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Network architecture associated with the highly specialized hindlimb of frogs

Network architecture associated with the highly specialized hindlimb of frogs

  • Daniel Andrés Dos Santos, 
  • Jéssica Fratani, 
  • María Laura Ponssa, 
  • Virginia Abdala


Network analyses have been increasingly used in the context of comparative vertebrate morphology. The structural units of the vertebrate body are treated as discrete elements (nodes) of a network, whose interactions at their physical contacts (links) determine the phenotypic modules. Here, we use the network approach to study the organization of the locomotor system underlying the hindlimb of frogs. Nodes correspond to fibrous knots, skeletal and muscular units. Edges encode the ligamentous and monoaxial tendinous connections in addition to joints. Our main hypotheses are that: (1) the higher centrality scores (measured as betweenness) are recorded for fibrous elements belonging to the connective system, (2) the organization of the musculoskeletal network belongs to a non-trivial modular architecture and (3) the modules in the hindlimb reflect functional and/or developmental constraints. We confirm all our hypotheses except for the first one, since bones overpass the fibrous knots in terms of centrality. Functionally, there is a correlation between the proximal-to-distal succession of modules and the progressive recruitment of elements involved with the motion of joints during jumping. From a developmental perspective, there is a correspondence between the order of the betweenness scores and the ontogenetic chronology of hindlimbs in tetrapods. Modular architecture seems to be a successful organization, providing of the building blocks on which evolution forges the many different functional specializations that organisms exploit.


Network analyses have been increasingly used in the context of comparative vertebrate morphology due to their undoubtedly fresh perspective regarding issues such as anatomical topology, morphogenetic integration, and modularity [1,2]. Addressing anatomical systems as networks and exploring their patterns of connections can lead to useful insights. For instance, one of the most interesting properties of networks is intermediacy in information flow, and the betweenness score as a measure of centrality can be used for detecting the bridging role a given node can achieve in the flow of information through the network [3]. The development of a novel methodology for anatomical studies, such as anatomical network analysis (AnNA, [1]) has allowed treating the skeletal units of the vertebrate body as elements of a network (nodes), whose interactions at their physical contacts (links) determine the phenotypic modules, with an implicit correspondence between topology and anatomical organization.

Individuals are composed of several parts that are more or less different of each other in terms of function, anatomical structure, and embryological origins. This organization in subunits implies a modular organization [413]. Complex systems often evolve in a modular fashion, i.e. with traits integrated into groups (modules), which can then change in a coordinated manner and independently of other modules [13]. In the framework of evolutionary biology, a morphological module is a complex of phenotypical characters that meet three criteria: 1) they serve together to a primary function, 2) they are integrated by strong pleiotropic effects of genetic variation, and 3) they are relatively independent from other units [1416]. Recently, several studies assessing morphological evolution have focused on modularity, including studies of the evolution of insect wings [1720], rodent mandibles [2129], and skulls of lizards [30], birds [31] and various mammals, including humans [2,3242].

The simplest definition of a morphological module refers to a semi-independent set of body elements with more numerous and stronger interactions among themselves than with outer elements [16]. In the context of network analysis, modules are sets of densely connected nodes more strongly linked to each other than to the rest of the network. In addition to having the same name, the deep similarity between the definitions for both concepts (i.e. morphological and structural modules) is remarkable. Thus, the quantitative procedures and algorithms developed for community detection in networks, and built around the notion of modularity [3], have attracted the attention of morphologists to shed light about module issues in comparative biology [16]. Morphological modularity remains poorly studied both in basal lineages of tetrapods as well as in key anatomical systems, but the motivation to fill these gaps of information increases greatly with these new opportunities of research. For instance, the modularity of the tetrapod limbs is crucial to understand changes associated to different locomotion modes. Certainly, a network approach could lead to new insights about the integration of the musculoskeletal system in limbs, and an example in such direction is a recently published study on humans [43].

Among vertebrates, network modularity studies might be especially important in anurans. All anurans can jump, an activity that can be described as the paired extension of hindlimbs propelling the animal off the ground [44]. The specialized morphology associated to jumping in frogs includes a shortened trunk and tail, elongated ilia, and elongated hindlimbs [4547]. These morphological traits were already present in the earliest fossils such as Prosalirus [47,48]. Even though the biomechanics of jumping in anurans is reasonably simple [49], several morphological features potentially determine the ability to jump of a given animal, and they are generally dependent of each other. The exclusive combinations of structural and functional properties of each specimen will determine its locomotion performance, which may originate from their individual elements in non-obvious ways [50]. Delimiting modules and analyzing their correspondence with anatomical features is a big contribution to the understanding of the development and evolution of morphological structures [51]. The identification of modules can also contribute to the understanding of the ways by which the anatomical parts of the body of an animal evolve into very different forms, but still fit together and function properly [5256].

Here, we use a graph-theoretic approach to model the hindlimb of frogs as an anatomical network in which the fibrous knots, the skeletal and muscular units are represented as nodes, while their physical contacts are represented as edges. The resultant network model is then used to further identify patterns of organization. Our main hypotheses sustain that (1) the higher betweenness values are recorded for fibrous elements belonging to the connective system, (2) the musculoskeletal network exhibits a modular organization or non-trivial architecture, (3) the modules in the hindlimb reflect functional and/or developmental constraints, and these restrictions are not necessarily overlapped.

