Anatomical network analysis of the musculoskeletal system reveals integration loss and parcellation boost during the fins‐to‐limbs transition

Tetrapods evolved from within the lobe‐finned fishes around 370 Ma. The evolution of limbs from lobe‐fins entailed a major reorganization of the skeletal and muscular anatomy of appendages in early tetrapods. Concurrently, a degree of similarity between pectoral and pelvic appendages also evolved. Here, we compared the anatomy of appendages in extant lobe‐finned fishes (Latimeria and Neoceratodus) and anatomically plesiomorphic amphibians (Ambystoma, Salamandra) and amniotes (Sphenodon) to trace and reconstruct the musculoskeletal changes that took place during the fins‐to‐limbs transition. We quantified the anatomy of appendages using network analysis. First, we built network models—in which nodes represent bones and muscles, and links represent their anatomical connections—and then we measured network parameters related to their anatomical integration, heterogeneity, and modularity. Our results reveal an evolutionary transition toward less integrated, more modular appendages. We interpret this transition as a diversification of muscle functions in tetrapods compared to lobe‐finned fishes. Limbs and lobe‐fins show also a greater similarity between their pectoral and pelvic appendages than ray‐fins do. These findings on extant species provide a basis for future quantitative and comprehensive reconstructions of the anatomy of limbs in early tetrapod fossils, and a way to better understand the fins‐to‐limbs transition.

The limbs of tetrapods evolved from the lobe-fins of sarcopterygian fishes around 370 Ma through a series of anatomical innovations (Fig. 1A). Although at first sight the limbs and lobe-fins of extant species look different, they share some deep similarities in their anatomical organization-the way in which bones and muscles are arranged together-that reveal their common origin. The study of the origin of limbs involves working with uncertain homologies between anatomical structures, reconstructing soft tissue in transitional fossil taxa, and gathering information from the few extant taxa close to the fins-to-limbs transition (e.g., Molnar et al. 2017). These circumstances present a challenge for quantitative methods comparing the anatomical organization of appendages, especially in very disparate forms.
To overcome this problem, here we propose to, and exemplify the use of, a systems biology approach to the study of the fins-to-limbs transition. A systems biology approach to anatomy focuses on the quantification and comparison of anatomical organization, which other properties such as integration, modularity, and functioning depend on (Rasskin-Gutman and Esteve-Altava 2014). The intuitive notion of anatomical organization evokes a group of parts establishing physical interactions that define the overall structure and function of a system (Weiss 1971). Here, we formalized the anatomical organization of fins and limbs using network models that capture the basic physical relationships among bones and muscles. Working with network models of the musculoskeletal anatomy of appendages allows us to directly compare forms with incomplete homologies , to integrate skeletal and muscular data Molnar et al. 2017;Santos et al. 2017), and to quantify patterns of morphological complexity, integration, and modularity in a manner not available for comparative methods that focus on shape and size (Kerkman et al. 2017; Esteve-Altava 2017a; Murphy et al. 2018).
Anatomical organization has traditionally helped in identifying homologies among disparate taxa (e.g., Remane 1956;Jardine 1969). Homologies are generally more straightforward for the bones and muscles of the girdle, stylopod (arm/thigh), and zeugopod (forearm/leg), because more proximal regions of appendages tend to preserve their anatomical organization across species more often (Diogo and Abdala 2010). One example is the homology between the two most proximal mesomeres and the first radial of lobe-fins and the humerus, radius, and ulna of tetrapod forelimbs, respectively (Coates et al. 2002). Another example is the homology between the adductor profundus muscle of lobefins and the puboischiofemoralis internus muscle of limbs . In contrast, homologies between more distal regions of appendages are far more controversial, because phylogenetically distant species barely share their anatomical organization in these regions, if at all. For example, there is still debate on whether tetrapod autopod (hand/foot) are homologous to any fin structure or if they evolved de novo (Sordino et al. 1995;Johanson et al. 2007;Woltering and Duboule 2010;Nakamura et al. 2016). Furthermore, the same uncertainty applies to the origin of autopod intrinsic muscles . Uncertainties in homologies between lobe-fins and limbs pose a problem to quantitative comparative analyses of their anatomical organization and morphology, limiting such comparisons to a few anatomical elements or to general developmental patterns.
Bones and muscles are equally important in measuring the anatomical organization of appendages and reconstructing the evolution of limbs from lobe-fins. However, most studies on the origin and evolution of limbs focus almost exclusively on the appendicular skeleton. Because skeletons fossilize more easily than soft tissues, they provide direct evidence of the evolution of appendages. For example, from fossils of early Devonian Sarcopterygii we know that tetrapodomorphs already had elbows and knees, and autopods with digits, but that they lacked radials (e.g., Coates and Clack 1990;Coates et al. 2002;Ahlberg 2011). In contrast, we must infer the presence of specific muscles and their attachments in fossil taxa through the scars they left on bones and through phylogenetic inference methods, such as extant phylogenetic bracketing (Witmer 1995). Thus, we rely on the musculoskeletal anatomy of extant species, such as lobe-finned fishes and amphibians (e.g., Boisvert et al. 2013;Diogo et al. 2016;Miyake et al. 2016), to bracket the fins-to-limbs transition and to infer transitional morphologies (Molnar et al. 2017). Likewise, we rely on extant species to understand how the anatomical organization of appendages has evolved, and how pectoral-pelvic similarity changed before and after the fins-to-limbs transition. Furthermore, comparative studies must deal with limitations in the number of specimens available that come from studying scarce fossil materials or rare extant species. These challenges hinder quantitative morphological analysis of important evolutionary events such as the fins-to-limbs transition.
A question that often emerges when studying the origin and evolution of limbs is the apparent similarity in anatomical organization between pectoral and pelvic appendages. Richard Owen labeled pectoral and pelvic appendages as serially homologous, precisely because they shared a similar skeletal anatomy, albeit having different shapes and functions (Owen 1849). Modern evolutionary theory reinterpreted serial homologs as structures derived from evolutionary changes of repeated identical parts in a last common ancestor. The concept of "deep homology," a common developmental-genetic toolkit regulating growth and differentiation of different body parts across distantly related animals (Wagner 1989;Shubin et al. 1997), helped cement the idea that pectoral and pelvic appendages are anatomically similar because pelvic fins evolved by a duplication and redeployment of the same genetic information directing the development of pectoral fins (e.g., Ruvinsky and Gibson-Brown 2000;Young et al. 2005;Abbasi 2011). However, studies in paleontology, comparative muscle anatomy, and development disagree with the conclusion that pectoral and pelvic appendages are serially homologous in a strict modern sense. For example, the fossil record of osteostracans has been interpreted to show that pelvic fins evolved after pectoral fins did, as originally distinct appendages (e.g., pelvic fins lacked a girdle and mineralized radials); and later in evolution pectoral and pelvic fins became more similar Cohn 1998, 1999;Diogo et al. 2013;Miyashita and Diogo 2016; but see Wilson et al. 2007 for an alternative explanation due to lack of preservation). It is thought that the first fishes having both pectoral and pelvic fins had, mainly, only adductor and abductor muscle masses, while tetrapods can have up to more than 50 muscles in the anterior and posterior limbs. Because most muscles of the zeugopod and autopod are topologically similar in both limbs, it was inferred that topologically similar muscles evolved independently in the fore-and hindlimbs (i.e., derived topological similarity) (Diogo and Molnar 2014;Diogo and Ziermann 2015;Diogo et al. 2016). Finally, recent studies on genetic regulatory networks have revealed also clear differences in patterns of gene expression between the pectoral and pelvic appendages of tetrapods (Sears et al. 2015). Together, these studies expand a debate on whether pectoral-pelvic similarity evolved by serial homology, by parallelism related to "deep homology," or by convergent evolution.
Linked to the idea of serial homology, the more traditional hypothesis states that pectoral and pelvic appendages originated as mostly identical copies that gradually diversified in form and specialized in function ( Fig. 1B left funnel) (reviewed in Diogo et al. 2013). Contrary to this hypothesis, various studies have proposed the presence of derived bottlenecks in pectoral-pelvic similarity within gnathostome evolution. A "similarity bottleneck" is a relatively high degree of similarity between pectoral and pelvic appendages in a particular derived lineage or at an evolutionary event (e.g., during the fins-to-limbs transition). For example, Ahlberg (1989) proposed similarity bottlenecks in the lineage leading to extant coelacanths (Latimeria) and at the origin of tetrapods ( Fig. 1B central funnel). Others have proposed that pectoral and pelvic fins were originally different and only started to become more similar after a first similarity bottleneck leading to bony fishes and to sarcopterygians, which was followed by a second, more profound similarity bottleneck at the origin of tetrapods ( Fig. 1B right funnel) (Coates and Cohn 1998;Coates et al. 2002;Diogo et al. 2013;Diogo and Molnar 2014). These studies have evaluated pectoral-pelvic anatomical similarity mostly by qualitative comparisons of fossils (e.g., Ahlberg 1989;Coates and Cohn 1998;Coates et al. 2002) or by counting topologically equivalent muscles in pectoral and pelvic appendages (Diogo et al. 2013;Diogo and Molnar 2014). Using quantitative tools to measure anatomical organization for entire appendages may help in reconstructing the evolution of the pectoral-pelvic similarity and in testing the presence of such similarity bottlenecks.
Here, we quantified the anatomical organization of extant sarcopterygian appendages (lobe-fins and limbs) to assess how similar they are to each other and how similar their pectoral and pelvic appendages are. Specifically, we tested (1) whether lobe-fins and limbs share a similar underlying anatomical organization or a new organization emerged in tetrapods during the fins-to-limbs transition; (2) whether lobe-finned fishes and tetrapods show equal values of pectoral-pelvic similarity; and (3) whether the evolution of pectoral-pelvic similarity agrees with previously proposed hypotheses on this evolutionary pattern (as described above; Fig. 1B). To answer these questions, we studied the pectoral and pelvic appendages in five extant taxa that phylogenetically bracket the fins-to-limbs transition: two lobefinned fishes, the African coelacanth Latimeria chalumnae and the Australian lungfish Neoceratodus forsteri; and three tetrapods, the axolotl Ambystoma mexicanum, the fire salamander Salamandra salamandra, and the tuatara Sphenodon punctatus. As an outgroup for comparison, we also included a representative of the phylogenetically most basal (i.e., widely presumed to have the most plesiomorphic anatomy) extant lineage of ray-finned fishes, the gray bichir Polypterus senegalus. See Methods for further details about the selection of taxa.
To quantify the anatomical organization of these appendages, we carried out an anatomical network analysis. First, we built skeletal and muscular network models that capture the gross anatomy of appendages (Fig. 2). A network model comprises nodes that formalize discrete anatomical parts-bones and muscles-and links that formalize pair-wise physical connections among them. Next, we measured a set of seven network parameters to quantify anatomical organization, namely: number of nodes (N), number of links (K), density of connections (D), mean clustering coefficient (C), mean shortest path length (L), heterogeneity of connections (H), and parcellation (P). Figure 3 shows the calculation of these parameters in a toyexample network (see Methods for further details). Network parameters serve as quantitative descriptors of anatomy, but they also carry morphological and functional information. This information derives from the underlying processes of development, which are inherited from one generation to another, and from the role of connections in force transmission among bones and muscles. Box 1 summarizes the morphofunctional interpretation of network parameters as proposed in previous studies (Esteve-Altava et al. 2011; Rasskin-Gutman and Esteve-Altava 2014); we used these interpretations to discuss our results. Finally, we compared the similarity among species' appendages and between pectoral and pelvic appendages, as the relative difference for each parameter and on average.

