Organisms can gain information about their environment from their ancestors, their parents or their own personal experience. 'Cue integration' models often start with the simplifying assumption that information from different sources is additive. Here, we test key assumptions and predictions of cue integration theory at both the phenotypic and molecular level in threespined sticklebacks (Gasterosteus aculeatus). We show that regardless of whether cues about predation risk were provided by their father or acquired through personal experience, sticklebacks produced the same set of predator-adapted phenotypes. Moreover, there were nonadditive effects of personal and paternal experience: animals that received cues from both sources resembled animals that received cues from a single source. A similar pattern was detected at the molecular level: there was a core set of genes that were differentially expressed in the brains of offspring regardless of whether risk was experienced by their father, themselves or both. These results provide strong support for cue integration theory because they show that cues provided by parents and personal experience are comparable at both the phenotypic and molecular level, and draw attention to the importance of nonadditive responses to multiple cues.