Randomness as a driver of inactivity in social groups.

Social insects, such as ants and bees, are known for their highly efficient and structured colonies. Division of labour, in which each member of the colony has a specific role, is considered to be one major driver of their ecological success. However, empirical evidence has accumulated showing that many workers, sometimes more than half, remain idle in insect societies. Several hypotheses have been put forward to explain these patterns, but none provides a consensual explanation. Task specialisation exploits inter-individual variations, which are mainly influenced by genetic factors beyond the control of the colony. As a result, individuals may also differ in the efficiency with which they perform tasks. In this context, we aimed to test the hypothesis that colonies generate a large number of individuals in order to recruit only the most efficient to perform tasks, at the cost of producing and maintaining a fraction of workers that remain inactive. We developed a model to explore the conditions under which variations in the scaling of workers' production and maintenance costs, along with activity costs, allow colonies to sustain a fraction of inactive workers. We sampled individual performances according to different random distributions in order to simulate the variability associated with worker efficiency. Our results show that the inactivity of part of the workforce can be beneficial for a wide range of parameters if it allows colonies to select the most efficient workers. In decentralised systems such as insect societies, we suggest that inactivity is a by-product of the random processes associated with the generation of individuals whose performance levels cannot be controlled.