Theoretical morphology of tetrapod skull networks

Network models of the tetrapod skull in which nodes represent bones and links represent sutures have recently offered new insights into the structural constraints underlying the evolutionary reduction of bone number in the tetrapod skull, known as Willistonʹs Law. Here, we have built null network model-derived generative morphospaces of the tetrapod skull using random, preferential attachment, and geometric proximity growth rules. Our results indicate that geometric proximity is the best null model to explain the disparity of skull structures under two structural constraints: bilateral symmetry and presence of unpaired bones. The analysis of the temporal occupation of this morphospace, concomitant with Willistonʹs Law, indicates that the tetrapod skull has followed an evolutionary path toward more constrained morphological organizations.