> – l <dig> vertebrae.
c, t, and l stand for cervicals , thoracics , and lumbars , respectively.
filled circles describe landmarked vertebrae
in the anterior vertebral column, support for the ‘developmental model disruption’ hypothesis is less clear, as the first two cervicals were not supported as a separate module.
however, c <dig>  which did not support the two-module developmental model in our analysis of intravertebral modularity  <cit> , only displayed significant covariation with two of the other analysed vertebrae.
additionally, two well-supported modules were found either near or involving the suggested boundary between the last cervical and first thoracic: a module composed of c <dig> – t <dig>  and another of c <dig> – t <dig>  as discussed above, these vertebrae have been suggested to be highly constrained by development  <cit> , and show significant phylogenetic signal, but no ecological signal, in shape across felids  <cit> .
the analyses presented here revealed surprisingly strong covariation between the most anterior and most posterior presacral vertebrae .
this result was unexpected as we had hypothesized higher covariation between more thoracic and lumbar vertebrae instead  <cit> .
however, the origin of this pattern may lie in vertebral ossification timing.
a study of ossification sequences in the domestic cat skeleton  <cit>  reported that thoracic elements developed prior to both the cervical and lumbar regions.
in this case, this shared later ossification of cervical and lumbar vertebral elements could relate to the observed covariation of these two regions.
additionally, a more recent study of vertebral ossification in  <dig> species of mammals  <cit>   has shown that, although neural arches ossify first and begin ossification in the first cervicals and first thoracics, these are followed by ossification in the other cervicals and lumbar regions.
subsequently, centra ossify first in the thoracic region and ossification spreads both cranially and caudally  <cit> .
this progression of centra ossification in both directions could indeed cause a coincidence in ossification timing in cervicals and posterior t <dig> – l <dig>  while this potential explanation for the pattern of covariation among these two regions is speculative, it could be tested with more detailed ossification sequence data from felids, vertebral modularity studies across mammals, and biomechanical analyses of the axial skeleton across felids and other mammals.
the results from the phylogenetic pls on centrum or neural-spine-related coordinates also offer some support to this new hypothesis of integration between cervicals and t12-l <dig>  tentatively due to ossification timing .
there was a clear and strong association between the neural-spine landmarks of cervical vertebrae  and vertebrae in the t <dig> – l <dig> region.
this covariation was slightly less consistent but still present in the analysis of the centrum-related landmarks, although in this case the atlas  and c <dig> also displayed fewer covariations with posterior vertebrae in addition to c <dig>  additionally, those posterior vertebrae with significant covariation were generally the more anterior ones, from t <dig> – l <dig>  with the exception of t <dig>  reflecting the direction of centrum ossification.
however, we would expect a stronger signal of this covariation in the centrum landmarks, rather than the neural spine landmarks, contrary to our results.
the separate centrum and neural-spine analyses also supported the other modules found in the pls analyses of whole vertebrae.
results from centrum-only landmarks showed modularity of the vertebral column into an anterior cervicothoracic module from c <dig> – t <dig>  with five pairwise exceptions between axis  and t <dig>  c <dig> and t <dig>  c <dig> and c <dig>  c <dig> and t <dig>  and c <dig> and t <dig>  this analysis also showed stronger interaction between the thoracics and lumbars, with a strong t <dig> – l <dig> module, and among vertebrae in the t <dig> – l <dig> module.
neural-spine traits further supported this t <dig> – l <dig> module, as well as the c <dig> – c <dig> module , and the anticlinality t <dig> – t <dig> module.
CONCLUSIONS
here we have performed an empirical analysis of intervertebral integration and compared our results to previously suggested hypotheses of developmental and functional modularity across the presacral vertebral column.
our results demonstrate that modularity is prevalent in the axial skeleton of felids, but that modules do not necessarily agree with the traditional regions of cervical, thoracic and lumbar vertebrae.
instead, vertebral morphological modules reflect five main groupings which organise the vertebral column according to either developmental constraints or function.
those regions have also been shown to differ considerably in their morphological disparity, phylogenetic signal, and ecological specialisation, and have been suggested to present opposing levels of evolvability.
additionally, the observed interaction between the cervicals and lumbars may reflect their shared ossification timing.
finally, the recovered modules supported the hypothesis that overall modularity of the vertebral column reflects the positions of the few vertebrae which show disruption of the intravertebral developmental two-module model.
specifically, the few vertebrae in which the developmental two-module model was not supported form the boundaries of the intervertebral modules found here.
although this study is limited to a subset of representatives from a single family, the similarities in the modular organisation found here to developmental patterns shared across mammals suggest that these results may reflect a common mammalian condition.
importantly, the modular organisation of the vertebral column demonstrated here highlights that both development and function are important factors shaping vertebral shape diversification.
therefore, it may be the trade-off between these influences that control the disparity observed in the axial skeleton across mammalian families.

