Grist for Riedl's mill: a network model perspective on the integration and modularity of the human skull

Riedl's concept of burden neatly links development and evolution by ascertaining that structures that show a high degree of developmental co-dependencies with other structures are more constrained in evolution. The human skull can be precisely modeled as an articulated complex system of bones connected by sutures, forming a network of structural co-dependencies. We present a quantitative analysis of the morphological integration, modularity, and hierarchical organization of this human skull network model. Our overall results show that the human skull is a small-world network, with two well-delimited connectivity modules: one facial organized around the ethmoid bone, and one cranial organized around the sphenoid bone. Geometric morphometrics further support this two-module division, stressing the direct relationship between the developmental information enclosed in connectivity patterns and skull shape. Whereas the facial module shows a hierarchy of clustered blocks of bones, the bones of the cranial modules show a regular pattern of connections. We analyze the significance of these arrangements by hypothesizing specific structural roles for the most important bones involved in the formation of both modules, in the context of Riedl's burden. We conclude that it is the morphological integration of each group of bones that defines the semi-hierarchical organization of the human skull, reflecting fundamental differences in the ontogenetic patterns of growth and the structural constraints that generate each module. Our study also demonstrates the adequacy of network analysis as an innovative tool to understand the morphological complexity of anatomical systems.