Material and methods

Anatomical data and network elements

In this paper, we studied the musculoskeletal and tendinous anatomy of the pelvic girdle and hindlimb of adult specimens of Leptodactylus latinasus. Specimens are housed in the herpetological collection of Fundación Miguel Lillo (FML). The list of examined specimens includes material from Argentina: 1) Jujuy, Aguas Blancas: FML 29482, 2) Salta, La Unión: FML 29480–81, 3) Salta, Orán: FML 29478–79, and 4) Tucumán, Lules, FincaNougués: FML 2983–84. Specimens were dissected and examined with a Zeiss Discovery. V8 Stereomicroscope. Anatomical nomenclature follows Diogo & Abdala [57], Diogo & Ziermann [58], and Diogo & Molnar [59]. Since some of the names used in [5759] do not correspond to those most commonly used for anurans in the literature [60,61], we provide a list of equivalent nomenclatural terms (Table 1).

Table 1. Pelvic and limb muscles of adults of Leptodactylus latinasus, following the nomenclature of Diogo & Molnar [59] and synonyms commonly used in anuran literature.

Networks are collections of discrete entities or elements (vertices or nodes) connected by some relationship of interest (links or edges). In our case, nodes correspond to anatomical elements (bones, muscles and fibrous knots) and edges encode physical contacts among such elements (e.g. tendinous and ligamentous junctions). Fig 1 shows the actual anatomical substrate from where the network is constructed.

Fig 1. Anatomical elements of the anuran hindlimb considered in this study.

Bones in red, muscles in yellow and fibrous knots in green.fdc, flexor digitorum communis; fdcot knot I+II, flexor digitorum communis origin tendon knots I+II; it B, ischiotrochantericus B; p, puboischiofemoralis; ten it knot, tenuissimus insertion tendon knot.

Fibrous knots are here defined as critical portions of connective tissues from which multiple (more than two) sets of identically aligned collagen fibers seem to branch out (Fig 2). They are hypothesized to act as gateways in the transmission of mechanical signals. Consequently, edges incident on the fibrous knots represent tendinous segments, or equivalently, they account for fibrous substrates exposed to uniaxial mechanical stress in the actual anatomical system. The adjacency list, with the respective set of neighbors of each node, can be found in Table 2.

Table 2. Nodes comprising the musculoskeletal network.

Typology and modular classification are reported. The adjacency list column includes the IDs' neighbors of the target vertex.

Fig 2. Illustrative example highlighting the concept of connective knot.

Anatomical (A and B) representation of the fleshy elements in the hindlimb of a frog. Drawings are modified from the classic work of Gaupp [60]. The Achilles tendon originates from the flexor digitorum communis (fdc) and then spreads out along the underside of the foot to form the aponeurosis plantaris, which in turn sends tendinous strands into each of the several digits. For this particular case, musculoskeletal connections between fdc and digits can be modeled through two alternatives, one more naïve (C) and one more realistic (D) network representation. In the naïve case, several edges are incident on the same muscular node suggesting that several tendons originate from such muscle. In the realistic case, just a single edge is incident on the muscular node, better reflecting the existence of the single Achilles tendon originated from the muscle under consideration. The inclusion of a fibrous knot enables us to better tackle the subtleties in the musculoskeletal connections. B bones; T tendons; M muscles and FK fibrous knots.

The anatomical elements of this study include intrinsic components of the pelvic girdle, stylopodium, and zeugopodyum, and extrinsic elements of the autopodium; except for the short muscles of the acetabular joint (quadratus femoris, gemelus, and obturador internus) (Fig 1). Due to the fact that the distal iliac area, ischium and pubis emerge as a single mesenchymal matrix during development [62,63], and are fused into one element in the adult stage, they were merged into the 'acetabulum' element of the matrix. We consider the same point of origin for all the flexor tendons of the foot, because they integrate the same superficial tendinous layer (i.e. the aponeurosis plantaris) despite their double origin (flexor tendons of digits I, II, and part of III arise from the aponeurosis plantaris and those of digits III, IV and V from m. flexor brevis superficialis). This study is performed with specimens that were already housed in herpetological collections; thus, permissions to collect specimens or the following of ethical regulations were not necessary.

Network analysis

General concepts.

A network is a collection of nodes (or vertices) and links (or edges) modeling the elements of a system and their relationships, respectively. Mathematically, networks are studied by the graph theory. Below, we introduce certain technical concepts in order to facilitate the lecture of the manuscript by a broad readership.

Links can be directed or undirected depending on the oriented nature of the relationship, and weighted or unweighted if the strength of the relationship is valued or not, respectively. A path in a graph represents an alternate sequence of vertices and edges from a certain origin to a certain destination by traversing edges. The first vertex of the first edge of a path is the origin and the second vertex of the last edge is the destination. Both origin and destination are called the endpoints of the path. The length of a path is the number of edges that it uses. Given a graph G, the distance d (x, y) between two vertices x and y is the length of the shortest (or geodesic) path from x to y, considering all the possible paths from x to y in G.


Centrality measures capture the relevance of the position of the individual nodes in the network. One of these quantitative indices is the betweenness score. Betweenness accounts for the frequency of occurrence of a given node in shortest paths between any pair of nodes in the network. It is useful for detecting the bridging role a given node can exhibit in the flow of information across the structure of the network. As nodes with high betweenness are removed, the remaining elements of the network are prone to be disconnected. In the context of muscle-skeletal networks, centrality indicates high exposure of elements to the propagation of force.

