The mosaic model of brain evolution postulates that different brain regions are relatively free to evolve independently from each other. Such independent evolution is possible only if genetic correlations among the different brain regions are less than unity. We estimated heritabilities, evolvabilities and genetic correlations of relative size of the brain, and its different regions in the three-spined stickleback (Gasterosteus aculeatus). We found that heritabilities were low (average h2 = 0.24), suggesting a large plastic component to brain architecture. However, evolvabilities of different brain parts were moderate, suggesting the presence of additive genetic variance to sustain a response to selection in the long term. Genetic correlations among different brain regions were low (average rG = 0.40) and significantly less than unity. These results, along with those from analyses of phenotypic and genetic integration, indicate a high degree of independence between different brain regions, suggesting that responses to selection are unlikely to be severely constrained by genetic and phenotypic correlations. Hence, the results give strong support for the mosaic model of brain evolution. However, the genetic correlation between brain and body size was high (rG = 0.89), suggesting a constraint for independent evolution of brain and body size in sticklebacks.