Network architecture associated with the highly specialized hindlimb of frogs

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.