Random Loss and Selective Fusion of Bones Originate Morphological Complexity Trends in Tetrapod Skull Networks

Abstract

The tetrapod skull has undergone a reduction in number of bones in all major lineages since the origin of vertebrates, an evolutionary trend known as Williston’s Law. Using connectivity relations between bones as a proxy for morphological complexity we showed that this reduction in number of bones generated an evolutionary trend toward more complex skulls. This would imply that connectivity patterns among bones impose structural constraints on bone loss and fusion that increase bone burden due to the formation of new functional and developmental dependencies; thus, the higher the number of connections, the higher the burden. Here, we test this hypothesis by exploring plausible evolutionary scenarios based on selective versus random processes of bone loss and fusion. To do this, we have built a computational model that reduces iteratively the number of bones by loss and fusion, starting from hypothetical ancestral skulls represented as Gabriel networks in which bones are nodes and suture connections are links. Simulation results indicate that losses and fusions of bones affect skull structure differently whether they target bones at random or selectively depending on the number of bone connections. Our findings support a mixed scenario for Williston’s Law: the random loss of poorly connected bones and the selective fusion of the most connected ones. This evolutionary scenario offers a new explanation for the increase of morphological complexity in the tetrapod skull by reduction of bones during development.