White matter volume and white/gray matter ratio in mammalian species as a consequence of the universal scaling of cortical folding

Because the white matter of the cerebral cortex contains axons that connect distant neurons in the cortical gray matter, the relationship between the volumes of the 2 cortical compartments is key for information transmission in the brain. It has been suggested that the volume of the white matter scales universally as a function of the volume of the gray matter across mammalian species, as would be expected if a global principle of wiring minimization applied. Using a systematic analysis across several mammalian clades, here we show that the volume of the white matter does not scale universally with the volume of the gray matter across mammals and is not optimized for wiring minimization. Instead, the ratio between volumes of gray and white matter is universally predicted by the same equation that predicts the degree of folding of the cerebral cortex, given the clade-specific scaling of cortical thickness, such that the volume of the gray matter (or the ratio of gray to total cortical volumes) divided by the square root of cortical thickness is a universal function of total cortical volume, regardless of the number of cortical neurons. Thus, the very mechanism that we propose to generate cortical folding also results in compactness of the white matter to a predictable degree across a wide variety of mammalian species.