Natural selection can act on between-individual variation in cognitive abilities, yet evolutionary responses depend on the presence of underlying genetic variation. It is, therefore, crucial to determine the relative extent of genetic versus environmental control of these among-individual differences in cognitive traits to understand their causes and evolutionary potential. We investigated heritability of associative learning performance and of a cognitive judgement bias (optimism), as well as their covariation, in a captive pedigree-bred population of red junglefowl (, > 300 chicks over 5 years). We analysed performance in discriminative and reversal learning (two facets of associative learning), and cognitive judgement bias, by conducting animal models to disentangle genetic from environmental contributions. We demonstrate moderate heritability for reversal learning, and weak to no heritability for optimism and discriminative learning, respectively. The two facets of associative learning were weakly negatively correlated, consistent with hypothesized trade-offs underpinning individual cognitive styles. Reversal, but not discriminative learning performance, was associated with judgement bias; less optimistic individuals reversed a previously learnt association faster. Together these results indicate that genetic and environmental contributions differ among traits. While modular models of cognitive abilities predict a lack of common genetic control for different cognitive traits, further investigation is required to fully ascertain the degree of covariation between a broader range of cognitive traits and the extent of any shared genetic control.This article is part of the theme issue 'Causes and consequences of individual differences in cognitive abilities'.