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

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Abstract

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.

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  1. Department of Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Tao Feng & Zhipeng Qiu

  2. Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ, 85212, USA

    Tao Feng & Yun Kang

  3. School of Life Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Daniel Charbonneau

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This research is funded by the NSF-DMS (Award Number 1716802); the NSF-IOS/DMS (Award Number 1558127); DARPA-SBIR 2016.2 SB162-005; and the James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award (UHC Scholar Award 220020472). T. Feng was partially funded by the Outstanding Chinese and Foreign Youth Exchange Program of China Association of Science and Technology; and the Scholarship Foundation of China Scholarship Council (Award Number 201806840120). Z. Qiu was funded by the National Natural Science Foundation of China (Award Number 12071217, 11671206)

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Feng, T., Charbonneau, D., Qiu, Z. et al. Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities. J. Math. Biol. 82, 42 (2021). https://doi.org/10.1007/s00285-021-01589-z

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