The efficiency of social insect colonies critically depends on their ability to efficiently allocate workers to the various tasks which need to be performed. While numerous models have investigated the mechanisms allowing an efficient colony response to external changes in the environment and internal perturbations, little attention has been devoted to the genetic architecture underlying task specialization. We used artificial evolution to compare the performances of three simple genetic architectures underlying within-colony variation in response thresholds of workers to five tasks. In the 'deterministic mapping' system, the thresholds of individuals for each of the five tasks is strictly genetically determined. In the second genetic architecture ('probabilistic mapping'), the genes only influence the probability of engaging in one of the tasks. Finally, in the 'dynamic mapping' system, the propensity of workers to engage in one of the five tasks depends not only on their own genotype, but also on the behavioural phenotypes of other colony members. We found that the deterministic mapping system performed well only when colonies consisted of unrelated individuals and were not subjected to perturbations in task allocation. The probabilistic mapping system performed well for colonies of related and unrelated individuals when there were no perturbations. Finally, the dynamic mapping system performed well under all conditions and was much more efficient than the two other mapping systems when there were perturbations. Overall, our simulations reveal that the type of mapping between genotype and individual behaviour greatly influences the dynamics of task specialization and colony productivity. Our simulations also reveal complex interactions between the mode of mapping, level of within-colony relatedness and risk of colony perturbations.