How does evolution grow bigger brains? It has been widely assumedthat growth of individual structures and functional systems inresponse to niche-specific cognitive challenges is the mostplausible mechanism for brain expansion in mammals. Comparison ofmultiple regressions on allometric data for 131 mammalian species,however, suggests that for 9 of 11 brain structures taxonomic andbody size factors are less important than covariance of these majorstructures with each other. Which structure grows biggest is largelypredicted by a conserved order of neurogenesis that can be derivedfrom the basic axial structure of the developing brain. Thisconserved order of neurogenesis predicts the relative scaling notonly of gross brain regions like the isocortex or mesencephalon, butalso the level of detail of individual thalamic nuclei. Specialselection of particular areas for specific functions does occur, butit is a minor factor compared to the large-scale covariance of thewhole brain. The idea that enlarged isocortex could be a “spandrel,”a by-product of structural constraints later adapted for variousbehaviors, contrasts with approaches to selection of particularbrain regions for cognitively advanced uses, as is commonly assumedin the case of hominid brain evolution.