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).