Effects of Brood Manipulation Costs on Optimal Sex Allocation in Social Hymenoptera

Abstract

In eusocial Hymenoptera, queens and workers are in conflict over optimal sex allocation. Sex ratio theory, while generating predictions on the extent of this conflict under a wide range of conditions, has largely neglected the fact that worker control of investment almost certainly requires the manipulation of brood sex ratio. This manipulation is likely to incur costs, for example, if workers eliminate male larvae or rear more females as sexuals rather than workers. In this article, we present a model of sex ratio evolution under worker control that incorporates costs of brood manipulation. We assume cost to be a continuous, increasing function of the magnitude of sex ratio manipulation. We demonstrate that costs counterselect sex ratio biasing, which leads to less female-biased population sex ratios than expected on the basis of relatedness asymmetry. Furthermore, differently shaped cost functions lead to different equilibria of manipulation at the colony level. While linear and accelerating cost functions generate monomorphic equilibria, decelerating costs lead to a process of evolutionary branching and hence split sex ratios.Keywords: kin selection, conflict, model, evolutionary branching.Queen-worker conflict over sex allocation has been an important area of research on social insects over the past 25 years. As first outlined by Trivers and Hare (1976) queens and workers in a hymenopteran colony differ in their optimal sex allocation. This difference is caused by relatedness asymmetries arising from haplodiploidy, the hymenopteran system of sex determination. In haplodiploid species, females develop from fertilized (diploid) eggs, whereas males develop from unfertilized (haploid) eggs. As a consequence, in a colony headed by one singly mated queen, workers are three times more related to female sexuals (their sisters; life-for-life relatedness r p ) than to male sexuals (their brothers; life-for-life re-0.75 latedness ). Corresponding to this asymmetry in r p 0.25 relatedness, equilibrium sex allocation under worker control is female biased, with three times more resources invested in females than in males. Queens, in contrast, are equally related to sons and daughters, and their equilibrium sex ratio is therefore an equal investment in the two sexes.Since Trivers and Hare, hymenopteran sex ratio theory has been greatly developed. Predictions of optimal sex allocation under queen and worker control have been generated to include a variety of genetic structures of colonies and populations (for reviews, see Bourke and Franks 1995;Crozier and Pamilo 1996). However, almost all theoretical work has assumed that there are no costs associated with sex ratio manipulation. This assumption is likely to be wrong, especially in the case of workers. In order to alter sex allocation, workers have to manipulate the primary egg sex ratio, which is controlled by the queen. There are two likely mechanisms of sex ratio manipulation. First, workers can eliminate male eggs or larvae to increase the relative investment...

Conflict Resolution in Insect Societies

“…Other such strategies may well be discovered in the future. On the theoretical side, models are increasingly considering the subtle ways in which different conflicts may interact or arms races may proceed (41,105,106). Empirically, we still need a better understanding of the information used in the recognition decisions central to manipulation of colony reproduction (Box S2).…”

“…At the two extremes of 50% and 75% female allocation, the nonoptimum party, whether queen or workers, can benefit if three units of allocation in the lessvaluable sex is traded for one unit of the more valuable. This favors ongoing conflict because the more the sex allocation ratio diverges from one party's optimum, the greater the incentive to manipulate the sex ratio and the greater the colony cost that can be tolerated in doing this (96,105).…”

“…This trend is also significant if phylogenetic nonindependence is controlled for (139). Data are from Reference 49, with additions and corrections as in Reference 139. conflict in which both the queen and the workers possess some power over sex allocation (72,105). In some species, allocation less extreme than 75% female may also be compatible with full worker control if the worker optimum is reduced by multiple mating by queens (87,88), multiple related queens (97,96), or worker production of males (87,125).…”

“…As in all conflicts (Box S1), relatedness among colony members contributes to at least a partial resolution of sex-allocation conflict. However, relatedness costs only partially resolve sex-allocation conflict (105). The colonylevel cost the conflicting parties can tolerate depends upon the overall sex allocation ratio.…”

“…conflict in which both the queen and the workers possess some power over sex allocation (72,105). In some species, allocation less extreme than 75% female may also be compatible with full worker control if the worker optimum is reduced by multiple mating by queens (87,88), multiple related queens (97, 96), or worker production of males (87, 125).…”