 numerous studies have demonstrated that organisms can be partitioned into sets of phenotypic traits or structures that show coordinated patterns of variation or evolution. these sets of traits, termed phenotypic modules, can be defined as units composed of multiple traits that display high levels of covariation with other traits within that unit, but relatively weak covariation with traits outside of the unit. the related concept of integration refers to the overall magnitude of covariation of phenotypic traits, and can refer to a single module, which would be expected to display relatively high within-module integration, or may span multiple modules or structures. the integration of traits, and their organisation into discrete phenotypic modules, has been hypothesised to arise and/or evolve as a product of shared developmental origin or pathways, genetic pleiotropy, or common function. strong integration within modules, and reduced integration between modules, is further hypothesised to promote coordination among functionally-related traits, while allowing independence and differential specialization of distinct modules. with its serial organisation and composition of vertebral units, distinguishable morphological differences among regions, and direct association of those regions with expression sites of genes in the hox family, the presacral axial skeleton would appear to encapsulate the concepts of regionalisation and modularity. although regionalisation of the vertebral column can be observed in amniotes in general, the mammalian axial skeleton shows the greatest differentiation in regional vertebral shape. this increased divergence is accompanied by strict constraints in regional vertebral number, particularly in the cervical region with seven vertebrae present in almost all of the ~ mammalian species. total presacral vertebral count is also highly conserved, although some variation does occur. this invariability with regards to vertebral count has been suggested to signal strong canalisation and developmental stability in the axial skeleton, and is thought to have evolved early in mammalian history. additionally, rather than being the target of selection themselves, highly fixed vertebral numbers in mammals may reflect developmental constraints related to the muscularisation of the diaphragm and the advantages of involving the lumbar region in abdomen expansion during inspiration and in sagittal bending during locomotion. in addition to the almost universally fixed count of seven vertebrae in the cervical region in mammals, species of the order carnivora also show little variation in thoracolumbar count, generally between and vertebrae. moreover, some families, such as felidae, display absolutely no variation in vertebral numbers between taxa: all felid species present presacral vertebrae which are traditionally divided into the three main vertebral column regions by clear morphological differences. in accordance with the observed trade-off between vertebral count invariability and high morphological disparity, both linear and landmark-based analyses of vertebral shape have shown evident functional regionalisation in the axial skeleton of felids. these analyses revealed regions which differ in magnitude of phylogenetic and ecological signal and both ontogenetic and evolutionary allometric scaling. specifically, the highest covariation between vertebral shape and prey size choice or locomotory mode were found in the posterior region of the vertebral column, composed of the vertebrae caudal to the posterior attachment of the diaphragm, from t to l conversely, vertebrae in the cervical region displayed high phylogenetic signal and little significant ecological signal. these examples of conspicuous morphological and functional regionalisation are strong indicators of modularity in the vertebral column, and not surprisingly, modularity has indeed already been described, or at least suggested, at different levels within the mammalian axial skeleton. one example of a hypothesised vertebral module is composed of the mid-cervicals c to c these vertebrae, whose somites have migratory muscle precursor cells which are committed to diaphragm transformation, have been suggested to be involved in the muscularisation of the septum and consequent fixed cervical number across almost all mammals. a larger hypothesised module stems from the relatively fixed count of total thoracolumbar vertebrae and has been suggested to arise from close association of these two regions, with any changes in regional vertebral number being counteracted by the inverse change in the opposite series, and thus no change to the total count. our previous studies of vertebral shape evolution in felids have already suggested some hypotheses of modularity specific to this study system. the observation of regionalised patterns of allometric scaling in a linear morphometric study both supported the mid-cervical vertebral module and suggested the presence of three additional modules: an anterior cervicothoracic module, a lumbar module, and a functional ‘anticlinality module’ composed of the t10-t vertebrae. additionally, we have previously demonstrated that presacral vertebral shape in felids is driven by the developmental origins of vertebral components, with two morphological modules found in adult vertebral shape: the ‘centrum’ and the ‘neural spine-related’ modules. interestingly, this model of modularity, although widespread through most the presacral column, was not supported in vertebrae that are positioned immediately at or adjacent to the borders of morphological vertebral column regions: specifically, c t t l and l this observation led to the suggestion of a disruption of developmental modularity – or a functional overprint – in order to maintain the larger modular organisation of