Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities

The mechanisms through which work is organized are central to understanding how complex systems function. Previous studies suggest that task organization can emerge via nonlinear dynamical processes wherein individuals interact and modify their behavior through simple rules. However, there is very limited theory about how those processes are shaped by behavioral variation within social groups. In this work, we propose an adaptive modeling framework on task allocation by incorporating variation both in task performance and task-related metabolic rates. We study the scaling effects of colony size on the resting probability as well as task allocation. We also numerically explore the effects of stochastic noise on task allocation in social insect colonies. Our theoretical and numerical results show that: (a) changes in colony size can regulate the probability of colony resting and the allocation of tasks, and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks; (b) increased response thresholds may cause colonies to rest in varied patterns such as periodicity. In this case, we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time; (c) stochastic noise can cause work activities and task demand to fluctuate within a range, where the amplitude of the fluctuation is positively correlated with the intensity of noise.