The Significance of Protandry in Social Hymenoptera

An optimization model is constructed for an annual eusocial wasp or bee which may at any time produce workers and/or male and female reproductives. The optimal policy is to produce only workers at first, and at some critical time switch to producing only reproductives, confirming the conclusion of Macevicz and Oster (1976). In the reproductive stage, males should on average be made before females, either with a sudden transition from making males only to making females only, or with a gradual transition from males to females at first followed by a sudden switch to females only. Under queen control of the sex ratio, a slightly male-biased overall sex ratio is predicted, the size of the bias depending on the female mortality. The results from this optimization argument are confirmed by a genetic analysis of a simplified version of the model.