Modularity and network layout.

Modularity refers to densely connected clusters of nodes embedded into a more global network. It quantifies the extent, relative to a null model network, to which vertices are grouped into dense sub-graphs [3]. The critical issue for quantifying it relies on the definition of a modularity matrix B = AP, in which A is the adjacency matrix of the network that defines a graph with n vertices and m edges, and the matrix P contains the probability of two nodes to be connected by an edge under the prescriptions of a random configuration model. In other words, each element of P = [pij] corresponds to the probability of existence of an edge between vertices i and j in a random network in which the degrees of all vertices are the same as in the input graph. For unimodal networks, the usual null model sets such probability as proportional to the product of degrees k (number of actual neighbors) of the nodes involved, namely pij = kikj/(2m). A measure of modularity, called coefficient Q, is devised in [3] and consists of adding the entries of the modularity matrix for pairs of vertices belonging to the same group of a given vertex set partition. Thus, the modularity Q, for a given assignment g of vertices to groups or modules, reflects the extent to which edges are formed within modules instead of between modules, relative to a null model. Formally, modularity is defined as where the right hand factor is the Kronecker delta, which is equal to 1 if nodes i and j are in the same module and is otherwise 0. The partition, or division of vertices into modules, that maximizes Q is preferred. Since modularity optimization is NP-hard, heuristic procedures have been developed. Among the many available algorithms implemented in the igraph package of R, we achieve the best performance with the method of Brandes et al. [64] coded in a function named cluster_optimal. This method uses an Integer Linear Programming formulation to maximize modularity.

Information about the topology of network relationships is encoded in the adjacency matrix, but structural patterns, such as modularity, can be easily revealed through appropriate network drawings. Force-directed algorithms for the placement of nodes within a rectangular frame of simple undirected graphs are noteworthy. Besides aesthetically pleasing, their output frequently reveals aspects about the organization of links, because such algorithms calculate the layout of a graph using only information contained within the structure of the graph itself. The layout method of Fruchterman & Reingold [65] belongs to that category of graph drawing and is inspired in spring forces proper of natural systems. In this method, the final location of a node is dictated by the interplay between repulsive and attractive forces between nodes. Repulsive forces act among all pairs of nodes, while attractive forces act between adjacent nodes. The final output aims to capture as much symmetry as possible and pursues to evenly distribute the vertices in the frame. Since vertices connected by an edge tend to be drawn near each other, modules can be recognized as proximate subsets of connected nodes. When dealing with sparse small graphs (such as ours), this method is highly recommended for cluster detection. Different analyses and graphics were performed through the add-on package igraph, available in R software [66].


Overall network layout

The network associated with the musculoskeletal system of the anuran hindlimb is showed in Fig 3. The two-dimensional arrangement of nodes aims to reflect the modular structure underlying the network. This layout, automatically obtained after applying the Fruchterman-Reinglod algorithm, largely mirrors the overall architecture of the hindlimb: the modular organization and proximal-distal arrangement of elements.

Fig 3. Musculoskeletal network associated with the frog hindlimb.

Nodes are colored by common membership to modules. ID numbers are shown in Table 2. The schematic representation of the involved anatomical elements is provided below.

We compiled 27 muscles, 20 bones and 7 fibrous knots as nodes. With the exception of the cruralis and the extensor iliotibialis B, all pairs of muscular elements remain without a direct link between them. Additionally, 22 out of 27 muscles are of degree 2 reflecting origin and insertion into skeletal elements in a simple way.


The system includes a few nodes with higher centrality values. Nine out of 54 nodes (about 17%) show the highest values of betweenness in the data set (larger than 100, Fig 4). The decreasingly ordered sequence of betweenness scores evokes an exponential decay. The osteological elements account for the majority of elements belonging to the set with higher centrality values: femur, tibiofibula, acetabulum, iliac shaft and tibiale. Comparatively, muscles yield the lower centrality values. All the elements related to the autopodium show low betweenness values. A final remark about betweenness profile involves the high performance of fibrous knots such as the aponeurosis plantaris, with a key role in connecting the shank with the feet.

Fig 4. Elements of the anatomical network, ordered by their decreasing betweenness scores.


The modules obtained through the usual null model yield a Q value of 0.49 and are represented in Fig 3. Table 3 shows the different elements comprising each module. These modules are interpreted as the following morpho-functional complexes: (1) hip complex, tied with hip movements such as rotation, protraction, and flexion (green nodes in Fig 3); (2) thigh complex, including most of the nodes of the stylopod. This module is related to the distal movements, including adduction, retraction and protraction of the femur and the knee (black nodes in Fig 3); (3) shank complex, embracing the elements associated to the tibiofibula and fibulare, with associated muscles (blue nodes in Fig 3); (4) calf complex, including the prominent flexor digitorum communis and its origin fibrous knots (cian nodes in Fig 3); and (5) foot complex, embracing the fibulare and the multiple bones of the autopodium in addition to one extensor element and to the flexor surface of the foot (red nodes in Fig 3).

Table 3. Composition of the modules detected through the network analysis.


We accept a basic statement of our work in that there is a correspondence between the topographical arrangements of elements and the network topology derived from their physical connections. This finding reinforces the notion that modeling the hindlimb as a network is a valuable resource for testing an old hypothesis from the field of anatomy (e.g. principe des connexions about homologies [67]) and for studying scarcely explored ideas to date, such as tensegrity properties [68].

