Modeling the maintenance of a dependent lineage system: The influence of positive frequency-dependent selection on sex ratio

In insect societies, worker versus queen development (reproductive caste) is typically governed by environmental factors, but some Pogonomyrmex seed-harvester ants exhibit strict genetic caste determination, resulting in an obligate mutualism between two reproductively isolated lineages. Queens mate randomly with multiple males from each lineage and intralineage crosses produce new queens, whereas interlineage crosses produce workers. Early colony survival is negatively frequency dependent; when lineage frequencies are unequal, queens from the rarer lineage benefit because they acquire more interlineage sperm, and produce more workers. Here we examine theoretically and empirically the effect of relative lineage frequency on sex ratio. We predict that the ratio of inter- to intralineage sperm acquired by queens of each lineage will affect the sex ratio produced at colony maturity. Consistent with model predictions, we found that gyne production in mature colonies was positively frequency dependent, increasing significantly with increasing lineage frequency across 15 populations. Unequal lineage frequencies are common and likely maintained by a complex interplay between an ecological advantage specific to one lineage, and opposing frequency-dependent selection pressures experienced throughout the colonies life-cycle; rare lineage colonies benefit during early colony growth, and common lineage colonies benefit at reproductive maturity.