Emergent Workload Inequality in Collective Excavation

Living collectives and artificial swarms frequently employ a division of labor, wherein individuals take on different tasks or perform different amounts of work. However, the mechanisms used by collectives to divide labor remain poorly understood. Here, we study how workload inequality arises in collectives by monitoring excavation in Solenopsis invicta fire ants, whose coordination in constrained environments makes them an attractive system for studying division of labor. We vary group size (between 2 and 25 ants) and track digging activity to create Lorenz curves and corresponding Gini coefficients, which represent relative workload inequality. We find that that workload becomes more unequal as group size increases: the number of "active" ants scales with the square root of the group size. We implement a cellular automata (CA) model in which agents regulate their activity based on local crowding in the tunnel. The CA reproduces experimental Gini coefficients over a wide range of parameters and group sizes, indicating that local decisions emergently account for the scaling of workload inequality. An analytic rate equation model recovers the square root scaling with the assumption that individuals exit the tunnel at a rate which scales quadratically with the group size. Power law scalings in workload distribution have been observed in other systems, including social and natural sciences; however, these laws are primarily observational. Here, we provide a mechanistic explanation for the emergent workload scaling patterns in constrained biological collectives, offering insight into organization in both natural and future task capable engineered collectives and swarms.