BOX 1: Morphological interpretation of network parameters
Network nodes (N): interacting components of the anatomical structure, for example, bones and muscles. Network links (L): interactions or relations among components, for example, physical contacts. Links may directly or indirectly contribute to biological processes, such as growth or function. Density of connections (D): richness or complexity of the anatomical structure. Also anatomical integration, as it relates to the number of interactions. Mean clustering coefficient (C): anatomical integration, as it relates to functional and/or developmental interdependence among triplets of components. Mean shortest path length (L): anatomical integration, as it relates to the effective proximity between components that allows coordination, independently of their spatial or geometric distance. Heterogeneity of connections (H): differentiation or anisomerism of components in the anatomical structure. Also irregularity, as it contrasts with regular structures (zero heterogeneity). Parcellation (P): degree of modularity of the anatomical structure; how well distributed are the components into the largest number of modules possible.

Results
We measured seven network parameters that capture the anatomical organization of pectoral and pelvic appendages of extant taxa bracketing the fins-to-limbs transition (Table 1 for skeletal networks; Table 2 for muscular networks). We quantified the similar-ity of anatomical organization among species and between pectoral and pelvic appendages as the pair-wise relative difference (d r ). A lower value of d r indicates a greater similarity between two appendages. Tables S1-S6 show the exact values of d r for each comparison in skeletal and muscular networks.

