Facultative Sex Allocation by Workers and the Evolution of Polyandry by Queens in Social Hymenoptera

Abstract

Recent theoretical and empirical studies have shown that worker Hymenoptera may facultatively bias colony sex allocation according to the mating frequency of their queen, which results in more male-biased allocation in colonies with queens mated to an above-average number of males. Given the occurrence of this worker reproductive strategy, and because the queen-optimum sex-allocation ratio is more male biased than the population-wide worker-optimum ratio, individual queens may be able to enhance their inclusive fitness by mating with additional males. Using inclusive fitness models, we examine the fitness of single-, double-, and treble-mated queens in a population in which workers facultatively bias colony sex allocation with respect to queen mating frequency. We show that the relative inclusive fitness of double-versus single-mated queens can vary from 3:1 to 1:1. Low error rates in the assessment of queen mating frequency by workers, low worker production of males, low proportions of double-mated queens, and other factors enhance the relative fitness of the double-mated queens. Inclusive fitness gains to double-mated queens through more male-biased colony sex allocation must compensate for any costs arising from making additional matings. Double mating can be favored under some conditions but disfavored under others. Double- and single-mated queens may have equal total fitness at an intermediate proportion of double-mated queens in the population, which leads to a mixed mating strategy. We develop three nonexclusive scenarios under which treble mating can potentially be favored over double mating. The conditions favoring treble mating are more restrictive than those favoring double mating.