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The peloton superorganism and protocooperative behavior

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  • Trenchard, Hugh

Abstract

A theoretical framework for protocooperative behavior in pelotons (groups of cyclists) is proposed. A threshold between cooperative and free-riding behaviors in pelotons is modeled, together comprising protocooperative behavior (different from protocooperation), hypothesized to emerge in biological systems involving energy savings mechanisms. Further, the tension between intra-group cooperation and inter-group competition is consistent with superorganism properties. Protocooperative behavior parameters: 1. two or more cyclists coupled by drafting benefit; 2. current power output or speed; and 3. maximal sustainable outputs (MSO). Main characteristics: 1. relatively low speed phase in which cyclists naturally pass each other and share highest-cost front position; and 2. free-riding phase in which cyclists maintain speeds of those ahead, but cannot pass. Threshold for protocooperative behavior is equivalent to coefficient of drafting (d), below which cooperative behavior occurs; above which free-riding occurs up to a second threshold when coupled cyclists diverge. Range of cyclists’ MSOs in free-riding phase is equivalent to the energy savings benefit of drafting (1-d). When driven to maximal speeds, groups tend to sort such that their MSO ranges equal the free-riding range (1-d).

Suggested Citation

  • Trenchard, Hugh, 2015. "The peloton superorganism and protocooperative behavior," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 179-192.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:179-192
    DOI: 10.1016/j.amc.2015.08.006
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    References listed on IDEAS

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    1. Trenchard, Hugh & Ratamero, Erick & Richardson, Ashlin & Perc, Matjaž, 2015. "A deceleration model for bicycle peloton dynamics and group sorting," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 24-34.
    2. Dirk Helbing & Wenjian Yu, 2008. "Migration As A Mechanism To Promote Cooperation," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 641-652.
    3. Trenchard, Hugh & Richardson, Ashlin & Ratamero, Erick & Perc, Matjaž, 2014. "Collective behavior and the identification of phases in bicycle pelotons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 92-103.
    4. Zhong, Li-Xin & Xu, Wen-Juan & Shi, Yong-Dong & Qiu, Tian, 2013. "Coupled dynamics of mobility and pattern formation in optional public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 18-26.
    5. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    6. Zhang, Jun & Wang, Wei-Ye & Du, Wen-Bo & Cao, Xian-Bin, 2011. "Evolution of cooperation among mobile agents with heterogenous view radii," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2251-2257.
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    1. Hugh Trenchard & Matjaz Perc, 2016. "Equivalences in Biological and Economical Systems: Peloton Dynamics and the Rebound Effect," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-9, May.
    2. Li, Meng & Chen, Tao & Du, Hao & Ma, Na & Xi, Xinwei, 2022. "The speed and configuration of cyclist social groups: A field study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).

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