COMPARISON OF SKELETAL NETWORKS
The skeletons of fore-and hind limbs of tetrapods ( Fig. 4) have more elements (N) than the pectoral and pelvic ray-fins of Polypterus and lobe-fins of Latimeria, but fewer than the lobe-fins of Neoceratodus. This difference between Latimeria and Neoceratodus is due to the derived anatomy of Neoceratodus fins, which are composed of a long series of mesomeres (up to 14), each one articulating with preaxial and postaxial radials (for a total N = 55 and N = 65 skeletal elements in the pectoral and pelvic fin, respectively). The number of articulations among skeletal elements (K) follows a similar evolutionary pattern, with Latimeria having values within the range of tetrapods. However, the evolution of D, C, and L suggests a partial decrease of anatomical integration in limbs compared to fins and reconstructed ancestral character states: lower D, constant C, greater L. Tetrapods, and Neoceratodus have lower values of D in pectoral and pelvic appendages compared to ancestral state reconstructions and to Latimeria and Polypterus. In turn, the values of C in tetrapods and Neoceratodus are more similar to those of ancestral state reconstructions than in the coelacanth Latimeria, whereas Polypterus has the lowest values for both appendages. Inversely to D, the parameter L increases notably in limbs compared to ancestral state reconstructions, lobefins, and ray-fins. At the same time, parameter H in skeletal networks has similarly low values in tetrapods and Latimeria, relative to ancestral state reconstructions, Neoceratodus, and Polypterus. The relatively high H of Neoceratodus might be again due to the apomorphic anatomy of Neoceratodus fins with a large series of radials (poorly connected, 2-3 connections each) all articulating with the lepidotrichia (highly connected); thus increasing the ratio between variance and mean of connections among elements. The observation that Latimeria has a similar H to tetrapods is presumably due to the fact that their lepidotrichia are more distal, and only contact to the most distal radials; whereas in Neoceratodus and Polypterus the lepidotrichia occupy a broader preaxial and postaxial area and contact all radials. Finally, the evolution of P shows that lobe-fins and limbs have a similarly greater parcellation compared to the ray-fins of Polypterus (especially in the pelvic appendage), with Latimeria showing the lowest values of all sarcopterygians and Neoceratodus showing values close to the reconstructed ancestral state of Tetrapoda (Tables S12-S13). In general, lobe-fins and limbs deviate greatly from the low values of P in Polypterus ray-fin skeleton. This pattern is consistent with the aforementioned decrease of integration in the skeletal networks of limbs.

(F) Parcellation (P) is calculated after a community detection algorithm has identified the connectivity modules; two in this example: module A and module B (dashed yellow circles)
. Module A has four nodes and module B has five nodes of a total of nine nodes in the network; thus, P = 1 -[(4/9) 2 + (5/9) 2 ] = 0.49. If the network were divided less uniformly, for example, into one large module of seven nodes and one small module of two nodes, then P = 1 -[(7/9) 2 + (2/9) 2 ] = 0.35. In contrast, if the nine nodes of the network were divided into three modules of equal size (i.e., three 3-node modules), then P = 1 -[(3/9) 2 + (3/9) 2 + (3/9) 2 ] = 0.67. Regarding the similarity of the pectoral skeleton among the taxa analyzed (Table S1), on average the greatest disparity occurs between the pectoral lobe-fins of Latimeria and Neoceratodus (d r = 68%), whereas the lowest disparity occurs, as expected, between Salamandra and Ambystoma (d r = 4%). The disparity between the pectoral ray-fins of Polypterus and pectoral lobefins and limbs is almost as wide (d r = 18-61%) as it is between pectoral lobe-fins and limbs (d r = 22-58%). Also, the disparity between the pectoral lobe-fins of Latimeria and of Neoceratodus is greater (d r = 68%) than it is among the pectoral limbs of Ambystoma, Salamandra, and Sphenodon (d r = 4-28%). Without muscles, the pectoral limbs of tetrapods are more similar (i.e., less disparity) to the pectoral lobe-fins of Latimeria (d r = 22-42%) than to that of Neoceratodus (d r = 42-58%). Interestingly, over the average of all comparisons, parameter P shows the lowest disparity (d r = 7%) compared to all other parameters (d r = 27-66%), which makes the degree of modularity the least variable feature of the anatomical organization among the pectoral appendages studied. In turn, in the pelvic skeleton (Table S2) the greatest disparity occurs between the pelvic ray-fins of Polypterus and the pelvic lobe-fins of Neoceratodus (107%), whereas the lowest disparity occurs, again, between Salamandra and Ambystoma (d r = 5%). The disparity between the pelvic ray-fins of Polypterus and pelvic lobe-fins and limbs is greater (d r = 72-107%) than it is between pelvic lobe-fins and limbs (d r = 31-59%). Furthermore, the disparity between the pelvic lobe-fins of Latimeria and of Neoceratodus is greater (d r = 71%) than it is among the pelvic limbs of Ambystoma, Salamandra, and Sphenodon (d r = 5-14%). Without muscles, the pelvic limbs of tetrapods are more similar to the pelvic lobe-fins of Latimeria (d r = 31-42%) than to the lobe-fins of Neoceratodus (d r = 54-59%). Again, P shows the lowest disparity (d r = 12%) of all other parameters (d r = 39-96%), which makes the degree of modularity the least variable organizational feature also among pelvic appendages.

