D3214: A model of resource allocation in eusocial insects

Resource allocation among eusocial insects refers to the distribution of resources to the various individuals or activities of the colony. New queens, upon mating, must choose how to allocate their energy to ultimately maximize reproductive fitness. Macevicz and Oster (1976) proposed a model for optimal reproductive strategy they called the “bang-bang strategy”—that is, queens initially only spend energy on raising workers, then switch to only producing reproductives at the end of the season. Here, I use a novel system of ordinary differential equations detailed by a previous student to confirm Macevicz and Oster’s results. The system consists of three equations modeling the rate of change of worker populations, reproductive populations, and total energy. Total worker and reproductive populations were examined over one season. Manipulating model parameters such that resources are allocated to reproductives only at the end of the season yields much greater fitness (determined by number of reproductives at the end of the season), provided resource availability is high enough. Decreasing resource availability throughout the season means that workers use more energy than they produce, rendering them as costly instead of advantageous. In this case, fitness is maximized by a bet-hedging resource allocation strategy instead of the bang-bang strategy. Bet-hedging describes when percent allocation of resources to reproductives is increased gradually throughout the season. Results suggest that successful queens must be able to assess their environmental conditions early enough to choose the best resource allocation strategy.