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Worker Control of Sex Ratios and Selection for Extreme Multiple Mating by Queens

Pamilo (1991b) used inclusive fitness theory (Hamilton 1964a, 1964b) to model the evolution of mate number and queen number in social insects, focusing on the invasion of new strategies. One model showed that polyandry (multiple mating by queens) could evolve because of worker-queen conflict over sex ratios. In this note, I extend this model in two ways. First, I argue that the selective advantage is slightly different. Pamilo considered his model to be a formalization of the hypothesis that polyandry evolves as an adaptation to reduce sex-ratio conflict (Starr 1984; Moritz 1985). While this is true for the invasion criteria studied by Pamilo, extending the argument makes it clear that polyandry can be an adaptation of queens to win the genetic conflict with workers over sex ratios. Though worker and queen interests are convergent both at the beginning and at the end of the selection process, the process itself is an arms race with a stage in which some workers are exploited against heir better interests. I also argue that, unless the costs of mating are high, the process is expected to lead to extreme multiple mating but this seems to be rare in social insects. Therefore it may often be true that workers are unable to bias sex ratios in the manner equired by the model. The root cause of the conflict between queens and workers is the unusual asymmetrical relatednesses in the haplodiploid Hymenoptera (Trivers and Hare 1976). Workers, who are always female, are related by 3/4 to their full sisters and by only 1/4 to their brothers (these are Hamilton's [1972] life-for-life relatedness coefficients hat include the 50% reproductive value devaluation for males). Workers are therefore s lected to favor greater investment infemales than males. Queens are related symmetrically to the two sexes of their offspring (r = 1/2 for both) and are therefore selected to favor more equal investment. The preferred investment ratios are often said to be 3: 1 for workers and 1: 1 for queens, but they may differ depending on the current population sex ratio, the presence of multiple mating or multiple gg layers (Trivers and Hare 1976), the distribution of investment among different colonies (Grafen 1986; Boomsma and Grafen 1990, 1991), and efficiencies and inefficiencies ofscale (Taylor 1981). For the purposes of this discussion, we can ignore the predicted population ratio to focus on the general rule that workers prefer more female-biased investment ratios than those preferred by queens. If workers control sex investment ratios, differences in relatednesses among