COMPARISON OF MUSCULAR NETWORKS
The muscular system of fore-and hind limbs of tetrapods (Fig. 5) has more muscles (N) than in lobe-fins, ray-fins, and ancestral state reconstructions. The lobe-fins of Latimeria and Neoceratodus also have more muscles than the ray-fins of Polypterus. The number of connections among muscles (K, i.e., common anchoring sites) follows the same evolutionary pattern. However, in both parameters, the pectoral fin musculature of Neoceratodus is more similar to that of Polypterus than that of Latimeria and tetrapods. This is because, as in Polypterus, the pectoral fins of Neoceratodus have only a few differentiated muscles: retractor lateralis ventralis pectoralis, superficial abductor, and adductors, and deep abductor and adductor. As in the skeletal network evolution, the patterns inferred for D, C, and L portray a marked trend toward a decrease in anatomical integration of the muscular system from fins to limbs. The network of muscles in tetrapod limbs has lower D and C and higher L than the ancestral state reconstructions for lobe-fins and ray-fins. The decrease in anatomical integration is notable in salamanders compared to Sphenodon, with the limbs of the tuatara showing values closer to those for ancestral state reconstructions of tetrapods. In line with this trend, the lobe-fins of Latimeria and Neoceratodus have higher D and C, and lower L, than ancestral state reconstructions. The pectoral and pelvic ray-fins of Polypterus show extreme values of D, C, L, and H, because of the presence of only a few muscles sharing common sites of attachments (6 and 3, respectively) completely interconnected to each other. The evolution of H in muscular networks points to the presence of a shift toward greater differentiation/specialization of muscles in limbs (higher H) compared to ancestral state reconstructions and to lobe-fins. This shift is more pronounced in the pectoral appendages and less pronounced in the pelvic appendages. Similar to the results for integration parameters, the limbs of Sphenodon present values that are closer to those of ancestral state reconstructions of tetrapods. Lastly, the  evolution of P shows also a shift toward a greater parcellation of the appendages, in which limbs are more parcellated than in ancestral state reconstructions, lobe-fins (except for the pelvic fin of Neoceratodus that is in the range of the values of P in tetrapods), and ray-fins. This pattern is consistent with the aforementioned decrease of integration and increase of differentiation in muscular networks in tetrapods.
Regarding the similarity of the pectoral musculature among the taxa examined (Table S4), on average the greatest disparity occurs between the pectoral ray-fins of Polypterus and the pectoral limbs of tetrapods (d r = 105-114%), while the lowest disparity separates the pectoral limbs of Ambystoma and Salamandra (d r = 3%). The disparity between the pectoral ray-fins of Polypterus and the pectoral lobe-fins of Latimeria and Neoceratodus is in the same range (d r = 53-81%) as it is between pectoral lobe-fins and limbs (d r = 53-86%); while the disparity between Latimeria and Neoceratodus pectoral lobe-fins themselves is at the lower side of this range (d r = 53%). As for the average of parameters, in contrast to the pectoral skeleton, C shows the lowest disparities (d r = 14%) and P the second lowest (d r = 17%) of all other parameters (d r = 36-126%), which makes the integration by interdependence the least variable organizational feature also among the musculature of pelvic appendages. In pelvic appendages (Table S5), the greatest disparity occurs between the pelvic ray-fins of Polypterus and the pelvic limbs of salamanders (d r = 146-147%), while the lowest disparity occurs, as expected, between the pelvic limbs of Ambystoma and Salamandra (d r = 1%). The disparity between the pelvic ray-fins of Polypterus and pelvic lobe-fins and limbs is greater (d r = 110-147%) than it is between pelvic lobe-fins and limbs (d r = 31-79%). As expected, the lowest disparity occurs among tetrapods limbs (d r = 1-27%). Likewise in the pelvic musculature, parameter C shows the lowest disparities (d r = 29%) of all other parameters (d r = 38-108%), which makes the integration by interdependence the least variable organizational of the pelvic musculature.

COMPARISON OF PECTORAL-PELVIC SIMILARITY
Phylomorphospace plots (Figs. 4 and 5) were used to show the evolution of the pectoral-pelvic similarity of appendages; a red dashed line marks the equality line (1:1 line) between pectoral and pectoral values. On average, Polypterus shows the lowest pectoral-pelvic similarity (i.e., highest percentage of relative difference, d r ) of all studied taxa, both in skeletal networks (d r = 100%; Tables S3; Fig. S1) and in muscular networks (d r = 67%; Table S6; Fig. S2). In skeletal networks, the pectoral-pelvic similarity of lobe-fins (Latimeria: d r = 15%; Neoceratodus: d r = 13%) is comparable to that of the limbs of salamanders (d r = 14-15%), whereas Sphenodon shows the greatest pectoral-pelvic similarity of all taxa analyzed (d r = 10%). Among parameters, P shows the highest similarity between pectoral and pelvic skele-tons (d r = 6%) of all other parameters (d r = 12-44%), which indicates that pectoral and pelvic skeletons are not very different in the modular organization of the skeletal anatomy. In muscular networks, the pectoral-pelvic similarity is equally high in Latimeria's lobe-fins (d r = 17%) and tetrapod limbs (d r = 11-16%); but it is much lower (d r = 60%) in Neoceratodus. However, this high disparity of Neoceratodus at the muscular level is mainly driven by the differences in the number of muscles (five in the pectoral fins and 37 in the pelvic fins) and of contacts (seven and 471, respectively), which is most likely related to a derived reduction of the pectoral fins in Dipnoi. Interestingly, parameters D, C, L, and H (which correct for network size) in Neoceratodus show relative differences in muscular networks that are closer to those of Latimeria and tetrapods; excluding N and K, pectoral-pelvic relative difference in Neoceratodus muscular networks average only 15%. Among parameters, L and C show the highest similarity between pectoral and pelvic musculatures (L d r = 3%; C d r = 7%) of all other parameters (d r = 20-73%), which indicates that pectoral and pelvic musculature established similar degrees of anatomical integration of connections. Both skeletal and muscular evolutionary patterns of the pectoral-pelvic similarity reported are in line with the presence of a similarity bottleneck in the hypothetical ancestor of sarcopterygians, but not a second similarity bottleneck at the origin of tetrapods. The secondary increase of disparity in Neoceratodus (as expected in the hypothesis illustrated in the right funnel of Fig. 1B, and most likely related to a secondary reduction of pectoral fins in Dipnoi) is only observed at the muscular level for the number of muscles (N) and their connections (K). In contrast, parameters measured in muscular networks related to anatomical integration (D, C, L), differentiation (H), and modularity (P) show that Neoceratodus pectoralpelvic similarity is in the range values observed for Latimeria and tetrapods. Finally, the ancestral state reconstructions of sarcopterygians and tetrapods tend to occupy positions in the phylomorphospaces of skeletal and muscular networks that are closer to the maximum pectoral-pelvic similarity (Figs. 4 and 5). However, a broader sample of taxa would be needed to conclusively map the positions of hypothetical last common ancestors in these morphospaces.

