Optimal investment allocation in primitively eusocial bees: a balance model based on resource limitation of the queen

Abstract.

The classical model of colony dynamics developed by Macevicz and Oster predicts that optimal colony fitness in annual eusocial insects is achieved by a bang-bang strategy of reproduction: exclusive production of workers (ergonomic phase) followed by exclusive production of sexuals (reproductive phase). We propose an alternative model that assumes colony development in discrete broods and a limited overall investment potential of the queen. Based on the costs for producing eggs, workers, and sexuals and efficiency of individuals we predict the optimal number of workers and sexuals in the colony for each brood of the colony cycle that maximizes overall colony fitness. To link our model assumptions to the real world we chose model parameters according to field data of the halictid bee Lasioglossum malachurum. However, our model is representative of a large number of species with an annual life cycle and with discrete broods. Our model shows that the optimal partitioning of resources, i.e. the optimal workers/sexuals ratio depends on rearing cost for sexuals as well as productivity of workers but not on the queens’ total investment, egg cost, or rearing cost for workers. In complete accordance to Macevicz and Oster we predict a bang-bang reproduction strategy despite the differences in the basic assumptions. Potential deviations from this strategy and transitions from social to solitary breeding are discussed in the framework of our model.