Multiple regression modeling for estimating endocranial volume in extinct Mammalia

The profound evolutionary success of mammals has been linked to behavioral and life-history traits, many of which have been tied to brain size. However, studies of the evolution of this key trait have yet to explore the full potential of the fossil record, being limited by the difficulty of obtaining endocranial data from fossils. Using measurements of endocranial volume, length, height, and width of the braincase in 503 adult specimens from 199 extant species, representing 99 of 133 extant mammalian families, we expand upon a simple method of using multiple regression to develop a formula for estimating brain size from external skull measurements. We also examined non-mammalian synapsids to assess the phylogenetic limits of our model's application. Model-predicted volume correlates strongly with measured volume ( R 2 = 0.993) and prediction error is between 16% and 19%. Error decreases if models developed for well-sampled subclades such as primates or rodents are used, demonstrating that some differential evolution of the relationship between brain size and skull size has occurred. However, reanalysis using phylogenetically independent contrasts demonstrates weak phylogenetic dependency, indicating that our model is appropriate for estimating the endocranial volume of species of unknown phylogenetic affinity. Thus, the model represents a generally applicable, fast and cost-efficient way to dramatically expand the taxonomic and temporal scope of mammalian brain size data sets. Even endocranial volumes of taxa with highly derived crania, such as cetaceans and monotremes, can be estimated confidently. However, the model works best for generalized placental crania. Fundamental differences in cranial architecture suggest that the model cannot provide accurate estimates of endocranial volume in non-mammalian synapsids more basal than Morganucodon (ca. 200 Ma). Therefore, use of the model for taxa phylogenetically distant from the mammalian crown group is not warranted, but it might be used to establish relative brain sizes between closely related subgroups.