PARCELLATION OF LIMBS
Our results show that the anatomical integration of the appendages (as estimated by proxies D, C, and L) decreased from lobe-fins to limbs. This is an evolutionary pattern we see in both the pectoral and pelvic appendages. This pattern is consistent with a transition from a web-like appendage of interconnecting bones, as in coelacanths and extinct tetrapodomorphs (e.g., Tiktaalik; Shubin et al. 2006Shubin et al. , 2014, to a more tree-like appendage with digits and series of phalanges in tetrapods. In this context, the tree-like organization of Neoceratodus would be a secondarily derived feature or convergence, which comes from the radial structure of the fins, rather than the presence of digits with phalanges. Because tetrapods still conserve part of a web-like arrangement among the mesopod bones, their values of clustering (C) did not decrease compared to Neoceratodus lobe-fins and Polypterus ray-fins, which lack such an arrangement in any part of their fins. Moreover, most newly evolved muscles have fewer attachments (i.e., connections) compared to the undivided muscle masses of lobe-fins (e.g., deep and superficial adductors and abductors) ). Together, these findings suggest that the increased number of autopodial bones and newly differentiated muscles in evolving limbs was not accompanied by a proportional increase of new physical contacts. Hence, limbs became less anatomically integrated compared to lobe-fins.
Another consequence of limbs being sparsely integrated compared to fins is the increase of modularity or parcellation in limbs, both at a skeletal and a muscular level. In morphology, integration and modularity are largely opposite properties, with modules originating because of a loss of integration at the boundary of two or more regions (Simon 1962;Eble 2005;Wagner et al. 2007;Klingenberg 2008;Goswami et al. 2015; Esteve-Altava 2017a, 2017b). The proxy used to evaluate the parcellation of fins and limbs in anatomical networks (P) shows a marked shift toward an increase of modularity from fins to limbs. This means that tetrapod limbs have more, and more balanced, modules than ray-fins. In this scenario of increasing modularity, lobefins adopted intermediate values between ray-fins and limbs, as expected by their phylogenetic position. This may indicate that evolving a greater degree of modularity of appendages was a novelty acquired prior to the fins-to-limbs transition, which was later reinforced in tetrapods.
Here, we show also that integration and parcellation have evolved differently for the skeletal and for the muscular components of appendages. Anatomical parcellation is the most similar organizational feature among skeletons of different taxa and between pectoral and pelvic appendages of the same taxon. In contrast, anatomical integration (specifically, C and L) is the most similar feature for the musculature, for all comparisons among and within appendages. Although coordinated morphological responses are necessary for organisms to adapt to new conditions, bones and muscles respond differentially in time and magnitude to evolutionary pressures (Diogo et al. 2013). This difference between skeletal and muscular networks suggests a decoupled modularity response to different functional demands for the skeleton and the musculature during evolution. Further studies including more taxa, and in different groups, will be needed to test this preliminary inference.
In tandem with the relative reduction in anatomical integration in tetrapods, muscle groups also changed their connectivity patterns, becoming more functionally specialized in tetrapods than in lobe-finned fishes ). The evolution of heterogeneity (H) or anisomerism in muscular networks matches this specialization of appendicular muscles. In fins, muscle masses are few and similarly connected (lower H), and tend to be more generalized in their potential actions (e.g., adductor and abductor muscles) Molnar et al. 2016Molnar et al. , 2017. In limbs, we find a wider variety of muscles between two extremes (higher H): some limb muscles establish a few short-range connections and function more locally (e.g., intermetatarsales, flexores breves profundi, and contrahentes pedis, each of which has two connections), while others establish many long-range connections and function more globally (e.g., flexor digitorum communis, contrahentium caput longum, extensor digitorum longus) (Diogo and Abdala 2010). We speculate that this increase in heterogeneity and specialization of the anatomy of limbs enhanced or facilitated the evolution of a wide range of locomotion strategies within tetrapods.
To what extent is the reported evolution of network integration and parcellation related to variational (shape) and developmental modularity in fins and limbs? This remains highly uncertain. Unfortunately, studies on the morphological integration and modularity of pectoral and pelvic fins are scarce (reviewed in Esteve-Altava 2017b). For example, the modularity of fins has been studied in fishes, comparing patterns of presence and disparity among pectoral, pelvic, dorsal, anal, and caudal fins (Larouche et al. 2015(Larouche et al. , 2017; however, these studies did not test whether each fin has variational modules or it is entirely integrated. To our knowledge, there are no studies of variational modularity in lobefins. The vast majority of studies of morphological integration and modularity in appendages focus on limbs and use morphometrics to assess skeletal shape variation (Esteve-Altava 2017a). These studies found variational modules in many tetrapod groups, including salamanders (Kolarov et al. 2011). However, morphological integration among modules may vary within limbs due to, for example, ecological specialization (Young et al. 2010;Martín-Serra et al. 2015) or developmental stage (Kolarov et al. 2011;Maxwell and Dececchi 2012). On the other hand, developmental studies highlight the differences in modularity we observed in the parcellation of fins and limbs. For example, ray-fins have been suggested to have fewer skeletal compartments or modules (one radial domain + fin ray) than sarcopterygian fins (three endoskeletal domains + fin ray) and limbs (stylopod, zeugopod, and autopod) (Yano and Tamura 2013). In addition, tetrapods have pectoral and pelvic girdles that also show a developmental semiindependence (Sears et al. 2015). From a developmental point of view, some studies have speculated that the different degree of parcellation between fins and limbs might be a consequence of a combination of various developmental mechanisms; for example, decoupling of the Meis/HoxA11/HoxA13 expression, the more distal and late expansion of the 5'HoxD genes, and timing of the apical ectodermal ridge (AER) to apical fold (AF) transition (Yano and Tamura 2013).

NEOCERATODUS IS AN UNUSUAL FISH
As our results show, the corresponding forelimbs and hindlimbs of the three tetrapod taxa resemble each other more than pectoral and pelvic fins of lobe-finned fishes do, respectively. Interestingly though, lobe-fins vary in their similarity to limbs, with Latimeria often being more similar to tetrapods than Neoceratodus despite their phylogenetic positions. In fact, most analyses place Neoceratodus closer than Latimeria to the tetrapod stem (e.g., see Irisarri et al. 2017). Neoceratodus deviates from Latimeria, for example, in the number of parts, anatomical integration, and parcellation. A closer look at the gross anatomy of Neoceratodus, compared to that of Latimeria, demonstrates that the lobe-fins of Neoceratodus have an extremely derived anatomy, which comprises a long series of mesomeres (often 14, but sometimes more), each accompanied by four or five pre-and postaxial radials. In addition, the musculature of the pectoral fin is secondarily simplified, with only five muscle masses, whereas the pelvic fin presents a sequence of pronator and supinator muscles (one of each for each mesomere) . This reduction in number of muscles is most likely related to the secondary (derived) reduction of the pectoral fins of Neoceratodus that occurred during dipnoan evolutionary history . The anatomy of Neoceratodus fins is unusual, especially, when compared with what is known of stem tetrapodomorphs such as Eusthenopteron (Andrews and Westoll 1970), Panderichthys (Boisvert 2005;Boisvert et al. 2008), or Tiktaalik (Shubin et al. 2006. Only when we compare Neoceratodus to extinct porolepiform lobe-finned fishes like Glyptolepis (Ahlberg 1989) can we see a similarly derived anatomy, with a long series of mesomeres and radials. Based on our findings about the network topology of lobe-fins and limbs, we infer that Latimeria retains more ancestral traits for Sarcoptergii for extant phylogenetic bracketing in reconstructing the muscular anatomy of intermediate forms between lobe-finned sarcopterygians and tetrapods (e.g., Molnar et al. 2017), and for comparisons based on anatomical network analysis. Furthermore, the addition of dipnoan fossils to future analyses could clarify the patterns of change in that clade and more broadly in Sarcopterygii that led to the unusual form of lobe-fins in derived dipnoan taxa such as Neoceratodus.

