Recent studies revealed a variety of left–right asymmetries among vertebrates and invertebrates. In many species, left- and right-lateralized individuals coexist but in unequal numbers (ʻpopulation-levelʼ lateralization). Using mathematical theory of games, it has been shown that, in the context of prey– predator interactions, population-level lateralization can arise as an evolutionarily stable strategy when individually asymmetrical organisms must coordinate their behaviour with that of other asymmetrical organisms (Ghirlanda and Vallortigara, 2004). Recently, I took part in further modelling (Ghirlanda et al., 2009) showing that populations consisting of left- and right-lateralized individuals in unequal numbers can be evolutionarily stable, based solely on strategic factors arising from the balance between antagonistic (competitive) and synergistic (cooperative) interactions. Empirical evidences supporting the model have been provided by comparative studies in insects, Hymenoptera Apoidea family, showing social and non-social organization (Anfora et al., 2010), suggesting that stable polymorphism with an uneven distribution of left- and right-forms can be expected to emerge spontaneously in species in which left-right biases have behavioural consequences during everyday interactions between individuals. The aim of my research project will be to consider how strategic factors interact with other potential determinants of lateralization, in particular genetic mechanisms of lateralization, integrating our game-theoretical approach with more traditional genetic models based on research on human handedness. As to the empirical part of the project, I would be interested to investigate other species of insects showing different degrees of sociality. Comparative research with several species of Hymenoptera both in the field and in the laboratory may provide important insights on the evolution of left-right asymmetries in behaviour and in the nervous system.