A mathematical model of anarchy in bees

Abstract

Functional worker sterility in queenright honey bees (Apis mellifera) is fostered by the colony-level costs of this behavior. However, anarchy in the beehive can occur when a fraction of workers lay eggs, which, if reared, will develop into males (drones). Because males do not gather resources but still consume them, they represent an additional energic cost for the colony. This small number of anarchic worker-laid eggs is normally found and eaten by non-anarchic bees via worker policing, a controlling mechanism induced by queen’s pheromones. However, worker policing by anarchic bees is possible by mimicking the pheromone marker of the queen. Here, we show that the intensity of worker policing has an upper-bound limit set by the loss in its population-level benefits. We developed a mathematical model to assess the benefits of worker policing at different intensities and costs of anarchy in the beehive. We found that there is an optimal rate in which workers should police in order to maximize colony-level benefits. The adjustment of worker policing intensity depending on the degree of anarchy in the population can keep the number of drones descending from workers low. However, this control can collapse when worker policing gets saturated due to high frequencies of anarchism. Our findings can help to advance the understanding on the maintenance of eusociality in bees by showing how the balance between anarchic behavior and worker policing regulates productivity in the beehive.