Bones are among the most central nodes, actually overpassing the fibrous knots. This result contradicts our first hypothesis, which considered the fibrous elements of connective tissue to be more prominent in this regard. Consequently, bones play a leading role on the integrity of the system. The fact that bones exhibit higher centrality values than elements such as fibrous knots is worth remarking, since the latter have been classically considered to present a main role connecting bones and muscles. Our network analysis, however, tells a different story in which bones are the frame connecting muscles and fibrous entities. A similar result was obtained by Diogo et al. [43] in relation to the human hindlimb. These results indicate that the main role of fibrous knots probably resides in their biomechanical properties, which would be much more important than their role as connectors. In fact, most of these fibrous knots tend to undergo metaplasic processes generating fibrocartilage, or even bones (e.g. the fibrocartilaginous patella in the knee knot [69], the plantar sesamoid in the plantar aponeurosis [70], and the cartilaginous sesamoid in the ligamentun calcanei [70]) as a response to the strong mechanical stress to which they are exposed [71]. This is another argument supporting their consideration as particular nodes in our network. Interestingly, in a recent work of Taglaferri et al. [72], the concept of bone-muscle unit is studied once again, without consideration of the tendinous system, thus reinforcing the notion of tendons as biological devices to handle the energetic intake needed to perform body movements, rather than as elements connecting other anatomical structures. Other authors [73,74] also concluded that one of the main functions of tendons is to facilitate joint motion, which exceeds the contractile capacities of the muscles.

There is a certain degree of correlation between osteological elements ordered by betweenness and the ontogenetic chronology of the hindlimbs in tetrapods. This is worth remarking, because it calls for a model of preferential attachment behind the organization of the network [75]. In other words, the osteological nodes which are first to come up are more likely to be connected with other elements that progressively arrive, and are thus prone to capture new connections, increasing their betweenness. In the ontogeny of the anuran hindlimb, the first osteological element to mature (chondrogenesis and osteogenesis) is the femur, followed by the tibiofibula and finally, by the autopodial elements [63]. More precisely, the elements with the higher level of betweenness, femur and tibiofibula, are the first to differentiate in the hindlimb. These elements have a pioneer role in determining a topographical differentiation inside the limb bud [63,76]. Interestingly, the acetabulum exhibits a lower level of betweenness than the long bones of the hindlimb, a rather counter intuitive result when considering the proximal-distal ontogenetic differentiation of the hindlimb. However, Manzano et al. [63] showed that the mesenchimal condensations of the hindlimb long bones originate in their diaphyses when the acetabulum is still in the interzone stage and when no joint cavity is visible, providing evidence of its late differentiation. Indeed, the level of betweenness of the pelvic girdle elements display the same phenomenon: they all exhibit lower level of betweenness than the hindlimb, in a consistent pattern with their ontogenetic sequence. Thus, our data reinforce the idea that the limb is incorporated as an almost complete framework for the development of the pelvic girdle. This topographical arrangement, together with the location of the tendon primordia as described by Manzano et al. [63], likely collaborates in the organization of the position of the muscular complexes [76].

The modularity analysis reveals a clustered organization of the tendon-musculo-skeletal network, supporting the implicit assertion of our second hypothesis. The modular arrangement adjusts to a topographical scheme of proximal-distal organization. Although this conclusion might seem obvious, it should be noted that other results, involving the mixing of distal and proximal elements, could have been obtained. Following this interpretation, the modular arrangement shows evidence of developmental and functional constraints in the structural organization of the frog hindlimb, sustaining thus our third hypothesis. Modules, interpreted as sets of densely connected elements, can be considered as an epiphenomenon comparable to that of anatomical modules from the evo-devo perspective. A clear example of this kind of reciprocal illumination includes the pervasive assignation of the autopodium to a module in its own right [77,78]. The modular construction of vertebrate appendages has been a major factor throughout their evolution. Shubin & Davis [79] conceive modules as existing at several hierarchical levels in limbs, from the whole organ to combinations of their endoskeletal constituents.

Two layers of nodes (skeletal and muscular) seem to exist, in which the elements of the latter are largely unconnected. If the single exception of muscle-to-muscle link is disregarded, the network as a whole would subsume into a type of graph known as quasi-bipartite graph. In a quasi-bipartite graph there are two sets of nodes: one partition with connections among them and another set of nodes with no connection. The adequacy of the quasi-bipartite model for musculoskeletal networks deserves a more in-depth consideration because of its potential impact for modularity studies. Given the explicit dependence of modularity upon the null model, it is clear that the specific choice of the null model largely influences modularity [80]. In fact, a quasi-bipartite graph calls for a different null model than the usual to study modularity, in which the constraints of the absence of a connection for the disjoint set of vertices should be considered. Therefore, the development of a more realistic null model for assessing the modular structure in musculoskeletal networks is of urgent need. For instance, P must assign zero likelihood to edges between vertices of the same independent set of vertices, precluding such edges in the null model. Thus, pairs of vertices from the naturally disjoint set should not receive a modularity penalty.