the vertebral column. although there have been recent additions to the literature on the morphological, biomechanical and developmental changes to the vertebral column in mammals or across vertebrates in general, much is yet unknown on its evolution and how patterns of trait integration or modularity may affect its response to selection. here we analyse patterns of shape covariation across the presacral vertebral column in order to quantify the modular organisation of the axial skeleton in felids. specifically, we use three-dimensional geometric morphometrics to describe presacral vertebral shape and quantify intervertebral integration with pairwise comparisons of presacral vertebrae using phylogenetic two-block partial least square analysis. the results of the pairwise pls analyses were used to test whether specific sets of vertebrae show higher magnitude of shape integration within the set than with vertebral units outside of the set, therefore forming a ‘module’. the hypothesised intervertebral modules assessed with pairwise pls results were drawn from the literature and are as follows: 1) the ‘traditional regions’ hypothesis: traditional regional boundaries in the felid vertebral column form discrete morphological modules; 2) the ‘cervicothoracic and lumbar modules’ hypothesis: two modules composed of multiple vertebrae that share a common allometric pattern can be found in the presacral axial skeleton: an anterior cervicothoracic module and a lumbar module; 3) the ‘thoracolumbar’ hypothesis: thoracic and lumbar vertebrae show high covariation; 4) the ‘anticlinality’ hypothesis: vertebrae t to t compose an ‘anticlinality module’; and 5) the ‘developmental model disruption’ hypothesis: boundaries of modular organisation of the vertebral column match vertebral positions where the intravertebral developmental two-module model is not supported, specifically at the edges of the c – c cervical module, between cervicals and thoracics, the division of the vertebral column into pre- and postdiaphragmatic regions at t and at the last two presacral vertebrae l and l.fig. illustration of the five hypotheses of intervertebral phenotypic modularity tested here. black rectangles illustrate sets of vertebrae which are hypothesized to show high integration among themselves and, therefore, to represent a module. see text for detailed description of hypotheses. hypothesis 1: traditional regions. hypothesis 2: cervicothoracic and lumbar modules. hypothesis 3: thoracolumbar module. hypothesis 4: anticlinality model composed of vertebrae t t and t hypothesis 5: developmental model disruption. c, t, and l stand for cervicals, thoracics, and lumbars, respectively. filled circles describe landmarked vertebrae we further conducted separate analyses of intervertebral integration for the two intravertebral developmental modules. specifically, the same pairwise phylogenetic pls analyses were conducted across the presacral vertebral column, but traits were limited to those from either the neural spine or the centrum. following from our previous results showing the widespread developmental two-module model of intravertebral covariation, this latter analysis allows us to assess if the patter of intervertebral covariation across the vertebral column is the same for the whole vertebral morphology and for when only trait units regarding each of these modules are considered.  vertebral shape covariation phylogenetic pls analysis demonstrated that out of the total pairwise analyses were not significant, suggesting extensive modularity of the presacral vertebral column. the remaining significant pairwise analyses allowed for identification of sets of vertebrae which presented particularly strong within-group covariation. according to these results, six sets of highly covarying vertebrae were identified as follows: 1) c to t1; 2) c to t2; 3) t to t8; 4) t to t11; 5) t to l7; and 6) a set showing covariation between c to c and t to l with the exception of the pairwise comparisons between c and the lumbars l and l and c and l table results of phylogenetic partial least squares analysis of all landmarks. above diagonal cells show the pairwise covariation values between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction. results in bold and in grey shaded cells show significant covariations and suggested modules, while results in italics and with white shaded cells are not significant after benjamini-hochberg correction, the number of covariation tests that were not significant increased to leaving significant results. those tests that were rendered not significant after this correction were concentrated between the first cervicals and c and t c and the end-thoracics and lumbars, and some of the covariation results between the pre-diaphragmatic thoracics. thus, the overall pattern of intervertebral modularity was similar after correction for multiple comparisons. covariation across centrum versus neural spine modules throughout the vertebral column centrum: results from the phylogenetic pls on centrum-only landmarks supported modules largely similar to those found when whole vertebral morphology was analysed: 1) c – t with three exceptions in pairwise comparisons between c and t c and c and c and t formed a cervical and first thoracics set; and 2) t to l composed a set with very strong within module covariation. however, other vertebral combinations were also apparent: 3) t - l vertebrae; 4) between c – c and t – l with the exception of t which only presented significant shape covariation with c and c among the cervicals; and 5) c and every other vertebra included in this analyses, with the exception of c table results of phylogenetic partial least squares analysis of landmarks concerning the ‘centrum’ module. above diagonal cells show the pairwise covariation values