Split sex ratios in perennial social Hymenoptera: a mixed evolutionary stable strategy from the queens' perspective?

In social Hymenoptera, relatedness asymmetries due to haplodiploidy often generate conflicts of genetic interest between queens and workers. Split sex ratios are common in ant populations and may result from such conflicts, with workers favoring the production of males in some colonies and of gynes in others. Such intercolonial differences may result from variations in relatedness asymmetries among colony members, but several examples are now known in which this hypothesis does not hold. We develop here a simple model assuming monogynous, monoandrous, worker-sterile, perennial colonies without dispersal restrictions. Workers may eliminate eggs of either sex and determine the caste of the female brood, but the queen controls the number of eggs of each sex she lays. In such conditions, we demonstrate that split sex ratios can result from queens adopting a mixed evolutionary stable strategy (ESS), with one option being to put a strict limit to the number of diploid eggs available and the alternative one to provide diploid eggs ad lib. In the former situation, workers should raise all diploid eggs as workers and release only male sexuals. In the latter, workers should adjust the caste ratio so as to reach the maximum sexual productivity for the colony, which is entirely invested into gynes. For a particular relative investment in gynes at the population level, between 0.5 (ESS under full queen control) and 0.75 (ESS under full worker control), an equilibrium is reached at which both strategies yield an equal genetic payoff to the queen. Male-specialized colonies are predicted to be equally abundant but less populous and less productive than gyne-specialized ones. Available data on the monogyne form of the fire ant, Solenopsis invicta, suggest that this model may apply in this case, although more specific studies are required to test these predictions.