Jumping is a primary locomotion mode in frogs [47,81,82] and particularly in Leptodactylus latinasus, an outstanding jumping frog [83]. This remarkable and distinctive function can be disaggregated into functional sublevels, namely rotation, adduction, articulation, extension, etc. The coordinated action performed by modules within the hindlimb is thought to maximize jumping [84]. This is to be expected in the context of evolutionary biology, since modules are considered as autonomous anatomical parts, influenced by local factors and integrated through common developmental factors [40]. Functionally, there is a correlation between the proximal-to-distal succession of modules and the progressive recruitment of elements involved in joint motion during jumping. In a typical jump of a frog, the iliosacral and hip joint movements start almost simultaneously, followed by the knee joint and finally by the ankle joint [84,85]. This sequential movement of joints assures an extended acceleration of the center of mass [84].

The two elements that form the ilium -the iliac shaft and the acetabular portion-, belong to two different modules. One of them denotes the relationship between the pelvic girdle and the body, while the other exhibits a stronger relationship with the proximal elements of the thigh, i.e. the link between the pelvic girdle and the hindlimb. This separation of the same bone in two modules could be interpreted from a functional perspective, since the elongated ilial shafts of anurans are specifically modified for jumping [86]; the acetabular portion, instead, acts as an attachment element with the hindlimbs, through the joint with the head of the femur, in a similar way than in other tetrapods.

The thigh module is mostly related to the flexion and extension of the shank at the knee [87] and is marked by a relatively high percentage of fibrous elements (fascia latae, knee knot, tenuissimus it knot). In the network layout, guided by topological information alone, this module seems to bisect the proximal and distal pools of anatomical elements.

The flexor digitorum communis muscle is clearly the strongest muscle of the hindlimb, and is the main muscle used by frogs in jumping [88]. It is the only muscular element which comprises the calf module, along with its fibrous origin knots. The outer links of this module correspond to the distal part of the femur and the aponeurosis plantaris. This last edge is the Achilles tendon, responsible of the storage of elastic energy for the amplification of power output during jumping [89]. Further studies are needed to assess whether these modules are also recovered in the network of hindlimbs of other species of jumping tetrapods.

The anuran hindlimb presents an additional functional segment composed by the tibiale and fibulare [90,91], which is also incorporated in musculoskeletical modeling [92]. These bones are usually short bones belonging to the autopodium, but in anurans they elongate to form the additional functional segment mentioned above. In our analysis, the tibiale is included in a common module, also integrated by the tibiofibula. Therefore, at least in relation to this bone, our network reinforces the notion of zeugopodization experienced by certain mesopodial bones that receive signals coming from the zeugopodial area to start elongation [93].

The most distal module comprises the many bones of the foot, the aponeurosis plantaris and two muscles which are responsible of the extension of the digits and of the dorsiflexion and pronation of the foot [88]. Diogo et al. [43] included more elements in the autopodial segment than those included in our analysis, and they were able to outline six modules in their study. In our analysis, the elements of the foot are grouped in a single module. Our data show a lower degree of resolution and the discrepancy in the number of modules might be a matter of scale. To conclude, modular architecture seems to be a successful organization that provides the building blocks over which evolution forges the many different functional specializations that organisms can exploit.


We would like to thank CONICET, Argentina, for their continued support. We are also grateful to the reviewers Rasskin-Gutman D. and Diogo R. for their constructive criticisms and thoughtful comments.

Author Contributions

  1. Conceptualization: DADS MLP VA.
  2. Data curation: JF.
  3. Formal analysis: DADS.
  4. Funding acquisition: DADS VA.
  5. Investigation: DADS JF MLP VA.
  6. Methodology: DADS.
  7. Project administration: DADS JF MP VA.
  8. Resources: DADS JF MLP VA.
  9. Software: DADS.
  10. Supervision: VA.
  11. Validation: DADS JF MLP VA.
  12. Visualization: DADS JF MLP VA.
  13. Writing – original draft: DADS JF MLP VA.
  14. Writing – review & editing: DADS JF MLP VA.


