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 [1,2,3]. 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 [1, 2, 4, 5]. 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 [2, 6,7,8,9]. With its serial organisation and composition of vertebral units, distinguishable morphological differences among regions (cervical, thoracic, and lumbar), 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 [4, 10,11,12,13,14].
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 [10, 15,16,17,18,19,20]. 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 ~5000 mammalian species. Total presacral vertebral count is also highly conserved [21,22,23], although some variation does occur . This invariability with regards to vertebral count has been suggested to signal strong canalisation (i.e. limitation of variation between individuals due to the tendency of organisms to “follow predetermined developmental pathways in spite of environmental and genetic perturbations” , page 44, and also see ) and developmental stability in the axial skeleton, and is thought to have evolved early in mammalian history [22, 23]. 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 [6, 22].
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 19 and 20 vertebrae . Moreover, some families, such as Felidae (i.e. cats), display absolutely no variation in vertebral numbers between taxa: all felid species present 27 presacral vertebrae which are traditionally divided into the three main vertebral column regions (i.e. cervical, thoracic, and lumbar) by clear morphological differences [15, 27,28,29,30]. 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 (e.g. specialisation related to locomotor mode) and both ontogenetic and evolutionary allometric scaling [29, 31, 32]. Specifically, the highest covariation between vertebral shape and prey size choice or locomotory mode (i.e. the two main ecological categories that have been used to describe felid ecology in the literature [33,34,35,36,37,38,39]) were found in the posterior region of the vertebral column, composed of the vertebrae caudal to the posterior attachment of the diaphragm, from T10 to L7. Conversely, vertebrae in the cervical region displayed high phylogenetic signal and little significant ecological signal [29, 31].
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 (e.g. [4, 29, 40]). One example of a hypothesised vertebral module is composed of the mid-cervicals C3 to C5. 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 (i.e. homeotic changes) [4, 11, 21, 23, 40, 41].
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-T12 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 (referred to as the ‘developmental two-module model’ therein to reflect the different somitic origins of these modules; [27, 40, 42]). 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, C4, T1, T8, L6 and L7. 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 [6, 10, 40, 43,44,45,46,47], 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 (PLS). The results of the pairwise PLS analyses were used to test whether specific sets of vertebrae show higher magnitude of shape integration (i.e. greater covariation) within the set than with vertebral units outside of the set, therefore forming a ‘module’ [1,2,3]. The hypothesised intervertebral modules assessed with pairwise PLS results were drawn from the literature and are as follows (Fig. 1): 1) the ‘traditional regions’ hypothesis: Traditional regional boundaries (i.e. cervical, thoracic and lumbar) in the felid vertebral column form discrete morphological modules [4, 6, 21, 23, 30]; 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 (where vertebrae show positive allometry related to centrum and neural spine dimensions) and a lumbar module (with positive allometry of traits related to the neural spine lever arm) ; 3) the ‘thoracolumbar’ hypothesis: Thoracic and lumbar vertebrae show high covariation [4, 11, 21, 23, 41]; 4) the ‘anticlinality’ hypothesis: Vertebrae T10 to T12 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 (centrum and neural spine) model is not supported, specifically at the edges of the C3 – C5 cervical module, between cervicals and thoracics (i.e. at T1), the division of the vertebral column into pre- and postdiaphragmatic regions at T8, and at the last two presacral vertebrae L6 and L7 .
We further conducted separate analyses of intervertebral integration for the two intravertebral developmental modules (centrum and neural spine). 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 [27, 40, 42]. 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 (Additional file 1: Tables S1 and S2 for landmarks’ identity, following ).