Résumé : Understanding the adaptive significance of multiple mating (polyandry) by females has long been a challenge in evolutionary biology. Several genetic and nongenetic benefits have been proposed to explain the evolution and maintenance of polyandry. In eusocial Hymenoptera, a prominent hypothesis is that increased genetic diversity within colonies results in more polymorphic workers and facilitates division of labour. We analysed the genetic basis of worker size (i.e. worker head width) and task preference in Cataglyphis cursor, an ant showing natural variations in queen-mating frequency. Our data show that increased genetic diversity within colonies does not result in more polymorphic workers. Moreover, worker head width is not different between patrilines within colonies. Consistent with these findings, worker size has a low heritable component. Moreover, task performance is not correlated with patriline. By contrast, it is significantly associated with worker size: the first foragers leaving the nest at sunrise are significantly larger than workers remaining in the nest. Overall, these results do not support the hypothesis that multiple mating is favoured because increased genetic diversity within colonies translates into more polymorphic workers and facilitates genetic polyethism. We discuss other hypotheses to account for the evolution of polyandry in C. cursor.