BOTTLENECKS IN PECTORAL-PELVIC SIMILARITY
Ray-fins and sarcopterygian appendages (lobe-fins and limbs) differ in their pectoral-pelvic similarity, whereas lobe-finned fishes and tetrapods have closer values of pectoral-pelvic similarity. Although pectoral-pelvic similarity in lobe-fins is within the range observed in tetrapods for the skeleton, when muscles are compared, Neoceratodus deviates from the tetrapod range and occupies an intermediate position between Polypterus and tetrapods. However, this deviation is mostly driven by differences in the number of muscles and attachments derived likely from the loss of pectoral fin muscles in Neoceratodus, due to a secondary simplification of its pectoral appendages . In fact, network parameters related to anatomical integration and heterogeneity indicate that Neoceratodus has a pectoral-pelvic similarity partially within the range of tetrapods and Latimeria for muscular networks.
On a separate note, studies comparing shape variation between pectoral and pelvic appendages have also reported similarities of morphological integration in tetrapods (Hallgrímsson et al. 2002;Young et al. 2005Young et al. , 2010Goswami et al. 2014). These studies often link the presence of similar patterns of morphological integration between fore-and hindlimbs to serial homology and/or to shared developmental toolkits (Wagner 1989(Wagner , 2014Shubin et al. 1997;Hallgrímsson et al. 2002). However, patterns of integration of shape covariation between fore-and hindlimbs can change by differential functional specializations of each pair of appendages (Young et al. 2010;Villmoare et al. 2011). Our results at the anatomical network level support the idea of pectoral-pelvic integration in sarcopterygians, which evolved similarly higher anatomical integration compared to nonsarcopterygian fishes with ray-fins.
Finally, our results confirm the presence of a similarity bottleneck leading to sarcopterygians, which is only predicted by one of the three hypotheses presented (Fig. 1B, right funnel). These results partially supports the two-bottleneck hypothesis (osteichthyes and sarcopterygians) proposed by Coates and Cohn (1998), Coates et al. (2002), Diogo et al. (2013), and Diogo and Molnar (2014). However, this hypothesis also predicts an additional bottleneck leading specifically to tetrapods, which we cannot confirm or reject with the anatomical network analysis of appendages. This additional bottleneck is supported by the comparison of the number of muscles and bones that are topologically similar in the pectoral and pelvic appendages (see Diogo et al. 2013;Diogo and Molnar 2014). In general, our findings are in line with the idea that pectoral-pelvic similarity of limbs is mainly due to parallel or convergent evolution within gnathostomes, rather than due to serial homology, because tetrapods show larger average similarities in the organization of the skeleton and muscles of appendages than lobe-finned and ray-finned fish. Future anatomical network studies, including sarcopterygian fish fossils as well as early tetrapod fossils, could further test these ideas and can also help to clarify why some of the network patterns that we found differ between skeletal and muscular structures. We expect that the findings presented in this study on the anatomical similarities between lobe-fins and limbs, and between pectoral and pelvic appendages, will inform future reconstructions of the musculoskeletal anatomy in such fossil taxa and thus be helpful in gaining a better understanding of the origin and later diversification of tetrapod limbs.

GATHERING ANATOMICAL INFORMATION
We dissected the pectoral and pelvic appendages of Polypterus senegalus (Actinopterygii: Polypteridae), Latimeria chalumnae (Sarcopterigii: Coelacanthiformes), Neoceratodus forsteri (Sarcopterygii: Dipnoi), Ambystoma mexicanum (Urodela: Ambystomatidae), Salamandra salamandra (Urodela: Salamandridae), and Sphenodon punctatus (Lepidosauria: Rhynchocephalia). All specimens examined were wild-type adults, donated frozen or preserved; no experiments on live animals were performed for this study. Three frozen specimens of Polypterus senegalus (HU PS1, HU PS2, and HU PS5-1) were donated by the Department of Anatomy at Howard University College of Medicine, USA, and dissected under magnification. One formalin-fixed specimen of Latimeria chalumnae (SZ10378) was dissected and serial histological sections of one embryo of Latimeria (CCC163K) were examined at the Institüt für Evolution undÖkologie, Universität Tübingen, Germany. Two formalin fixed specimens of Neoceratodus forsteri (JVM-I-1051NC, JVM-I-1052NC) were donated by Macquarie University, Australia, and dissected under magnification. In addition, MRI scans of Latimeria chalumnae and Neoceratodus forsteri were provided by the Digital Fish Library, UCSD (www.digitalfishlibrary.org). Images were resized in Im-ageJ (NIH) and 3D reconstruction of fin skeleton and muscles was performed with Amira 5.2.1 (Visage Imaging) with manual segmentation of structures. Three specimens of Ambystoma mexicanum (HU AM1, HU AM2, and HU AM5-1) were donated by the Department of Anatomy at Howard University College of Medicine, USA, and dissected under magnification. Five specimens of fire salamanders (Salamandra salamandra; Royal Veterinary College (UK) specimens RVC-JRH-SAL1 through SAL5) that had died in captivity from reasons unrelated to this study were dissected under magnification. Two specimens of the tuatara Sphenodon punctatus were dissected under magnification; these were "no data" museum specimens (Natural History Museum (London, UK) specimen BMNH1935.12.6.1; California Academy of Sciences (San Francisco, USA) specimen CAS 208882) collected long before our study under unknown conditions. For simplicity, sesamoid bones (e.g., Regnault et al. 2017) were not coded in these networks, nor were soft tissue contacts/attachments such as cartilages and ligaments, but future analyses could add such data.
Taxa were selected because they possess the relatively most plesiomorphic anatomy of appendages of extant taxa bracketing the fins-to-limbs transition (i.e., rootward and crownward relative to Tetrapoda/Amniota) and because they were available for dissection. Thus, we chose tetrapod taxa with plesiomorphic anatomies, such as salamanders and tuatara, and excluded frogs which have highly specialized limbs. Of the two species of extant coelacanth species, Latimeria chalumnae (listed as critically endangered by the IUCN) and Latimeria menadoensis (listed as vulnerable by the IUCN), only the former was available for dissection and there is no indication that the latter taxon's anatomy is divergent from the former's. Of the six extant species of lungfishes, Neoceratodus forsteri is the only one not having extremely simplified appendages. Given the few available taxa of lobe-finned fishes, a larger sample size would only be possible by including more tetrapods (e.g., mammals, crocodiles, turtles). Importantly, we decided not to do this to avoid a bias toward tetrapod forms in our comparisons. Furthermore, it was qualitatively clear to us that the bones and muscles of these amniote taxa are not so divergent that they would greatly alter our conclusions about bottlenecks or general evolutionary patterns (e.g., close to the origin of Tetrapoda or more rootward of it). To minimize potential intraspecific variability in the arrangement of bones and muscles in the taxa selected, we carried out an extensive literature survey (Goodrich 1930;Francis 1934;Millot and Anthony 1958;Young et al. 1989;Diogo and Abdala 2010;Tanaka 2012, 2014;Boisvert et al. 2013;Wilhelm et al. 2015;Diogo et al. 2016;Miyake et al. 2016;Molnar et al. 2016;Regnault et al. 2017; and references therein) to establish, and use, the most common anatomical configuration for each taxon. In this survey, we found minimal or no clear discrepancies between studies; none of which would appreciably alter our results. Finally, because we focused on the muscular anatomy, we decided not to include any extinct taxa-for which there are only incomplete muscular reconstructions-in the present study. Our open dataset would allow future studies to add more extant and/or extinct taxa to modified analyses.

