The peloton superorganism and protocooperative behavior

• Below a critical threshold equivalent to (d) cyclists cooperate (by passing).
• Above threshold cyclists sustain pace of stronger front rider but cannot pass.
• When at max speeds pelotons sort so range of max capacity is equivalent to 1-d.
• Below this range weak cyclists separate from peloton at this max speed.
• Simulation experiments show a tendency towards predominantly free-riding behavior.

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).