between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction. results in bold and in grey shaded cells show significant correlations and suggested modules, while results in italics and with white shaded cells are not significant correction of this analysis’ significance level with the benjamini-hochberg procedure reduced and rendered non-significant most pairwise comparisons between c – c and t – l but had little effect on most other modules. neural spine there were fewer significant pairwise covariation results from the phylogenetic pls on neural spine-only landmarks than from the centrum-only analysis. the significant pairwise tests on neural spine-only landmarks displayed four distinct modules: 1) between c and c with the exception of c4; 2) between t and t11; 3) between vertebrae in the t – l region; and 4) between the cervicals c – c with the exception of c and t – l benjamini-hochberg correction did not change these patterns and mainly reduced the covariations between the cervicals and the vertebrae in the t – l region and other vertebral pairs in the thoracic region.table results of phylogenetic partial least squares analysis of landmarks concerning the ‘neural spine’ module. above diagonal cells show the pairwise covariation values between each pair of vertebrae, while below diagonal values display the covariation values with significance levels after benjamini-hochberg correction. results in bold and in grey shaded cells show significant covariations and suggested modules, while results in italics and with white shaded cells are not significant discussion the results presented here provide new information on the structural organisation of the vertebral column in felids, and potentially mammals in general. in light of the results presented here, the ‘traditional regions’ hypothesis and the ‘cervicothoracic and lumbar modules’ hypothesis could be rejected or considered insufficiently explanatory. although high covariation was found between vertebrae within each of these regions, those either did not include all or most vertebrae which compose the regions or, more commonly, sets of highly covarying vertebral shapes were inclusive of vertebrae beyond the traditional boundaries. specifically, in all of the analyses performed, with the exception of the phylogenetic pls of the neural-spine landmarks, covariation in the anterior portion of the axial skeleton included high pairwise covariation between cervicals and the first thoracics. additionally, all cervicals analysed here, with the exception of c displayed high covariation with the last thoracics and lumbar vertebrae. a distinct module composed of vertebrae in the cervicothoracic boundary was found. a developmental covariation had already been suggested for these units based on the migration of cells from somites bound to the forelimbs, which may additionally have been involved in the first evolutionary steps that contributed to the muscularisation of the diaphragm. due to the lack of vertebrae c and c in our dataset, it was not possible to test for higher covariation between those and c composing the suggested c – c developmental module in mammals. nevertheless, c presented very high covariation with both c and c indicating that a c – c set would likely not be distinguishable as a separate morphological module in the analyses presented here. high covariation was found between the two last thoracics, t and t and the lumbars. these two last thoracic vertebrae indeed have morphological characteristics that resemble lumbar shape more than they do the rest of the thoracics, such as a larger centrum, a cranially oriented neural spine and the presence of accessory processes. this result thus supports the ‘thoracolumbar’ modularity hypothesis, although only with regards to these last thoracics. additionally, when considering mammals in general, this t – l modularity could facilitate, or be driven by, the homeotic changes between the thoracic and lumbar regions which can promote vertebral column variation without changes in overall vertebral count. we found strong support for the ‘anticlinality’ hypothesis, although this was only composed of vertebrae t and t and not t this group comprises a biomechanically important region of the axial skeleton for two main reasons. firstly, t is the diaphragmatic vertebra, which marks the dorsocaudal attachment of this septum and is also the first of the thoracic vertebrae to present ribs which are vertebrochondral, commonly named ‘false’ or ‘floating’, instead of vertebrosternal ribs. this release from the physical constraint of direct attachment allows for greater sagittal bending towards the posterior end of the vertebral column, particularly in the rib-less lumbar region. secondly, t is the anticlinal vertebra, with a much reduced and usually perpendicular neural spine, marking the change in neural spine orientation from a caudally inclined process prior to this vertebra to the cranially orientated process present in vertebrae t through l. this change in neural spine orientation is especially well defined in carnivorans and, along with the observed increase in centrum length, promotes greater motion and sagittal bending of the posterior region of the axial skeleton. finally, the boundaries of the modules found here mostly supported the ‘developmental model disruption’ hypothesis, in which it was proposed that boundaries of intervertebral modules would reflect the positions of vertebrae that did not show significant intravertebral modularity. the intravertebral developmental modularity model of two modules was not supported in vertebrae c t t l and l, and the results presented here show that most of the intervertebral modules follow the hypothesized boundaries or have vertebral boundaries that only slightly differ from those by one vertebra. this result is best displayed in