Genetic Evolution of Sex Ratios in Eusocial Hymenoptera: Allele Frequency Simulations

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Abstract
Evolution of the population sex ratio in monogynous and monogamous eusocial Hymenoptera was examined by allele frequency simulations with multiallele (5 or 6 alleles) and multilocus (4 or 5 loci) models. In the gyne control model the genes were assumed to be expressed only in the gynes, in the worker control model only in the workers and in the gyne-worker conflict model in gynes and workers. The colony sex ratio may well have nonzero variance at the populational equilibrium, and the equilibrial population sex ratio determined by the specific sex ratio genes may be in conflict with that predicted on the basis of the genetic relatednesses of the rest of the genome. Under gyne control the population sex ratio will rapidly approach the 1:1 equilibrium, which may be obtained with widely varying allele frequency arrays. Worker control of the colony sex ratios biases the population equilibrium in favor of females, the exact value depending on the interaction of genetic dominance relationships and solution of the worker-worker conflict in nests with differing worker phenotypes. The multiallele and multilocus models gave congruent results. The gyne-worker conflict with caste-specific loci always led to the 1:1 population sex ratio, because 1/2 of the nests produce only males and the other 1/2 females. The solution of the gyne-worker conflict with a single multiallele locus expressed in gynes and workers varies from complete worker control to complete gyne control; the conflict may increase the internest variance of the sex ratio. The results depend on the characteristics of the model (genetic dominance, worker-worker conflict, mechanism of worker control) and the initial frequency of the all-male allele.