MODELING ANATOMICAL NETWORKS
We built skeletal and muscular network models of the pectoral and pelvic appendages of each species using the anatomical information gathered from dissections and the literature. A network model comprises a set of nodes and a set of links connecting the nodes (as in Fig. 2). Skeletal networks were modeled as undirected, unweighted networks in which nodes represent skeletal elements (ossified and cartilaginous) and links represent the presence of a physical joint or articulation between a pair of elements. Muscular networks were modeled as undirected, weighted networks in which nodes represent differentiated muscles and links represent the number of shared sites of anchoring (e.g., origin, insertion) between two muscles. Nodes disconnected from the largest component of each network were excluded from these analyses because some functions did not tolerate disconnected nodes or yield unreliable values when they were present. The weights of links in muscular networks were ignored for the quantification of parameters for the same reasons, but they were considered for the search of connectivity modules.

ANATOMICAL NETWORK ANALYSIS
We measured seven network parameters to evaluate the anatomical organization of pectoral and pelvic appendages, namely: the total number of nodes (N) and of links (K), density of connections (D), mean clustering coefficient (C), mean shortest path length (L), heterogeneity of connections (H), and parcellation (P). Parameters N, K, D, C, L, and H were computed in R using algorithms implemented in the package igraph version 1.0.1 (Csardi and Nepusz 2006). Parameters N and K are simple counts of the number of elements and interactions modeled. Parameters D, C, L, and H are well-known parameters in network sciences; details on their mathematical equations were given elsewhere (Rasskin-Gutman and Esteve-Altava 2014). In short, D measures the actual number of connections divided by the maximum number possible (it ranges from 0 to 1). C measures the average of the ratio of a node's neighbors that connect among them (it ranges from 0 to 1). L measures the average number of links required to travel between two nodes (minimum 1). H measures the variability in the number of connections of nodes (minimum 0) as the ratio between the standard deviation and the mean of the number of connections of all nodes in the network. Finally, the parameter P was computed from the connectivity modules identified in the best partition of the network (see below); connectivity module are groups of nodes with more links to nodes within the group than to nodes outside the group. P is defined as P = 1 − m=1 ( Nm N ) 2 , where N m is the number of nodes in module m, and N is the total number of nodes of the network. P is 0 when all nodes are in a same module, and P tends toward 1 when nodes are evenly distributed within many modules. To calculate P, we first needed to identify the number of modules and the nodes included in them. Connectivity modules were identified using the spin-glass model and simulated annealing algorithm (Reichardt and Bornholdt 2006) implemented in the package igraph for R. To account for stochasticity, we performed 1000 iterations of the algorithm and selected the best result. We provided the details of the modularity results in Tables S17-S29  for skeletal networks and Tables S39-S51 for muscular networks for further record.
The robustness of parameter values due to potential errors in identifying the particular bones and muscles and their connections from dissections was accounted by comparing the observed values to a randomly generated sample of 10,000 noisy networks for each one of the anatomical network of the study. A noisy network is generated by rewiring the links of the original mus-culoskeletal network with a probability of 5%; this introduces a 5% artificially generated error. To assess for robustness we compared observed values to the empirical distribution of values in the sample of noisy networks. Specifically, we tested the H 0 that observed value is equal to the sample mean. We rejected the H 0 with a P-value of 0.05 if the observed value is in the 5% end of the distribution of simulated values. Tables S7-S11 for skeletal  networks and Tables S30-S34 for muscular networks summarize the sample mean, standard deviation, standard error of the mean, the interval for the 95% of simulated values, and the result of the empirical statistical test ("TRUE," we cannot reject H 0 ; "FALSE," we reject H 0 with P-value 0.05). A value of "TRUE" in Tables S11 and S34 means that the observed value of this parameter in this anatomical network is not different from the average measured in the sample of 10,000 noisy networks with artificially generated errors. This is the case for every parameter on every network, with a few exceptions, namely: parameter H in Neoceratodus pectoral and pelvic skeletal networks, parameter C in Neoceratodus pelvic muscular network, and parameter P in Salamandra and Sphenodon pelvic muscular networks. There is no way to generate random variation without creating unrealistic connections, that is, connections in which we could not in reality had made a dissection/coding error or for which no such natural variation exists (e.g., an ulnare connecting with a femur, or a pelvis disconnected from a femur). Unfortunately, manually curating the 10,000 noisy networks one by one is unfeasible in practice, whereas dissecting more specimens is not possible because they are endangered species and/or difficult to obtain and time-consuming to code for detailed network parameters.

QUANTIFICATION OF ANATOMICAL SIMILARITIES
We measured the similarity among appendages, and between pectoral and pelvic appendages, as the relative difference of values for each parameter,d r = (x − y)/((x + y)/2), where x and y are the two values compared. Results are shown as percentage of d r for each pair of networks compared, and for each parameter, separately. We also computed the mean and standard deviation of d r for the seven parameters in every comparison. Note that similarity is inversely related to d r : higher values of d r indicate lower similarity between appendages; likewise, lower values of d r indicate greater similarity. Tables S1-S6 show the measured values.

