The sizes of mammalian brain components seem to be mostly related to the sizes of the whole brain (and body), suggesting a one-dimensional scale of encephalization(1-3). Previous multivariate study of such data concludes that evolutionary selection for enlargement of any one brain part is constrained to selection for a concerted enlargement of the whole brain(4). However, interactions between structurally related pairs of brain parts(5) confirm reports of differential change in brain nuclei(6), and imply mosaic rather than concerted evolution. Here we analyse a large number of variables simultaneously using multi-dimensional methods(7). We show that the relative proportions of different systems of functionally integrated brain structures vary independently between different mammalian orders, demonstrating separate evolutionary radiations in mammalian brain organization(8). Within each major order we identify clusters of unrelated species that occupy similar behavioural niches and have convergently evolved similar brain proportions. We conclude that within orders, mosaic brain organization is caused by selective adaptation, whereas between orders it suggests an interplay between selection and constraints.