  1. 1. Rasskin-Gutman D, Esteve-Altava B. 2014. Connecting the dots: Anatomical Network Analysis in morphological evodevo. Biol Theory. 2014; 9: 178–193.
  2. 2. Esteve-Altava B, Diogo R, Smith C, Boughner JC, Rasskin-Gutman D. Anatomical networks reveal the musculoskeletal modularity of the human head. Sci Rep. 2015; 5: 8298. pmid:25656958
  3. 3. Clauset A, Newman MEJ, Moore C. Finding community structure in very large networks. Phys Rev E. 2004; 70: 066111.
  4. 4. Olson EC, Miller RL. Morphological integration. Chicago: The University of Chicago Press; 1958.
  5. 5. Wagner GP. A comparative study of morphological integration in Apismellifera (Insecta, Hymenoptera). J ZoolSystEvol Res. 1990; 28: 48–61.
  6. 6. Cheverud JM. Developmental integration and the evolution of pleiotropy. Am Zool. 1996; 36: 44–50.
  7. 7. Von Dassow G, Munro E. Modularity in animal development and evolution: elements of a conceptual framework for EvoDevo. J Exp Zool. 1999; 285(4): 307–325. pmid:10578108
  8. 8. Bolker JA. Modularity in development and why it matters to Evo—Devo. Am Zool. 2000; 40: 770–776.
  9. 9. Winther RG. Varieties of modules: kinds, levels, origins, and behaviors. J Exp Zool. 2001; 291(2): 116–129. pmid:11479913
  10. 10. Schlosser G, Wagner GP. Modularity in development and evolution. Chicago: The University of Chicago Press; 2004.
  11. 11. Callebaut W, Rasskin-Gutman D. Modularity: Understanding the development and evolution of natural complex systems. Cambridge: MIT Press; 2005.
  12. 12. Wagner GP, Pavlicev M, Cheverud JM. The road to modularity. Nat Rev Genet. 2007; 8: 921–931. pmid:18007649
  13. 13. Klingenberg CP. Morphological integration and developmental modularity. Annu Rev EcolEvol Syst. 2008; 39: 115–132.
  14. 14. Wagner GP. Adaptation and the modular design of organisms. In: Morán F, Moreno A, Merelo JJ, Chacón P, editors. Advances in artificial life. Lecture Notes in Computer Science. Berlin: Springer Berlin Heidelberg; 1995. pp. 315–328.
  15. 15. Wagner GP. Homologues, natural kinds and the evolution of modularity. Am Zool. 1996; 36(1): 36–43.
  16. 16. Esteve-Altava B. In search of morphological modules: asystematic review. Biol Rev CambPhilos Soc. 2016.
  17. 17. Birdsall K, Zimmerman E, Teeter K, Gibson G. Genetic variation for the positioning of wing veins in Drosophila melanogaster. Evol Dev. 2000; 2(1): 16–24. pmid:11256413
  18. 18. Klingenberg CP, Zaklan SD. Morphological integration between developmental compartments in the Drosophila wing. Evolution.2000; 54: 1273–1285. pmid:11005294
  19. 19. Zimmerman E, Palsson A, Gibson G. Quantitative trait loci affecting components of wing shape in Drosophila melanogaster. Genetics.2000; 155: 671–683. pmid:10835390
  20. 20. Klingenberg CP, Badyaev AV, Sowry SM, Beckwith NJ. Inferring developmental modularity from morphological integration: analysis of individual variation and asymmetry in bumblebee wings. Am Nat. 2001; 157(1): 11–23. pmid:18707232
  21. 21. Atchley WR, Hall BK. A model for development and evolution of complex morphological structures. Biol Rev. 1991; 66(2): 101–157. pmid:1863686
  22. 22. Atchley WR, Cowley DE, Vogl C, McLellan T. Evolutionary divergence, shape change, and genetic correlation structure in the rodent mandible. Syst Biol. 1992; 41(2): 196–221.
  23. 23. Cheverud JM., Eric JR, Duncan JI. Pleiotropic effects of individual gene loci on mandibular morphology. Evolution. 1997; 2006–2016.
  24. 24. Ehrich TH, Vaughn TT, Koreishi SF, Linsey RB, Pletscher LS, Cheverud JM. Pleiotropic effects on mandibular morphology I. Developmental morphological integration and differential dominance. J ExpZool B MolDevEvol.2003; 296: 58–79.
  25. 25. Klingenberg CP, Mebus K, Auffray JC. Developmental integration in a complex morphological structure: how distinct are the modules in the mouse mandible? Evol Dev. 2003; 5(5): 522–531. pmid:12950630
  26. 26. Klingenberg CP, Leamy LJ, Cheverud JM. Integration and modularity of quantitative trait locus effects on geometric shape in the mouse mandible. Genetics. 2004; 166(4): 1909–1921. pmid:15126408
  27. 27. Monteiro LR, Bonato V, Dos Reis SF. Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae). Evol Dev. 2005; 7: 429–439. pmid:16174036
  28. 28. Márquez EJ. A statistical framework for testing modularity in multidimensional data.Evolution. 2008; 62(10): 2688–2708. pmid:18691262
  29. 29. Zelditch ML, Wood AR, Bonett RM, Swiderski DL. Modularity of the rodent mandible: integrating bones, muscles, and teeth. Evol Dev. 2008; 10: 756–768. pmid:19021747
  30. 30. Sanger TJ, Mahler DL, Abzhanov A, Losos JB. Roles for modularity and constraint in the evolution of cranial diversity among Anolis lizards. Evolution.2012; 66: 1525–1542. pmid:22519788
  31. 31. Klingenberg CP, Marugán-Lobón J. Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context. Syst Biol. 2013; 62: 591–610. pmid:23589497
  32. 32. Cheverud JM. Phenotypic, genetic, and environmental morphological integration in the cranium. Evolution. 1982; 36: 499–516.
