Behavioural ecologists have proposed various evolutionary mechanisms as to why different personality types coexist. Our ability to understand the evolutionary trajectories of personality traits requires insights from the quantitative genetics of behavioural reaction norms. We assayed > 1000 pedigreed stickleback for initial exploration behaviour of a novel environment, and subsequent changes in exploration over a few hours, representing their capacity to adjust their behaviour to changes in perceived novelty and risk. We found heritable variation in both the average level of exploration and behavioural plasticity, and population differences in the sign of the genetic correlation between these two reaction norm components. The phenotypic correlation was not a good indicator of the genetic correlation, implying that quantitative genetics are necessary to appropriately evaluate evolutionary hypotheses in cases such as these. Our findings therefore have important implications for future studies concerning the evolution of personality and plasticity.