Brain structure scaffolds intrinsic function, supporting cognition and ultimately behavioral flexibility. However, it remains unclear how a static, genetically controlled architecture supports flexible cognition and behavior. Here, we synthesize genetic, phylogenetic and cognitive analyses to understand how the macroscale organization of structure-function coupling across the cortex can inform its role in cognition. In humans, structure-function coupling was highest in regions of unimodal cortex and lowest in transmodal cortex, a pattern that was mirrored by a reduced alignment with heritable connectivity profiles. Structure-function uncoupling in non-human primates had a similar spatial distribution, but we observed an increased coupling between structure and function in association regions in macaques relative to humans. Meta-analysis suggested regions with the least genetic control (low heritable correspondence and different across primates) are linked to social cognition and autobiographical memory. Our findings establish the genetic and evolutionary uncoupling of structure and function in different transmodal systems may support the emergence of complex, culturally embedded forms of cognition.

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