Emergent Workload Inequality in Collective Excavation

Abstract

Collectives of entities, including groups of living systems and artificial swarms, self-organize to achieve common goals. Collective systems frequently employ a division of labor, wherein individuals take on different tasks or perform different amounts of work. However, the rules and mechanisms used by collectives to divide labor remain poorly understood. In this study, we investigate the methods used by biological collectives to complete tasks using experimental and theoretical approaches. We use social insects, which form remarkably integrated societies, as model systems to study division of labor. We specifically explore how workload inequality might arise by studying digging behavior in Solenopsis invicta fire ants. We introduce an experimental technique for estimating each ant's workload by tracking individual grain depositions during digging behavior. These experimental results suggest that workload distribution becomes more unequal for increasing group size. We then implement an agent-based cellular automata model which predicts experimental trends, and suggests that local decisions driven by crowding emergently account for the scaling of workload inequality. Finally, we examine experimental workload results and show that the number of ``active'' digging ants roughly scales with the square root of the total group size. This finding parallels scaling laws from other domains of social and natural science, such as Price's law, which suggest that a core group of individuals perform the majority of work. We introduce a simplified rate equation model which recovers the square root scaling via a quadratic failure rate. Together, these results provide a mechanistic explanation for the emergent workload scaling patterns in collectives.

Figures (19)

• Figure 1: Image of fire ant nest construction. (A) Cast of a fire ant (Solenopsis invicta) nest, created by Walter Tschinkel. The nest is approximately 40 cm in diameter, and consists of a complex array of narrow, branching tunnels. Adapted from tschinkel2021ant. (B) Tunnel excavation in a 2D "ant farm" experiment, over 9 hours, adapted from avinery_agitated_2023. Each image represents a 3 hour slice of ant activity. Tunnel color represents first-exploration time, ranging from darkest for earliest and brightest for latest activity within the time slice. (C) A group of fire ants excavates grains at the end of a narrow tunnel. Adapted from aguilar_collective_2018.
• Figure 2: Painting ants enables individual ant tracking. (A) Diagram of camera and container used to record simultaneous experimental trials. (B) Painted and color-coded ants used in trials with more than 10 individuals. (C) Camera view of trial at 4 different points in time over 6 hours.
• Figure 3: Automated high throughput ant tracking method for estimation of grain deposition events. (A) Lines representing tracked path of a single (red) ant across 44 seconds. (B) The corresponding horizontal position ($x$), vertical position ($y$) and distance from the tunnel entrance over time for the same ant. Asterisks indicate the local maxima in radial distance, which the tracking algorithm denotes as grain depositions. (C) Ant positions, as represented by distance from tunnel opening, over time for the 4 ants in a single trial. (D) A representation of the position data in (C), for a single ant across $\approx$15 mins. Black asterisks represent points automatically identified as a grain deposition based on the thresholding process described in Section \ref{['sec:tracking']}
• Figure 4: Workload inequality is revealed via Lorenz curve analysis of deposition events. (A) Plots of ant activity over the trial duration where a black dash indicates a grain transported at that time instance. Each row corresponds to a different ant, with the top row corresponding to the most active ant. Ants are ordered by total activity over 20 hours. (B) Number of deposited pellets, as estimated by the tracking algorithm, for each ant across 20 hours. Colored lines represent individual ant contributions, while the black curve represents the total pellets deposited. (C) Lorenz curves, representing cumulative fraction of grains moved, relative to cumulative fraction of workers involved, for the first 8 hours (blue) and full 20 hour trial (black) for these 4 ants. Inset shows mean Lorenz curve over all 4 trials, with error bars representing standard deviation.
• Figure 5: Increasing group size leads to greater workload inequality. (A1) Individual ant activity, as indicated by black dashes, sorted from highest to lowest total activity. (A2) Lorenz curves for the corresponding trial for 3 ants. Insets show mean Lorenz curves over 4 trials (error bars represent standard deviation). Representative trials are also shown for 6 (B1-2) and 10 (C1-2) ants.