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Dynamics of Information Flow and Task Allocation of Social Insect Colonies: Impacts of Spatial Interactions and Task Switching

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Abstract

Models of social interaction dynamics have been powerful tools for understanding the efficiency of information spread and the robustness of task allocation in social insect colonies. How workers spatially distribute within the colony, or spatial heterogeneity degree (SHD), plays a vital role in contact dynamics, influencing information spread and task allocation. We used agent-based models to explore factors affecting spatial heterogeneity and information flow, including the number of task groups, variation in spatial arrangements, and levels of task switching, to study: (1) the impact of multiple task groups on SHD, contact dynamics, and information spread, and (2) the impact of task switching on SHD and contact dynamics. Both models show a strong linear relationship between the dynamics of SHD and contact dynamics, which exists for different initial conditions. The multiple-task-group model without task switching reveals the impacts of the number and spatial arrangements of task locations on information transmission. The task-switching model allows task-switching with a probability through contact between individuals. The model indicates that the task-switching mechanism enables a dynamical state of task-related spatial fidelity at the individual level. This spatial fidelity can assist the colony in redistributing their workforce, with consequent effects on the dynamics of spatial heterogeneity degree. The spatial fidelity of a task group is the proportion of workers who perform that task and have preferential walking styles toward their task location. Our analysis shows that the task switching rate between two tasks is an exponentially decreasing function of the spatial fidelity and contact rate. Higher spatial fidelity leads to more agents aggregating to task location, reducing contact between groups, thus making task switching more difficult. Our results provide important insights into the mechanisms that generate spatial heterogeneity and deepen our understanding of how spatial heterogeneity impacts task allocation, social interaction, and information spread.

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Acknowledgements

The authors would like to thank Anna R Dornhaus for her comments. This research is partially supported by NSF-DMS (Award Number 1716802 &2052820); and The James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award (DOI\(-\)10.37717/220020472); National Science Foundation grant IOS/DMS 1558127.

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Authors and Affiliations

  1. Simon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State University, 1031 Palm Walk, Tempe, AZ, 85281, USA

    Jun Chen

  2. School of Life Sciences, Arizona State University, Tempe, AZ, 85281, USA

    Xiaohui Guo & Jennifer Fewell

  3. School of Information, University of Arizona, Tucson, AZ, 85719, USA

    Daniel Charbonneau

  4. Department of Mathematics, Kennesaw State University, Marrieta, GA, 30060, USA

    Asma Azizi

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

    Yun Kang

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Appendix

Appendix

See Fig. 13 and Table 5.

Fig. 13
figure 13

Black and red curves which are \(\beta _A=\beta _B=0.5\) and \(\beta _A=\beta _B=1\), separately. The blue curve is task switching probability to task A is \(\beta _A=0.75\); however, to task B is \(\beta _A=0.25\). a: Black, red, and blue shadows are standard deviations

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Table 5 P values of the Welch ANOVA test and T-test
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Chen, J., Guo, X., Charbonneau, D. et al. Dynamics of Information Flow and Task Allocation of Social Insect Colonies: Impacts of Spatial Interactions and Task Switching. Bull Math Biol 86, 50 (2024). https://doi.org/10.1007/s11538-024-01280-6

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