Structural Equation Modelling Reveals How Allometry Shapes Integration in Avian Cranial Evolution

Testing hypotheses of phenotypic modularity involves assessing whether groups of traits covary more strongly with each other than with parts outside the group. Structural Equation Modelling (SEM) is a flexible statistical framework for interrogating complex relationships between sets of variables, making it ideally suited to studies of hierarchical modularity and integration. However, quantifying the modular organization of high-dimensional traits using SEM in a phylogenic context has only recently become possible through new methodological advances. Here, we applied SEM to investigate patterns and correlates of phenotypic modularity in the skull and brain of birds. Birds independently evolved relatively large brains multiple times, as well as a wide range of different skull and brain morphologies. While some have proposed the bird skull is composed of several functional or developmental modules, others have suggested the skull is highly integrated, with share allometric scaling structuring trait correlations. The data best supported a model in which brain shape is influenced by changes in shape of the neurocranium as well as a ‘jaw’ module consisting of the rostrum shape and jaw musculature. Rostrum shape itself does not strongly covary with other aspects of the skull and brain, suggesting decoupling of beak morphology from the rest of the avian cranium. All variables, with the exception of rostrum shape, are strongly influenced by size, supporting the idea that allometry is a major influence on craniofacial integration in birds. These results provide new insights into likely drivers shaping the evolution of the skull in birds and highlight the usefulness of phyloSEM testing hypotheses of evolutionary modularity and integration.