  33. 33. Cheverud JM. Morphological integration in the saddle-back tamarin (Saguinusfuscicollis) cranium. Am Nat. 1995; 145: 63–89.
  34. 34. Leamy LJ, Routman EJ, Cheverud JM. Quantitative trait loci for early and late-developing skull characters in mice: a test of the genetic independence model of morphological integration. Am Nat. 1999; 153: 201–214.
  35. 35. Lieberman DE, McBratney BM, Krovitz GE. The evolution and development of cranial formin Homo sapiens. ProcNatlAcadSci USA. 2002; 99(3): 1134–9.
  36. 36. Bookstein FL, Gunz P, Mitteroecker P, Prossinger H, Schæfer K, Seidler H. Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution. J Hum Evol. 2003; 44(2): 167–187. pmid:12662941
  37. 37. Ackermann RR. Ontogenetic integration of the hominoid face. J Hum Evol. 2005; 48(2): 175–197. pmid:15701530
  38. 38. Bastir M, Rosas A. Hierarchical nature of morphological integration and modularity in the human posterior face. Am J PhysAnthropol.2005; 128: 26–34.
  39. 39. Goswami A. Morphological integration in the carnivoran skull.Evolution.2006; 60: 169–183. pmid:16568641
  40. 40. Mitteroecker P, Bookstein F. The evolutionary role of modularity and integration in the hominoid cranium.Evolution. 2008; 62(4): 943–958. pmid:18194472
  41. 41. Porto A, de Oliveira FB, Shirai LT, De Conto V, Marroig G. The evolution of modularity in the mammalian skull I: morphological integration patterns and magnitudes. Evol Biol. 2009; 36(1): 118–135.
  42. 42. Koyabu D, Werneburg I, Morimoto N, Zollikofer CP, Forasiepi AM, Endo H, et al. Mammalian skull heterochrony reveals modular evolution and a link between cranial development and brain size. Nat Commun. 2014; 5: 3625. pmid:24704703
  43. 43. Diogo R, Esteve-Altava B, Smith C, Boughner JC, Rasskin-Gutman D. Anatomical network comparison of human upper and lower, newborn and adult, and normal and abnormal limbs, with notes on development, pathology and limb serial homology vs. homoplasy. PLoS One. 2015; 10(10): e0140030. pmid:26452269
  44. 44. Simons VFH. Morphological correlates of locomotion in anurans: limb length, pelvic anatomy and contact structures. M.Sc. Thesis. Ohio University. 2008.
  45. 45. Gans C, Parsons TS. On the origin of the jumping mechanism in frogs. Evolution. 1966; 20(1): 92–99.
  46. 46. Lutz GJ, Rome LC. Built for jumping: the design of the frog muscular system. Science. 1994; 5145: 370–372.
  47. 47. Shubin NH, Jenkins FA. An early Jurassic jumping frog. Nature. 1995; 377: 49–52.
  48. 48. Jenkins FA, Shubin NH. Prosalirusbitis and the anuran caudopelvic mechanism. J VertPaleontol. 1998; 18(3): 495–510.
  49. 49. Nauwelaerts S, Aerts P. Take-off and landing forces in jumping frogs. J Exp Biol. 2006; 209: 66–77. pmid:16354779
  50. 50. Vanhooydonck B, Van Damme R, Aerts P. Speed and stamina trade-off in lacertid lizards. Evolution. 2001; 55(5): 1040–1048. pmid:11430640
  51. 51. Klingenberg CP. Evolution and development of shape: integrating quantitative approaches. Nat Rev Genet. 2010; 11(9): 623–635. pmid:20697423
  52. 52. Goswami A. Phylogeny, diet, and cranial integration in australodelphian marsupials. PLoS One. 2007; 2: e995. pmid:17912372
  53. 53. Lieberman DE. The evolution of the human head. London: Belknap Press; 2011.
  54. 54. Marroig G, Cheverud JM. A comparison of phenotypic variation and covariation patterns and the role of phylogeny, ecology, and ontogeny during cranial evolution of new world monkeys. Evolution. 2001; 55: 2576–2600. pmid:11831671
  55. 55. Marroig G, Cheverud JM. Size as a line of least evolutionary resistance: Diet and adaptive morphological radiation in New World monkeys. Evolution.2005; 59: 1128–1142. pmid:16136810
  56. 56. Marroig G, Shirai LT, Porto A, de Oliveira FB, De Conto V. The evolution of modularity in the mammalian skull II: Evolutionary consequences. Evol Biol. 2009; 36: 136–148.
  57. 57. Diogo R, Abdala V. Muscles of vertebrates—comparative anatomy, evolution, homologies and development. 1st ed. Oxford, UK: Taylor & Francis; 2010.
  58. 58. Diogo R, Ziermann JM. Development of fore‐and hindlimb muscles in frogs: Morphogenesis, homeotic transformations, digit reduction, and the forelimb-hindlimb enigma. J ExpZool B MolDevEvol. 2014;322(2): 86–105.
  59. 59. Diogo R, Molnar J. Comparative anatomy, evolution, and homologies of Tetrapod hindlimb muscles, comparison with forelimb muscles, and deconstruction of the forelimb-hindlimb serial homology hypothesis. Anat Rec. 2014; 297:1047–1075.
  60. 60. Gaupp E. Lehrevomskelet und vommuskelsystem. In: Ecker A, Wiedersheim R, editors. Anatomie des Frosches.Braunschweig: Friedrich Vieweg und Sohn; 1986. pp. 1–97.
  61. 61. Dunlap DG. The Comparative Myology of the Pelvic Appendage in the Salientia. J. Morphol. 1960; 106: 1–76. pmid:13818658
  62. 62. Howell AB. The saltatorial rodent Dipodomys: the functional and comparative anatomy of its muscular and osseous systems. ProcAmerAcad Arts Sci. 1932; 67(10).
