Final answer:
Worker hymenoptera should prefer to invest in sisters over brothers because of the genetic relatedness. This behavior is explained by the theory of kin selection, which is observed in social insects such as bees, wasps, ants, and termites.
Step-by-step explanation:
Worker hymenoptera should prefer to invest in sisters over brothers because they're closely related to sisters while unrelated to brothers. This preference is a result of kin selection, a theory that explains seemingly altruistic behaviors in social insects such as bees, wasps, ants, and termites. Sterile worker bees take care of the queen because they are genetically related to her, indirectly passing on their genes through her offspring.