Cortical scaling in mammals: a repeating units model

A simple scaling model germane to the gyrencephalic mammalian cortex is proposed. The model aims to account for the empirical scaling of morphometric variables such as cortical thickness, surface area and volume, as a function of brain size. Several assumptions are made. Gyrencephalic cortices are assumed to be modular in construction, comprised of identical repeating units. Both the number and size of cortical units are assumed to increase with increasing brain size. The shape of the brain and of the repeating units are assumed not to vary systematically with brain size. The surface-density of repeating units is taken to be invariant. The model exponents for cortical thickness, folded surface area and volume, each as a function of cerebral volume, are one-ninth, eight-ninths and one, respectively. These discrete model exponents, and others, are in reasonable agreement with a diverse body of scaling data, both phylogenetic and ontogenetic. One interpretation is that phylogenetic scaling simply reflects ontogenetic scaling, extended over a wide range of adult brain sizes. The model is confined to ontogenetic/phylogenetic scaling. It is suggested that the model exponents are not adaptive, in the usual sense of that term.