  63. 63. Manzano A, Abdala V, Ponssa ML, Soliz M. Ontogeny and tissue differentiation of the pelvic girdle and hind limbs of anurans. Acta Zool. 2013; 94(4): 420–436.
  64. 64. Brandes U, Delling D, Gaertler M, Gorke R, Hoefer M, Nikoloski , et al. On Modularity Clustering. IEEE Trans Knowl Data Eng. 2008; 20(2): 172–188.
  65. 65. Fruchterman T, Reingold E. Graph drawing by force-directed placement. SoftwPract Exp. 1991; 21(11): 1129–1164.
  66. 66. R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2016.
  67. 67. Geoffroy Saint-Hilaire E. Philosophieanatomique (vol. 1) des organesrespiratoires sous le rapport de la determination et de l’identité de leurspiècesosseusses. Paris: Baillière; 1818.
  68. 68. Kassolik K, Andrzejewski W. Role of the tensegrity rule in theoretical basis of massage therapy. J Back MusculoskeletRehabil. 2007; 20(1): 15–20.
  69. 69. Abdala V, Vera MC, Ponssa ML. On the presence of the patella in frogs. Anat Rec. In press.
  70. 70. Ponssa ML, Goldberg J, Abdala V. Sesamoids in anurans: new data, old issues. Anat Rec. 2010; 293(10), 1646–1668.
  71. 71. Vickaryous MK, Olson WM. Sesamoids and ossicles in the appendicular skeleton. In: Hall BK, editor. Fins into limbs: evolution, development and transformation. Chicago: The University of Chicago Press; 2007. pp. 323–341.
  72. 72. Tagliaferri C, Wittrant Y, Davicco MJ, Walrand S, Coxam V. Muscle and bone, two interconnected tissues. Ageing Res Rev. 2015; 21:55–70. pmid:25804855
  73. 73. Apostolakos J, Durant TJ, Dwyer CR, Russell RP, Weinreb JH, Alaee F, et al. The enthesis: a review of the tendon-to-bone insertion. Muscles Ligaments Tendons J. 2014; 4(3), 333. pmid:25489552
  74. 74. Roberts TJ. The integrated function of muscles and tendons during locomotion. Comp BiochemPhysiol A MolIntegr Physiol. 2002; 133(4), 1087–1099.
  75. 75. Newman ME. Clustering and preferential attachment in growing networks.Phys Rev E. 2001; 64(2): 025102.
  76. 76. Kardon G. Muscle and tendon morphogenesis in the avian hind limb. Development. 1998; 125(20): 4019–4032. pmid:9735363
  77. 77. Wagner GP, Chiu CH. The tetrapod limb: a hypothesis on its origin. J Exp Zool. 2001; 291(3): 226–240. pmid:11598912
  78. 78. Davis MC, Dahn RD, Shubin NH. An autopodial-like pattern of Hox expression in the fins of a basal actinopterygian fish.Nature.2007; 447: 473–476. pmid:17522683
  79. 79. Shubin NH, Davis MC. Modularity in the Evalution of Vertebrate Appendages. In: Schlosser G, Wagner GP, editors. Modularity in development and evolution. Chicago: The University of Chicago Press; 2004. pp. 429.
  80. 80. Barber MJ. Modularity and community detection in bipartite networks.Phys Rev E. 2007; 76(6): 066102.
  81. 81. Azizi E, Roberts TJ. Muscle performance during frog jumping: influence of elasticity on muscle operating lengths. ProcBiol Sci. 2010; 277(1687): 1523–1530.
  82. 82. Reilly SM, Montuelle SJ, Schmidt A, Krause C, Naylor E, Jorgensen ME, et al. Pelvic function in anuran jumping: Interspecific differences in the kinematics and motor control of the iliosacral articulation during take‐off and landing. J Morphol. 2016; 277(12): 1539–1558. pmid:27577689
  83. 83. Jorgensen ME, Reilly SM. Phylogenetic patterns of skeletal morphometrics and pelvic traits in relation to locomotor mode in frogs. J Evol Biol. 2013; 26(5): 929–943. pmid:23510149
  84. 84. Astley HC, Roberts TJ. The mechanics of elastic loading and recoil in anuran jumping. J Exp Biol. 2014; 217(24): 4372–4378.
  85. 85. Nauwelaerts S, Stamhuis E, Aerts P. Swimming and jumping in a semi-aquatic frog. Anim Biol. 2005; 55(1): 3–15.
  86. 86. Reilly SM, Jorgensen ME. The evolution of jumping in frogs: morphological evidence for the basal anuran locomotor condition and the radiation of locomotor systems in crown group anurans. J Morphol.2011; 272: 149–168. pmid:21210487
  87. 87. Přikryl T, Aerts P, Havelková P, Herrel A, Roček Z. Pelvic and thigh musculature in frogs (Anura) and origin of anuran jumping locomotion. J Anat. 2009; 214(1): 100–139. pmid:19166476
  88. 88. Minkoff E. A laboratory guide to frog anatomy. New York: Pergamon; 1975.
  89. 89. Roberts TJ, Abbott EM, Azizi E. The weak link: do muscle properties determine locomotor performance in frogs? Phil Trans R Soc B. 2011; 366(1570), 1488–1495. pmid:21502120
  90. 90. Lecointre G, Le Guyader H. The tree of life: a phylogenetic classification. Harvard University Press; 2006.
  91. 91. Nauwelaerts S, Ramsay J, Aerts P. Morphological correlates of aquatic and terrestrial locomotion in a semi-aquatic frog, Ranaesculenta: no evidence for a design conflict. J Anat. 2007; 210(3), 304–317. pmid:17331179
  92. 92. Kargo WJ, Rome LC. Functional morphology of proximal hindlimb muscles in the frog Ranapipiens. J Exp Biol. 2002; 205(14), 1987–2004.
  93. 93. Reno PL, Kjosness KM, Hines JE.The role of Hox in pisiform and calcaneus growth plate formation and the nature of the zeugopod/autopod boundary.J ExpZool B MolDevEvol. 2016; 326(5): 303–321.