the mid-posterior region. anterior to the suggested boundary at t between the prediaphragmatic and postdiaphragmatic vertebrae, the t1-t or mid-thoracics t – t composed a distinct set; while the postdiaphragmatic vertebrae were divided into two modules with very high within-module covariation. as discussed above, these postdiaphragmatic vertebrae undergo more pronounced bending due to the release from the physical constraints of the ribs and diaphragm. accordingly, previous studies have shown that the t10-l region shows higher ecological signal in felids and that measurements from this region are best at separating species in a vertebral morphospace. furthermore, our previous study has shown that these vertebrae also displayed the greatest overall intravertebral integration and morphological variance, an observation which supports the hypothesis of high integration being able to facilitate increased levels of disparity, and therefore promoting morphological evolution on those preferred axes of variation. taken together, these results indicate that the postdiaphragmatic vertebrae t –l compose an evolutionarily highly responsive region which is organised into two strongly covarying modules. this modularity may therefore be responsible for maintaining the organisation and relative independence of this region, while the high integration both within each module and within individual vertebrae may contribute to higher levels of shape disparification while retaining functionality.fig. schematics of vertebral column modules based on pairwise covariation between vertebrae. a vertical dashed lines are hypothesized regional boundaries based on vertebrae showing disruption of the two-module model for intravertebral shape covariation. b rectangular boxes showing suggested vertebral column modules. dashed boxes and connecting line describe covariation between the cervicals and the t – l vertebrae. c, t, and l stand for cervicals, thoracics, and lumbars, respectively. filled circles describe landmarked vertebrae in the anterior vertebral column, support for the ‘developmental model disruption’ hypothesis is less clear, as the first two cervicals were not supported as a separate module. however, c which did not support the two-module developmental model in our analysis of intravertebral modularity, only displayed significant covariation with two of the other analysed vertebrae. additionally, two well-supported modules were found either near or involving the suggested boundary between the last cervical and first thoracic: a module composed of c – t and another of c – t as discussed above, these vertebrae have been suggested to be highly constrained by development, and show significant phylogenetic signal, but no ecological signal, in shape across felids. the analyses presented here revealed surprisingly strong covariation between the most anterior and most posterior presacral vertebrae. this result was unexpected as we had hypothesized higher covariation between more thoracic and lumbar vertebrae instead. however, the origin of this pattern may lie in vertebral ossification timing. a study of ossification sequences in the domestic cat skeleton reported that thoracic elements developed prior to both the cervical and lumbar regions. in this case, this shared later ossification of cervical and lumbar vertebral elements could relate to the observed covariation of these two regions. additionally, a more recent study of vertebral ossification in species of mammals has shown that, although neural arches ossify first and begin ossification in the first cervicals and first thoracics, these are followed by ossification in the other cervicals and lumbar regions. subsequently, centra ossify first in the thoracic region and ossification spreads both cranially and caudally. this progression of centra ossification in both directions could indeed cause a coincidence in ossification timing in cervicals and posterior t – l while this potential explanation for the pattern of covariation among these two regions is speculative, it could be tested with more detailed ossification sequence data from felids, vertebral modularity studies across mammals, and biomechanical analyses of the axial skeleton across felids and other mammals. the results from the phylogenetic pls on centrum or neural-spine-related coordinates also offer some support to this new hypothesis of integration between cervicals and t12-l tentatively due to ossification timing. there was a clear and strong association between the neural-spine landmarks of cervical vertebrae and vertebrae in the t – l region. this covariation was slightly less consistent but still present in the analysis of the centrum-related landmarks, although in this case the atlas  and c also displayed fewer covariations with posterior vertebrae in addition to c additionally, those posterior vertebrae with significant covariation were generally the more anterior ones, from t – l with the exception of t reflecting the direction of centrum ossification. however, we would expect a stronger signal of this covariation in the centrum landmarks, rather than the neural spine landmarks, contrary to our results. the separate centrum and neural-spine analyses also supported the other modules found in the pls analyses of whole vertebrae. results from centrum-only landmarks showed modularity of the vertebral column into an anterior cervicothoracic module from c – t with five pairwise exceptions between axis and t c and t c and c c and t and c and t this analysis also showed stronger interaction between the thoracics and lumbars, with a strong t – l module, and among vertebrae in the t – l module. neural-spine traits further supported this t – l module, as well as the c – c module, and the anticlinality t – t module.  