PHYLOGENETIC COMPARISONS
With the sole purpose of helping to visualize the relative similarity among appendages, we plotted phylomorphospaces for every network parameter measured in skeletal and muscular networks. These plots project the phylogeny into a morphospace of two traits-values of a parameter for the pectoral and pelvic appendage-which allows us to compare visually the differences in similarity among taxa. Values for the pectoral appendages were plotted along the x-axis; values for the pelvic appendage were plotted along the y-axis. For reference we added lines of equality, or identity, to phylomorphospaces to mark complete pectoral-pelvic similarity (dashed red lines), not to be confused with correlation lines. We created these phylomorphospaces using the function phylomorphospace in the R package phytools (Revell 2012). This function internally estimates the values for hypothetical taxonomic units using maximum likelihood. However, such estimations must be taken with caution because of the small sample size. For reference, we provided the reconstructed values and 95% CI in Tables S12 and S13 for skeletal networks and Tables S35 and S36 for muscular networks.
Limitations of our sample size, described above, prevent performing meaningful statistical tests. Nevertheless, for completeness, we have included in the Supporting Information the results of a Moran's I test of autocorrelation using neighboring weights (Tables S15 and S37). Moran's I tests were performed using the function Moran.I of the package ape (Paradis et al. 2004). Likewise, we performed correlations through the origin of phylogenetic independent contrasts between pectoral and pelvic appendages (Tables S16-S38). This test was performed using the functions pic and lmorigin of the package ape. As expected, parameters in pectoral and pelvic skeletal networks show nonsignificant phylogenetic autocorrelation; while only two parameters in pectoral muscular networks (D, L) and three (D, L, H) in pelvic muscular networks show a significant phylogenetic autocorrelation below the 5% significance level (and none of them below the 1%). In turn, pectoral and pelvic appendages correlate significatively for parameters of skeletal networks (which do not show phylogenetic autocorrelation), while only two out of seven correlations between pectoral and pectoral appendages in muscular networks are significant (D pec-pel , L pec-pel ). Because of the small size of our sample, we have refrained from discussing these results further in the main text. This problem would not easily be ameliorated by including more extant tetrapods because more extant nontetrapods would then need inclusion to prevent imbalance in the analyses.
Phylogenetic visualizations and tests were performed using a consensus phylogeny of the studied taxa created using information from Tree of Life Web Project (Janvier 1997). Branch lengths were calibrated in millions of years of evolution for the minimal divergence time of each taxa crown group according to the Paleobiological Database (available at https://paleobiodb.org/). For example, the split of Sphenodon from the two salamanders was set as the split between amniotes (Reptiliomorpha) and lissamphibians (Temnospondyli), 312 Ma. Note that the branch lengths shown in phylomorphospaces do not correspond to the actual tree lengths, but represent differences in the values of parameters among taxa.

Supporting Information
Additional Supporting Information may be found in the online version of this article at the publisher's website: Figure S1. Relative differences between pectoral and pelvic skeleton. Figure S2. Relative differences between pectoral and pelvic musculature. Table S1. Percentage of relative difference of parameters among pectoral skeletal networks. Table S2. Percentage of relative differences of parameters among pelvic skeletal networks. Table S3. Percentage of relative difference between pectoral and pelvic skeletal networks. Table S4. Percentage of relative difference of parameters among pectoral muscular networks. Table S5. Percentage of relative differences of parameters among pelvic muscular networks. Table S6. Percentage of relative difference between pectoral and pelvic muscular networks. Table S7. Mean values of parameters in 10000 noisy skeletal networks. Table S8. SD values of parameters in 10000 noisy skeletal networks. Table S9. SEM values of parameters in 10000 noisy skeletal networks. Table S10. Inter 95% distribution range values of parameters in 10000 noisy skeletal networks. Table S11. Test of observed values in skeletal network falling within the 95% range of 10000 noisy skeletal networks. Table S12. Ancestral state reconstruction of pectoral skeletal network parameters (95% CIs). Table S13. Ancestral state reconstruction of pelvic skeletal network parameters (95% CIs). Table S14. Moran's I test of autocorrelation on skeletal networks parameters. Table S15. Regression through the origin of phylogenetic independent contrasts for pectoral-pelvic skeletal networks. Table S16. Summary of the modularity analysis in skeletal networks. Table S17. Connectivity modules in the pectoral skeletal network of Polypterus. Table S18. Connectivity modules in the pelvic skeletal network of Polypterus. Table S19. Connectivity modules in the pectoral skeletal network of Latimeria. Table S20. Connectivity modules in the pelvic skeletal network of Latimeria. Table S21. Connectivity modules in the pectoral skeletal network of Neoceratodus. Table S22. Connectivity modules in the pelvic skeletal network of Neoceratodus. Table S23. Connectivity modules in the pectoral skeletal network of Ambystoma. Table S24. Connectivity modules in the pelvic skeletal network of Ambystoma. Table S25. Connectivity modules in the pectoral skeletal network of Salamandra. Table S26. Connectivity modules in the pelvic skeletal network of Salamandra. Table S27. Connectivity modules in the pectoral skeletal network of Sphenodon. Table S28. Connectivity modules in the pelvic skeletal network of Sphenodon. Table S29. Mean values of parameters in 10000 noisy muscular networks. Table S30. SD values of parameters in 10000 noisy muscular networks. Table S31. SEM values of parameters in 10000 noisy muscular networks. Table S32. Inter 95% distribution range values of parameters in 10000 noisy muscular networks. Table S33. Test of observed values in muscular network falling within the 95% range of 10000 noisy muscular networks. Table S34. Ancestral state reconstruction of pectoral muscular network parameters (95% CIs). Table S35. Ancestral state reconstruction of pelvic muscular network parameters (95% CIs). Table S36. Moran's I test of autocorrelation on muscular networks parameters. Table S37. Regression through the origin of phylogenetic independent contrasts for pectoral-pelvic muscular networks. Table S38. Summary of the modularity analysis in muscular networks. Table S39. Connectivity modules in the pectoral muscular network of Polypterus. Table S40. Connectivity modules in the pelvic muscular network of Polypterus. Table S41. Connectivity modules in the pectoral muscular network of Latimeria. Table S42. Connectivity modules in the pelvic muscular network of Latimeria. Table S43. Connectivity modules in the pectoral muscular network of Neoceratodus. Table S44. Connectivity modules in the pelvic muscular network of Neoceratodus. Table S45. Connectivity modules in the pectoral muscular network of Ambystoma. Table S46. Connectivity modules in the pelvic muscular network of Ambystoma. Table S47. Connectivity modules in the pectoral muscular network of Salamandra. Table S48. Connectivity modules in the pelvic muscular network of Salamandra. Table S49. Connectivity modules in the pectoral muscular network of Sphenodon. Table S50. Connectivity modules in the pelvic muscular network of Sphenodon.