Scaling the Brain and Its Connections

The mammalian neocortex varies over five orders of magnitude and undergoes so many changes that the brains of a shrew and a whale appear qualitatively very different. Here I summarize the variety of ways in which a large neocortex differs from a small one, including convolutedness, the number of areas, white matter volume and neuron density. I then show how from these empirical relationships it is possible to distill two fundamental connectivity laws that the mammalian cortex conforms to. The first of these laws is that the number of synapses per neuron increases with brain size proportionally with the number of neurons in an area, which allows an invariant level of intra-area connectivity across brains. The second is that the number of areas to which an area connects increases proportionally with the total number of areas, which allows an invariant level of area-area connectivity across brains. Finally, I describe how these two principles, together with a volume-optimality hypothesis, allows one to explain how the neocortex changes with brain size.