here we have performed an empirical analysis of intervertebral integration and compared our results to previously suggested hypotheses of developmental and functional modularity across the presacral vertebral column. our results demonstrate that modularity is prevalent in the axial skeleton of felids, but that modules do not necessarily agree with the traditional regions of cervical, thoracic and lumbar vertebrae. instead, vertebral morphological modules reflect five main groupings which organise the vertebral column according to either developmental constraints or function. those regions have also been shown to differ considerably in their morphological disparity, phylogenetic signal, and ecological specialisation, and have been suggested to present opposing levels of evolvability. additionally, the observed interaction between the cervicals and lumbars may reflect their shared ossification timing. finally, the recovered modules supported the hypothesis that overall modularity of the vertebral column reflects the positions of the few vertebrae which show disruption of the intravertebral developmental two-module model. specifically, the few vertebrae in which the developmental two-module model was not supported form the boundaries of the intervertebral modules found here. although this study is limited to a subset of representatives from a single family, the similarities in the modular organisation found here to developmental patterns shared across mammals suggest that these results may reflect a common mammalian condition. importantly, the modular organisation of the vertebral column demonstrated here highlights that both development and function are important factors shaping vertebral shape diversification. therefore, it may be the trade-off between these influences that control the disparity observed in the axial skeleton across mammalian families. 
these modules reflect shared developmental pathways, ossification timing, and observed ecological shape diversification in living species of felids. here we investigate the modular organisation of the presacral vertebral column of modern cats with pairwise comparisons of vertebral shape covariation and evaluate our results against hypotheses of developmental and functional modularity. we show here that patterns of shape integration reflect modular organisation of the vertebral column of felids. we used three-dimensional geometric morphometrics to quantify vertebral shape and then assessed integration between pairs of vertebrae with phylogenetic two-block partial least square analysis. this modularity may also have permitted vertebral partitions, specifically in the posterior vertebral column, to be more responsive to selection and achieve higher morphological disparity than other vertebral regions. further, several lines of evidence suggest that the mammalian axial skeleton is a highly modular structure. whereas this pattern corresponds with hypotheses of developmental and functional regionalisation in the axial skeleton, it does not simply reflect major vertebral regions. integrationtwo-block plsaxial skeletonvertebracarnivoramodulesgeometric morphometricshttp://dx.doi.org/ /501100000275leverhulme trustrpg 2013-124goswami anjali synthesysissue-copyright-statement© the author 2017 previous studies have demonstrated that the clear morphological differences among vertebrae across the presacral column are accompanied by heterogeneous functional signals in vertebral shape. these include its composition of serial units, a trade-off between high shape variance and strong conservation of vertebral count, and direct association of regions with anterior expression sites of hox genes.
 previous studies have demonstrated that the clear morphological differences among vertebrae across the presacral column are accompanied by heterogeneous functional signals in vertebral shape. further, several lines of evidence suggest that the mammalian axial skeleton is a highly modular structure. these include its composition of serial units, a trade-off between high shape variance and strong conservation of vertebral count, and direct association of regions with anterior expression sites of hox genes. here we investigate the modular organisation of the presacral vertebral column of modern cats with pairwise comparisons of vertebral shape covariation and evaluate our results against hypotheses of developmental and functional modularity. we used three-dimensional geometric morphometrics to quantify vertebral shape and then assessed integration between pairs of vertebrae with phylogenetic two-block partial least square analysis.  six modules were identified in the pairwise analyses: an anterior module; a transitional module situated between the last cervicals and first thoracics; an anterior to middle thoracic set; an anticlinal module; a posterior set composed of the last two thoracics and lumbars; and a module showing covariation between the cervicals and the posterior set. these modules reflect shared developmental pathways, ossification timing, and observed ecological shape diversification in living species of felids.  we show here that patterns of shape integration reflect modular organisation of the vertebral column of felids. whereas this pattern corresponds with hypotheses of developmental and functional regionalisation in the axial skeleton, it does not simply reflect major vertebral regions. this modularity may also have permitted vertebral partitions, specifically in the posterior vertebral column, to be more responsive to selection and achieve higher morphological disparity than other vertebral regions. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords integrationtwo-block plsaxial skeletonvertebracarnivoramodulesgeometric morphometricshttp://dx.doi.org/ /501100000275leverhulme trustrpg 2013-124goswami anjali synthesysissue-copyright-statement© the author 2017 